The flavor interface (historically U_wall) is reduced to the selector triangle: with the dual anchor d = a·R⁻¹ and the torsion normal n, each column of R is the unique lattice point of the address box (v136/v139). The selectors det R = 8 and Spec(Q₊) = {1,2,3} are read off the bundle; the quark ratios are closed by Readout Rigidity, leaving only the absolute amplitude scale = v_geo. And v_geo is not an open gap: by the No-Unit Theorem (v153) a dimensionless compiler provably cannot select an absolute scale, so U_point ~ v_geo, 1/G ~ v_geo² and m/μ = e^{3/4} are one metrology unit in three readings — an irreducible primitive, not a missing derivation. The interface itself is now structurally closed as an R₊ scale torsor in calibration form (v725, VGEO.TORSOR.01: complete export table O_i = r_i·v_geo^{d_i}, dimension-matrix rank 1 with the flavor-block conditionality [A] named, all consistency conditions λ-homogeneous — the machine form of the No-Unit theorem — two-anchor consistency 0.11%; one external reference selects the point, everything else is prediction); no scale derivation — the one remaining dimensionless ratio is named, H_EW = ln(M̄_Pl/v_EW) = 37.1776.

The dual normal pair (d, n) pins R columnwise; d = (3/2)a − 2·1 is pure anchor data (the first selector is derived), and n is the unique covector with atom pairings (2, 8, 121) on the frame (1, a, σ) of determinant 11. Frame integrality cuts this further: integer covectors form an index-11 sublattice, so the σ-pairing is forced mod 11 — and the pairing values themselves are atom identities — in the cusp frame n pairs to (6,3,5) = (p₂,p₀,e₂)(a), so BOTH dual normals are anchor data (v145/v149); the residue is one discrete assignment; the historical U_wall machinery is over-engineering for the ratios.

The goal is the reflection-positive projective-limit measure over the diffeomorphism-quotiented metric sector. The Seeley–DeWitt R + R² terms (G2) and gap dominance (G5, the Decoupling Theorem) are certified, and the ambient measure is holographically reduced to a finite seam-boundary (Calderón) measure. The closing statement is the Simple-Current Extension Theorem (v154): A = (D₅)₁⊗(A₃)₁ extended by the isotropic glue L = ⟨(1,1)⟩ has index |L| = 4 = |μ₄|, c = 5+3 = 8 and μ(B) = 1 ⇒ holomorphic ⇒ B ≅ (E₈)₁ — exact algebraically, with the explicit target net checked (16 Majoranas, ω_k = |k|, 248 = 120+128, character E₄/η⁸; v156). On the glue census channels that underlie that Q-system, HECKE.GEOM.01 (v535; 25 checks, ~11 s) packages lattice-native Hecke: Kneser #iso_lines = σ₃·#ℙ³, ν_p = a Id + b T_p with a₃ = −4, a₅ = −2, and dim V = 7 as the 2-adic oldform hull with π_cusp = (28−T₃)/32; HECKE.GEOM.EICHLER.01 (v536; 23 checks, ~30 s) adds the Eichler/Witt layer (λ_Eis, λ_geom = λ_Eis+a_p², Type-A/B densities, signed a_p = −c(p)/8); HECKE.GEOM.HALFINT.01 (v537; 20 checks, ~90 s) adds the half-integral bridge (unique Sh_{t=2}(g)=−8 f₈, T(p²)-equivariance, Kohnen scope fence, Waldspurger R≡23.187…); HECKE.GEOM.RTF.01 (v538; 18 checks, ~14 s) synthesises v535/v536/v537 as three projections of one finite relative-trace identity (ONE-FORMULA; infinite RTF open); RTF.GNS.WEIL.01 (v539; 25 checks, ~6 s) identifies the family's Weil structure up to two isolated obstructions (minus doubling; non-automorphic Corr); RTF.GNS.AMP.01 (v540; 34 checks, ~3 s) consolidates the amplitude route out of the square plane (Dirac D² = family kernel; Cohen seed Θ(d) = −48·L(−1,χ_d); deletion = square-class double counting; positive linear carrier with plus balance; exact FE; open boundary = the FE-covariant gap functional λ* on n ≡ 6 mod 8); RTF.GNS.LEDGER.01 (v541; 33 checks, ~10 s) promotes the T78–T85 proof package (matching lemma proved exact-integer on [4, 10⁶]; transport ledger Q_Weil = Q_cert + Δ_arch + Δ₂ closes with Δ_pole ≡ Δ_conv ≡ 0 proven; character-exact signed envelope; arch internal via Legendre duplication; coherent class closed by the λ-equivariant CM channel; two named limits: one open classical correlated-cancellation lemma + I5 one-family ⟺ Weil ⟺ RH, equivalence typing only) — classical theorems named classical; weight-4 → GL(1) stays [O]; GL(2) centre s=2 (not ξ); Euler-region positivity only; NOT almost-RH; no RH; no marker moves. The free-bulk premise is not postulated but forced by rigidity: a holomorphic c=8 theory has no marginal (1,1) deformation and its lowest interaction is irrelevant (dimension 2), so freeness is a stable isolated fixed point (v157/v158); net existence and full-cone reflection positivity are then discharged to [E] on the 2¹⁶-dim Fock space (v175). The seam realisation is the keystone SEAM.EQUIV.01 (the raw RP seam IS the holomorphic (E₈)₁ net at τ=i), whose MMST route SEAM.EQUIV.MMST.01 is now closed modulo cited theorems: the lattice model (v367/v368) and the S3 stack (v376–v379, ground-state witnesses v489/v490) pin the target at every computable level, Lean-pinned (FORM.SEAM.MMST.01) to the published MMST/Adamo theorems, leaving [O] = the cited continuum scaling-limit existence only (v336). Its conformal-deck face QGEO.SYM.01 is a corollary (v335). The classical field equation supplied by entanglement equilibrium (v358/v359) is honestly typed 'equation of state, not a from-action quantisation' [O]; an external candidate for that missing action level — Bianconi's entropic action S_B = −Tr ln(G̃g̃⁻¹) (Gravity from entropy, PRD 111, 066001 (2025), arXiv:2408.14391) — is quantified in a dedicated keybox (v473): the carrier Hodge count 1+5+10 = 16 = dim S⁺ (the 16 requires the five-slot carrier), her free constant pinned exactly at β′_B = c₃/6 = 1/(48π), her emergent Λ quadratic-nonnegative reproducing the v60 branch with exact target Tr Q² = 32c₃⁴, and the R² kill test (gap exactly 3(8π)⁹ ≈ 10¹³) pre-registered; the compression conjecture P_Σ(G̃g̃⁻¹)P_Σ = Δ_Σ^{1/2} stays [C] and nothing closes. The operator level is executed in v474: the D₅ Clifford/spinor structure is exhibited on the carrier Fock space Λ•ℂ⁵ (ten exact gammas, the 45-dim so(10) preserving the 16-dim even subspace), the Hodge fold is identified as the 5 → 5̄ conjugation (her fiber 1+5+10 becomes the GUT 16 = 1+5̄+10), and the Q-target is decided — integer supports exactly {|ℤ₂|, rank E₈, 2^g_car} with minimal uniform q = c₃², the naive pair-block (10) reading killed. The R² kill test is executed in v475: on the maximally symmetric background the exact vacuum action is 3βR + (17/24)β²R² (tensorial factors now exact), giving a TRANS-PLANCKIAN raw scalaron m² = 4608π²/17 M̄² (≈ 51.7 M̄) — the light-trace-mode reading is dead, a viable mechanism must supply exactly (72/17)(8π)⁹ ≈ 1.7×10¹³ in mass², and KMS-spectral renormalisation is the only surviving R² route; the Lorentzian-positivity caveat now has an explicit timelike witness (1 − αv² ≤ 0). The compression conjecture (AP2) is made well-posed in v476: on a pure bulk the literal operator-side reading P f(C) P is ill-posed (f singular on spec {0,1}), so the state-side reading — build Δ_Σ from the compressed relative metric — is forced (matching Bianconi's own local construction); the mismatch between the readings is exactly second order in the cross-cut correlations and gap-suppressed, converging in the gap-dominated regime where TFPT operates; AP2 itself stays [O]. And the surviving R² route is typed as ONE moment condition in v477: the entropic action is the flat scale-integral of relative heat-kernel actions (Frullani), TFPT's S_rel,χ is the same family at one KMS scale — demanding m² = c₃⁷M̄² forces exactly μ₂/μ₁² = (72/17)(8π)⁹, with the closure identity (4608π²/17)/((72/17)(8π)⁹) = c₃⁷ holding identically: the 13 orders are a scale-measure datum which TFPT's own KMS moment (v36 f₀) fixes correctly — zero new dials, consistency not derivation [C]. First computable steps on the two remaining legs land in v478: the compressed critical state's modular data flows to the CHM/Bisognano–Wichmann geometric form (Calabrese–Cardy c_est → 1 at 2×10⁻⁴, CHM parabola corr → 0.99, even bands exactly zero) — the bridge's modular side meets TFPT's Einstein-derivation input (v323/v358) in the continuum limit; and the measure condition reduces to one exact KMS time t₀ = ln(72/17) + 9ln(8π) = 30.461, with the h(E₈) = 30 near-miss explicitly declined (no-free-pattern rule) — both legs stay [O]. The step-by-step reduction (v160 → v302) is on the changelog.

On top of G_net the boundary QFT is assembled and collapsed to ONE relative object TFPT_QFT. The emergent-QFT skeleton is read off the seam: modular flow σ_t = Δ^{it} is KMS at β=1 (the seam unit 2π = 1/(4c₃), v239); GNS/OS gives a positive H_OS = −log T with gap Δ = 6log(3/2) (v240); particles are the carrier DHR sectors (Gauss–Milgram returns c = 8, v241/v242). The carrier half-spinor 16 is exactly one anomaly-free SM generation (sin²θ_W = 3/8, v245); the plain SM not unifying (v246) is resolved natively by a carrier Pati–Salam UV branch ({1,10,16,45}, no 126, v247–v249), realised as a 96-dim KO-6 spectral triple with one Higgs doublet and no junk (v252/v254). Three closures collapse the layer: D_F is the modular/covariance induction of the seam KMS state (v258), the spectral cutoff IS that KMS weight (f₂/f₀ = 1, v259), and seam, carrier-16 and E₈ live on one Kummer/K3 surface (v260) — certified by one number 4 = [B:A] = |μ₄| = 2χ (v261). So the boundary QFT is closed as one relative object modulo cited theorems via SEAM.EQUIV.01's MMST route SEAM.EQUIV.MMST.01 (Lean FORM.SEAM.MMST.01; pinned at every computable level by the lattice model v367/v368 and the S3 stack v376–v379, ground-state witnesses v489/v490; residual [O] = the cited continuum existence only, v336); the ambient measure QG.AMB.01 is discharged as a [C] redundancy (v369/v379). 4D-GUT is not claimed by default (E₈ is the audit hull); the Pati–Salam branch is a separately-typed, falsifiable UV option with a proton-decay kill test (v265). The full derivation is in the PDF.

A new research contract (alongside U_wall, G_metric and CONTRACT.F.01), typed as a numbered chain of work packages with pre-registered kill tests — not a claim. THE OBJECT DIAGRAM (read this first; one row per arrow — where mathematics ends and physics begins is visible at a glance): (Σ, μ₄, ρ, Θ) → P¹∖μ₄ [E] (the SEAM.MARKS chain: four marks, clock, cross-ratio 2, τ = i pillowcase; v168/v214/v216/v180, bit reduction v506/v507/v510/v512; kill: a fifth mark, a non-order-4 clock, or a marks-preserving root without flag transitivity) · P¹∖μ₄ → ℂ²/ℤ₄ [E] (CELEST.WP1.01/WP2.01: the glue is the flat ℤ₄ monodromy on the A₃ ALE, clock = Kähler U(2) phase, clock² = deck; v492/v493; kill: equivariant-sector closure failure or a surviving shape modulus) · ℂ²/ℤ₄ → PT/Γ [E]/[C] (CELEST.WP5E.*: equivariant twistor uplift — anomaly ledger, level-from-flux, axion slot, back-reacted Ω_N, twisted KS measure, a₀ uplift, the δ₁ decision; v505/v509/v511/v513/v514/v515/v516/v517/v518; kill: the preregistered level kill; the M1–M3 kills were evaluated by v515/v516/v517 and did not fire; the δ₁ kill FIRED on the derived measure (v518) — the declared/derived measure tension is the named [O]) · PT/Γ → A_hol [O] (the INTERACTING holomorphic algebra: global BCOV+SDYM quantisation, WP5e proper — target of WOIT.OS.TWISTOR.01; kill: anomaly mismatch at the Costello–Li grade) · A_hol →_OS A_Mink [O] (OS reconstruction with the real structure Θ — the WOIT.OS.TWISTOR.01 target; the free-collar RP/OS witnesses v379/FORM.SEAM.MMST.01 are the free anchor only; kill: the seven WOIT.OS.TWISTOR.01 kill tests). THE GROUP EXTENSION, EXACTLY: Γ_ALE = ⟨Deck⟩ ≅ ℤ₄ ⊂ SU(2) — (z₁,z₂) ↦ (iz₁,i⁻¹z₂), triholomorphic, preserves Ω; THIS is the ℤ₄ that is quotiented (ℂ²/Γ_ALE = the A₃ singularity XY = Z⁴, and PT/ℤ₄ throughout means the quotient by Γ_ALE). ρ = Clock = diag(i,1) ∈ U(2) — Kähler, NOT triholomorphic (det ρ = i rotates Ω by the μ₄ generator, v492 S5); it is NOT quotiented — it NORMALISES Γ_ALE and survives as the residual clock symmetry. The global object: since ρ² = Deck exactly (v492/v506), ⟨Γ_ALE, ρ⟩ = ⟨ρ⟩ is cyclic — projectively ℤ₄ with ρ² generating the deck ℤ₂, and on the spin/fermionic level the canonical ℤ₈ tower (V² ∝ U, V⁴ ∝ (−1)^F, nonsplit; 8 = 2|μ₄|; v506/v507). Action table: K_PT — deck trivial, clock weight via det ρ = i [E] (v514); Ω — deck-preserved, clock-rotated by i [E] (v492; the back-reacted Ω_N closed-form with (2πi)²-integral periods and forced charge 4, v515); BCOV fields (O(−2) tower) — orbifold sectors / character series [E] ledger, [O] quantisation (v514); open-string SDYM(E₈) fields — glue-equivariant sector / sector rotation [E] (v492), [O] interacting; boundary states ((E₈)₁ shadow) — μ₄ sector split / clock phase [E] at character/GNS level (v497–v500), [O] as an actual net. THE A₃ ROLE TABLE (no silent identifications): A₃^family = the family factor in the lattice D₅⊕A₃ (su(4)-flavour, three families from its exponents) — related to A₃^ALE by the McKay correspondence OF TYPES only; NOT identical as realisations (one a sublattice of E₈, the other the singularity type of ℂ²/ℤ₄; the connecting bridge is the Kronheimer–Nakajima quiver, v479). A₃^ALE = the ADE type of ℂ²/ℤ₄; its resolution carries the three exceptional spheres. The three exceptional spheres = the Coxeter/Picard–Lefschetz structure (clock = Coxeter element of W(A₃) on H₂, eigenvalues {i,−1,−i}, v493; they carry the three twisted axion slots v505 and the lockstep fluxes v509). D₅^carrier = the carrier factor (g_car = 5), glued to A₃^family by the μ₄ Lagrangian glue into E₈ (v92/v125); no role on the ALE side beyond g₀ = D₅⊕A₃ (v492). Woit's SU(3)_color — external programme reference ONLY (colour as the rank-three quotient bundle on PT): NOT identical — no identification claimed; in particular A₃^family ≇ SU(3)_color. Woit's SU(2)_weak — external programme reference ONLY (the internal spin factor): NOT identical — no identification claimed; whether such an internal SU(2) can be realised on PT/Γ is exactly kill test (6) of WOIT.OS.TWISTOR.01. Hypothesis (as corrected by WP1): the seam is the glue-equivariant ℤ₄-orbifold sector of the celestial chiral algebra on the A₃ ALE space ℂ²/ℤ₄; the μ₄ clock is the Kähler U(2) phase diag(i,1) whose square is the deck group (spin bridge ℤ₈, 8 = 2|μ₄| — the c₃ = 1/(8π) winding integer); the twistorial bulk is the SELF-DUAL sector of TFPT gravity only. The spin bridge is no longer a bookkeeping convention: the NS deck implementation is forced to order 4 (U² = (−1)^F exactly, nonsplit ℤ₄; v506), and the nonsplit class is arrangement-sensitive — the edge (silver) arrangement splits (U² = +1, zero roots), so the seam fermions MEASURE the v506 alignment bit as a Fidkowski–Kitaev-type extension class (v507, SEAM.BIT.ORIGIN.01) — and that class is nonsplit iff the deck acts freely (all 17 seam-circle involutions, v510, SEAM.BIT.FREEDOM.01), which the covering deck does by topology: the edge class is excluded and the bit reduces to the square-modulus datum τ = i alone — restated by the flag-transitivity web (v512, SEAM.TAU.FLAG.01) as one discrete symmetry-lift bit (flag transitivity of the four marks, V₄ → D₄, ⟺ τ = i; since v528 a 15-fold exact equivalence web with the counterwitness passing all 10 established side-blind tests — free RP/Θ is the eighth (v521), the mark-decorated twist-state class the ninth (v525: the free-plus-twist class is exhausted), the interacting FK toy the tenth (v529, with Kill-Test 2 firing at toy level after the straddle law) — and the bit physically defined as the twist-class choice with a gauge-robust order parameter (v528, stays formal input)), narrowing the search space for a future [E] closure to the genuinely interacting algebra under the straddle-law constraint. WP1 is executed and verified (v492, sympy exact, verdict B): the E₈ μ₄-glue grading (v128) is INNER — h = (2,2,2,2,2;0⁴) reads the glue class mod 4 on all 240 roots, so the glue is a flat ℤ₄ monodromy in the Kronheimer–Nakajima sense, with the A₃-side detector reading the same diagonal (1,1) glue of ℤ₄×ℤ₄ (v92/v125); ℂ²/ℤ₄ is verified as the A₃ singularity XY = Z⁴; the glue-equivariant SDYM(E₈) sector closes with graded dimensions 60(d+1)/64(d+1) — possible only because dim g_j = (60,64,60,64) — zero modes = the carrier D₅⊕A₃+Cartan = 60, density 1/4 = 1/|ℤ₄|; the four glue-sector characters sum exactly to the (E₈)₁ character 1+248q+4124q²+34752q³ (v377), with sector weights = the v92/v125 discriminant form (5x²+3y²)/8 and integer glue-diagonal h = (0,1,1,1) (= locality of the (E₈)₁ extension). The critical correction (why verdict B): the A₃ deck acts on the celestial sphere as z → −z (order 2, the sheet flip), NOT as the order-4 clock z → iz; the clock is the U(2) phase diag(i,1) (normalising the deck, det = i rotating the holomorphic symplectic form by the μ₄ generator), with the exact spin bridge (spin clock)² = deck. Clock-invariance selects the 1-parameter A₃ deformation XY = Z⁴ + a₀ whose four branch points are one μ₄ orbit with cross-ratio 2 (the v168/v214 pillowcase marks). Negative controls kill the false spatial action diag(i,i) three ways and the false glue (3112/6720 additivity violations); rigidity = Aut(ℤ₄). Typing/non-circularity: the continuum existence of the (E₈)₁ net on the seam — the SEAM.EQUIV.01 target — is NOT an admissible input. WP2 is now also executed and verified (v493, sympy exact, 47 checks, verdict B): the clock-invariant deformation XY = Z⁴ + a₀ is selected SHARPLY (P(iZ) = P(Z) forces a₃ = a₂ = a₁ = 0, two-sided), is smooth iff a₀ ≠ 0 (disc = 256a₀³), and its binary-quartic invariants are I = 12a₀, J = 0 identically — so j = 1728 and the τ = i pillowcase shape (v168/v214) is FROZEN for every a₀: a₀ is a pure seam SCALE, no shape modulus survives clock-invariance (negative controls: a₁Z gives j = 0, an a₂-instance gives j = 1556068/81 — the test has teeth). The three resolution spheres carry exactly the three nontrivial μ₄ characters {i,−1,−i} under the clock, which acts on H₂ as a Coxeter element of W(A₃) (char x³+x²+x+1, h(A₃) = 4 = |μ₄| = N_fam+1), fixes no cycle, and IS the Picard–Lefschetz monodromy of the family; the surviving direction is the weight-1 χ₁-Fourier diagonal (1,i,i²), all three sphere volumes in lockstep (√2·t). The Bittleston–Homans–Sharma deformed-algebra pattern transfers ℤ₂ → ℤ₄: the fibre bracket −4·Nambu(XY−Z⁴−a₀), anchored at the a₀ = 0 orbifold, closes with corrections exactly linear in a₀ at the ℤ₄ wrap, conserving the μ₄ grade (no sector leak — the WP1 equivariant sector deforms consistently), with a₀ in BHS's weight-0 c² slot; verdict B via three named identifications (−4·Nambu as THE k = 4 CCA bracket; period = root difference; seam-scale reading via clock² = deck). The v216 residual is typed, not moved: given the order-4 clock the square is automatic — a relocation of the same order-4 carrier input, not a new derivation. WP3 is executed and verified (v495, exact Fraction/sympy, 25 checks, verdict B): the Okubo coefficient 5/(2(dim g+2)) is DERIVED as a polynomial identity for all 8 algebras on Costello's list (sl₄ negative control: 5/32 vs 3/32), the closed form λ̃² = 10h∨²/(dim+2) = h∨+6 holds across the Deligne series, and for E₈ the Green–Schwarz coefficient is exactly λ̃ = 6 (unit-trace) resp. λ_fund = 1/10 (adjoint-trace), so (κ/c₃)² = 12 = |μ₄|·N_fam resp. 1/300 — exact anchor rationals, with κ/c₃ itself irrational (2√3; a byproduct: the printed λ²(so₈) = 3/2 in Costello's appendix A is a factor-2 slip, the exact value is 3). The look-elsewhere caveat is part of the result: the same squared-rational alignment holds for ALL eight algebras (8/8 — zero selective power), λ̃-integrality passes 2/8 (shared with sl₃), and the only E₈-selective single test is g_car = 5 | h∨ (1/8); the isolating conjunction is post hoc. Alignment survives; selectivity does not — the c₃-connection is convention-level compatibility plus genuine λ-arithmetic, NOT E₈-selective evidence, and never a derivation of c₃. WP4 is executed and verified too (v496, exact integer/Fraction/sympy, 25 checks, verdict B(ii)): the (E₈)₁ character E₄/η⁸ = (1, 248, 4124, 34752, 213126, …) is NOT a conformal block of the celestial E₈[ℂ²] S-algebra in its own jet grading — the obstruction is localised three ways: (a) the CP grading gives spin 1 − d/2 unbounded below and 248 is never a jet-tower dimension (d ≤ 100); (b) the cumulative generator count is quadratic (31s²+92s+60, 31 = k+h∨), so the jet Fock grows as n^(2/3) against the character's n^(1/2) (f_n/χ_n strictly increasing, n = 1..12); (c) the level-2 null ideal of (E₈)₁ deletes exactly 27000 = 30³ = h∨³ out of Sym²(248) = 1+3875+27000 (the character keeps 4124 = 1+248+3875) — with no jet analogue. But the boundary/period reading holds exactly at the current stratum: the zero-mode slice is the 60 vacuum-sector currents, the jet slice cycles (60,64,60,64), one full μ₄ period of loop energies sums exactly to 248, and the glue-diagonal weights (0,1,1,1) are integers — while the free loop Fock counts 897266 ≫ 248 at level 1, so the rational truncation must be imposed in a limit. That is precisely the MMST scaling-limit shape of SEAM.EQUIV.01 (v336/v449): the character is a boundary/limit SHADOW of the S-algebra, and the constructive limit question passes to WP5. Kill tests evaluated: K1 survived (WP1+WP2), K3 did not fire but is scope-demoted (the alignment format passes 8/8 — compatibility, not evidence), K4 fires only against the exact-block reading (the sector arithmetic holds exactly, so no degradation to 'E₈ admissible'). WP5 is subdivided WP5a–e, and its first milestone WP5a is executed and verified (v497, exact integer/Fraction, 34 checks): the WP4 boundary-limit shadow is made a PRECISE coefficientwise limit — the one-parameter family χ_w of graded Fock characters on the chiral jet generators (E_w = m + w·r in quarter units u = q^(1/4)) contains the chiral jet grading as its w = 2 member (generator counts 64, 120, 128, 180, 192, 240, 256, 300) and its u^n coefficient equals the quarter-moded loop Fock for ALL w ≥ n+1, strictly larger for w ≤ n (n ≤ 8, w ≤ 10) — an explicit stabilisation threshold w = n+1, not a slice; and the null ideal is DERIVED from root data, not cited: Freudenthal + Weyl + character peeling give Sym²(248) = 27000 + 3875 + 1 with residual exactly zero, 27000 = 30³ = h∨³, and the level-2 quotient 31124 − 27000 = 4124 = 1+248+3875 equals the independent μ₄ theta-split sector sum (1036, 1024, 1040, 1024) at q² — two routes, one number. Negative controls: SO(16)₁ through the same pipeline gives FOUR components (5304+1820+135+1), 5304 ≠ 14³ (h∨³ is not generic), quotient 2076 = Θ_D8/η⁸ (the recipe validated on a second algebra), and block weights (0, 1/2, 1, 1) that cannot fuse into one local character; only P = 4 = |μ₄| periodisation reproduces the 248 layer. Honest limit: the limit does NOT generate the truncation (loop Fock 897266 ≫ 248 at level 1) — WP5a fixes the ideal's size and location quantitatively and gives the celestial route the same two-step shape as MMST (limit + maximal ideal). The second WP5 milestone WP5b is executed and verified too (v498, exact integer/Fraction, 53 checks, deterministic — success on the preregistered criterion): the deleting object exists and is explicit — |s⟩ = (E^θ_{−1})²|0⟩ (weight 2θ, level 2 = 8 quarter units = q², an integer level) is constructed in a machine-built Chevalley/Frenkel–Kac basis (cocycle asymmetry on all 57600 pairs, the [e_α,e_{−α}] sign FORCED by Jacobi with SGN = −1, κ derived with κ(θ∨,θ∨) = 2), and J^a_1|s⟩ = 0 is machine-verified for ALL 248 generators with the case classification 190 (first bracket) / 57 (second) / 1 (a = F^θ via the central-term cancellation — the only case that sees the level k); plus J^a_2|s⟩ = 0, E^a_0|s⟩ = 0, exact weight and Shapovalov norm 0; the affine PBW engine is unit-tested on all 61504 basis pairs. Level dial: the F^θ_1 coefficient is 2(1−k) — 2/0/−2 at k = 0/1/2: without the central extension the deletion operator does not exist. μ₄ compatibility: glue class j(θ) = 1 (machine-built h-adapted chamber, ⟨θ,h⟩ = 5, height 29 = h∨−1), clock phase i^(2j) = −1, class(2θ) = 2 sheet-even with the deleting θ-sl₂ crossing the sheet-odd classes (1,3); 8 quarters = q² via the per-period dictionary. The module it generates is THE ideal: weight 2θ has multiplicity 1 in the level-2 Fock, and the direct g₀-orbit BFS reproduces the Freudenthal multiplicities of V(2θ) exactly through depth 4 (27000 = h∨³, quotient 4124; Weyl complete reducibility beyond depth 4 typed [C]). Negative controls separate honestly: the level-1 current state and generic level-2 states are NOT singular; at k = 2 the CUBE is (generic Kac (E^θ)^(k+1) mechanics); SO(16)₁ has the same singular vector but keeps three extra level-1 primaries (h = 1/2 breaks one-block fusion) — the singular-vector mechanism is level-1 generic, the ONE-BLOCK closure is the E₈/μ₄-specific part. Honest handover to WP5c: in the twisted quarter-slot moding two sector-C₁ modes never sum to 8 quarters (minimum 6 = q^(3/2)) — the per-period dictionary (v496), not the per-slot identification, carries |s⟩ to q²; exactly the GNS/limit-state question (kernel ⊇ ideal) that WP5c answers. WP5c is executed and verified (v500, exact integer/Fraction, 35 checks, success on the preregistered criterion): the quasi-free family ω_w exists — loop sector = the affine k = 1 vacuum n-point functions via the machine-determined compact anti-involution θ(e_α) = −e_{−α} (the unique anti-automorphism sign on all 61504 basis pairs), radial sector = oscillator pairings x^(wr) (the exact Gibbs regulator) — is positive for every finite w, and stabilises EXACTLY at the WP5a threshold (ω_w = ω_∞ mod x^(N+1) for w ≥ N+1, sharp at w = N). Its limit carries the null ideal in its GNS kernel: the complete 9361-block exact level-2 Gram has rank 4124 exactly (the preregistered target), kernel 27000 = V(2θ) weight by weight (Freudenthal cross-check on all 9361 weights), every block PSD, rank table per Weyl orbit (0,0,1,8,44), level-1 rank 248 positive definite (the current layer survives); the clock descends to GNS with level-2 rank split (1036,1024,1040,1024) = Θ_Cj/η⁸ at q² — the two-routes identity at the STATE level — and |s⟩ IS the zero vector of GNS(ω_∞), resolving the WP5b twisted-slot tension. A CCR obstruction shows NO w-uniform state can damp the radial modes (the family formulation is NECESSARY, and the family exists — KILL not triggered); controls: k = 2 keeps everything (⟨s|s⟩ = +4), k = 0 has no current layer, D₈ gives one block of four, the wrong family erases the 248 layer (710955 ≠ 248), no damping keeps 897266 ≠ 248. WP5d-α is executed and verified too (v501, Gaussian lattice machinery ED-validated to 1e-15 + exact Fractions, 39 checks): the KLM two-interval index measured entropically on the 16-layer seam carrier — the fermionic two-interval MI is extensive (μ = 1 reference; c fit 0.5000, residual → 0 with N) while the sector-summed orbifold prescription pays exactly one classical bit (the ln 2 plateau at machine precision, |Δ₂ − ln 2| = 1.1e-15 at N = 512), so [F:F_even] = 2 and μ_gauged = 4 = the v490 parity census (two independent lattice witnesses); the orbifold breaks two-interval complementarity S(E) ≠ S(E′) (the direct duality-failure witness) with the complementary-pair budget ≤ ln 4 = ln μ(SO(16)₁) as a double-limit statement; the condensation arithmetic is anchored at both measured ends — det Cartan(D₅)·det Cartan(A₃) = 16, KLM/Longo–Rehren 16/4² = 4/2² = 1, Σd² = (4,4,1), θ_v = 1 exactly at ν = 2c₋ = 16 (rivals ≠ 1) — so μ = 1 after condensation and the preregistered KILL ('μ-offset ≠ 0 after condensation') does NOT fire; controls: the ν = 1 offset is non-removable (θ_v ≠ 1 — the discriminator has teeth), the trivial phase shows nothing, the wrong sector sum loses the full ln 2. WP5d-β is executed and verified as well (v504, Gaussian lattice machinery ED-validated + exact GF2/integer algebra, 37 checks): the two remaining KLM legs of complete rationality witnessed for the same orbifold prescription — strong additivity is algebraically EXACT with the shared boundary Majorana (Even(A) ∨ Even(B) = Even(A∪B): GF2 spans full 64/64, 256/256, 512/512, 1024/1024, matrix rank 32/32; disjoint exactly HALF, index 2 — the missing sector odd⊗odd is the v501 ln 2 bit, localised at the split point; the neutral U(1) algebras do NOT generate the union even with the shared site, gaps 2/10/52 growing); the entropic touching defect is BOUNDED < ln 2 with the Ising ¼-exponent approach ((ln 2 − Δ₂) ~ N^(−p), p = 0.2444 vs 2Δ_μ = 1/4; honest note: 'defect → 0' would be FALSE at the sharp lattice split — bounded ⟺ finite index, Longo–Xu) while the preregistered U(1)/Dirac control bursts ln 2 from L = 128 and grows as (1/2)ln Var Q_A (Klich–Levitov slope 0.10134 vs 1/π² = 0.10132: infinite index — the current-net failure reproduced); the split property is witnessed at the elliptic-nome rate πK(1−x)/K(x) to 1.3–2.0% (σ₁ ~ x^0.5044, trace norm summable) with EXACT orbifold inheritance (P_A flips C → −C, σ_k identical to 8.3e-17; the even-bilinear coupling Gram is the second compound Λ²C — Longo heredity); and Pimsner–Popa E(a) − a/2 = PaP/2 holds identically (λ = 1/2 = 1/[F:F_even] with exact integer attainment: 16384 + 2048 monomial sweeps, 0 violations; λ_E4 = 1/4 = 1/μ; index consistency exp(Δ∞) = 2 = 1/λ_PP over two independent routes; U(1): λ = 1/(m+1) → 0): with v501 ALL THREE KLM ingredients of complete rationality — split, strong additivity, finite μ — are witnessed on the lattice; the continuum uplift is honestly fenced ('finite-group orbifolds of completely rational nets are completely rational' is Xu's theorem — cited, not claimed; the concrete seam quotient net and the interacting condensed (E₈)₁ net stay WP5e/Costello–Li). WP5e is now subdivided, with its α stage executed (v502, exact sympy/Fraction, 33 checks, CELEST.WP5E.ALPHA.01 — the CFT-side prefactor + level pinning): the q^(−1/3) prefactor of E₄/η⁸ IS exact μ₄ vacuum-energy bookkeeping — the clock is INNER ((h,h) = 20, (h′,h′) = 12, sum 32), so the twist on the 8 torus bosons is θ = 0⁸ in all four sectors (a SHIFT orbifold, not a rotation orbifold) and every sector carries the same −c/24 = −1/3 at c = 8; the sector weights (0,1,1,1) ARE Casimir energies (spectral flow j²(h,h)/32 mod 1, and exactly via the 16-Majorana seam carrier, R–NS shift n/16 = 5/8, 3/8, 1); and k = 1 is forced THREE independent ways (current condition h(J) = k = 1; conformal embedding 47(k−1)(k+266/47) = 0 resp. 128k(1−k) = 0; central charge 248k/(k+30) = 8 ⟺ 240(k−1) = 0 — the prefactor itself) plus the WP5b singular-vector dial (31124 − 27000 = 4124 at k = 1 only); honest sharpening: glue-h integrality h(J^j;k) = k(0,1,1,1) holds for ALL k = 1..8 and fixes nothing — the naive integrality route is retired; controls: D₈ has the SAME prefactor but h = (0,1/2,1,1), ℤ₂/μ₄ rotation twists break the common prefactor, wrong k ∈ {2,3,4} fails all five dials. The β stage is executed as well (v505, exact sympy/Fraction, 47 checks, CELEST.WP5E.BETA.01 — the equivariant anomaly ledger on twistor space): the Atiyah–Bott/Lefschetz fixed-point skeleton of the one-loop box anomaly on ℂ²/ℤ₄ is exact — denominators (2,4,2) with Dedekind sum 5/4 = (|ℤ₄|²−1)/12, equivariant characters (248,0,−8,0) by two routes, invariant average 60 = the carrier, Frobenius 61568; only the INVARIANT sector is Okubo-quadratic (36⟨x,x⟩², 36 = λ̃²_e8 — v495 re-derived), the twisted sectors carry irreducible T₅/T₃ content, and the AB-weighted sum cancels the D₅ quartic exactly while leaving the RIGID residual 32·T₃ (no admissible reweighting fixes it; the graded GS exchange is rank-obstructed in sectors 1–3); the index bridge f(m) = (1/4)Σ_j(i^(jm)−1)/det_j = ch₂(T_m) = −(C⁻¹)_mm/2 holds EXACTLY (fixed-point ledger = McKay/Kronheimer intersection ledger) with the integral glue defect −78 by both routes; the level dials say k = 1 geometrically (lattice current count 240 at k = 1 and exactly 0 at k = 2,3,4; embedding residual (0,360,814,1362); one scale ⇒ one level; integrality alone fixes nothing — honest, as on the CFT side); and an honest REFUTATION: the clock-invariant modulus a₀ ∈ O(8) fills the BSS GRAVITON slot O(2), not the axion slot O(−2) (weight mismatch 4 = |μ₄|) — 'the theory brings its own GS axion as a₀' is false; instead the three H²(ALE) classes carry exactly the three twisted-sector Coxeter characters {i,−1,−i} (bijection), and the bulk axion must come from the O(−2) tower field itself; controls: diag(i,i) breaks the ledger four ways, SO(16) glue gives defect −30 ≠ −78 with a failing bulk Okubo, k = 2 dies on the closure dial; the preregistered kill ('inflow demands a level ≠ 1') does NOT fire on the equivariant skeleton. The γ stage is executed as well (v508, exact sympy/Fraction, 27 checks, CELEST.WP5E.GAMMA.01 — the sphere-axion pairing check, an honest rigid NEGATIVE result): the W(D₅)×W(A₃)-invariant vertex space on the glue Cartan is exactly dim 2 (quadratics = span{s₅, s₃}) and dim 5 (quartics = span{P₁,P₂,P₃,T₅,T₃}) by Weyl nullspace arithmetic, and the PRODUCT THEOREM kills every exchange image in the T₃ direction (any two invariant quadratics multiply into span{P₁,P₂,P₃}, while Φ_T3(A_fix) = 32 ≠ 0); the strict two-index rule collapses the sphere couplings entirely, the twist-insertion channels E₁₃ = (16,−96,144,0,0) and E₂₂ = (16,32,16,0,0) give rank([M | A_fix]) = 3 with the annihilator certificate (Φ_T5, Φ_T3, Φ_P)(A_fix) = (0, 32, 72) (side discovery: K⁽⁰⁾ = −15·K⁽²⁾, the even-sector quadratics are parallel); naturalness dissolves (ch₂-natural and AB-weight couplings both certify (0,0) vs required (32,72) — scale-independent); SO(16) has no sphere partners AND uncancelled T₅, D₈ no T₃ structure; the slot bijection is untouched and the level-kill still does not fire. The remaining roadmap is WP5e proper alone (the GLOBAL BCOV/Kodaira–Spencer quantisation on PT/ℤ₄: the partition function E₄/η⁸ including the q^(−1/3) prefactor derived FROM THE TWISTOR SIDE — neither the v502 CFT-side dials, nor the v505 equivariant skeleton, nor the v508 exchange no-go, nor the v509 flux/sector dials trigger the kill branch; the exchange sub-branch is closed by v508, and the ε₂ stage is now executed as well (v509, exact sympy/Fraction, 28 checks, CELEST.WP5E.EPS2.01 — the CPS level-from-flux dial, verdict B): the CPS skeleton exact (S³ period (2πi)²N, exceptional flux 2πN, level magnitude 2N), the pairing matrix pinned by complete enumeration (48 unimodular → 2 effective) with fluxes (64,60,64) and one quantum per current, the naive 'level = total flux' killed by the lockstep test itself, the per-current reading (1,1,1) anchored by the current count (240,0,0,0) and embedding index 1, the ord-4-vs-level-1 tension resolved (16 = ord² fractional sectors condense to 1) with the new sector-counter dial #primaries((E₈)_k) = 1 ⟺ k = 1, and the LOCKSTEP THEOREM lifting 'one scale ⇒ one level' to a theorem of clock invariance (det(A−1) = −4; falsifier Z⁴ − Z: 0/24 orderings lockstep); the CPS dictionary on PT/ℤ₄ stays [C], the type-I B-model back-reaction [O]; and the δ₂ stage is executed too (v511, exact Kostant/Weyl + sympy/Fraction, 41 checks, CELEST.WP5E.DELTA2.01 — the full-tensor ledger, intermediate verdict): the v508 collapse is CONFIRMED full-tensorially and arity-crossing by the innerness theorem (g₀ = d₅ ⊕ a₃ semisimple with no u(1), h in the g₀ Cartan ⇒ every invariant tensor carries total charge 0 mod 4; bilinear Hom table nonzero only at j′ = −j with dims 2/1/1/1, all 15 non-neutral trilinear triples Hom = 0), BUT one cubic door opens: the su(4) d-symbol — the unique symmetric trilinear on all of e₈ (so(10) has no cubic Casimir) — carries the exchange quartic Q_dd = (1/60)(T₃ − P₃/4) with Φ_T3(Q_dd) = 1/60 ≠ 0, so the v508 master kill does not extend to cubic vertices; the pairing stays obstructed in the charge reading with the WEAKER certificate {Φ_T5, ψ = Φ_P − Φ_T3/4}, ψ(A_fix) = 64 (= dim g₁, [C] fence), and becomes exactly solvable relaxed (A_fix = −u + 8v + 2w + 1920·Q_dd, c_d = 1920 = |W(D₅)| = 8·240 [C] — the |W(D₅)| reading since typed look-elsewhere-loaded (11/924 vs 8/924 for the control target 1800) and convention-contingent by the v513 negative certificate, CELEST.DTERM.NONDERIV.01: the convention-stable [E] core is c_d = 32×60); SO(16)/D₈ has no symmetric cubic and false g₀/sector controls separate; and the δ₁ stage is now executed and DECIDED (v518, CELEST.WP5E.DELTA1.01 — kill under the derived measure): the strict holomorphic q⁰ reading is refuted at the ℤ₂/Eguchi–Hanson anchor (a method boundary, not a kill of the contract), the contact term is the MODULAR COMPLETION of the Atiyah–Bott data (a Harvey–Moore-type τ-integral) with the forced leading (T₅,T₃) ratio 4:3, and the τ-integral has been evaluated under a DERIVED measure — the 16-component Weil completion closes exactly (E1.5 residual 2.91 → ~10⁻³⁹), the μ₄ multiplier obstruction is a CHARACTER of the orbit stabilisers (koboundary defects (1,1,1) on all 15 pairs, λ(γ) = i^(2B+C/4) on Γ₁(4)), the cancellation is the twisted fibre block f₁f₃ = G (exact identity; the three sphere axions leave residual order 4), and all three preregistered testers FAIL under both derived solutions (χ₄, χ₁₀) with no (N₁,N₂) rescue in the positive cone — a genuine kill on the derived surface, in stated TENSION with the declared v516 completion reading (which delivers ψ = 64) — a tension since DECIDED at probe level by v520 (CELEST.WP5E.MEASURE.01, ERFOLG-A: single-valuedness derived from F-independence + the Quillen pairing under the typed premises TP-1..TP-4, the completion reading wins, the kill sharpened), and the w_m normalisation since DERIVED constructively by v523 (CELEST.WP5E.WM.01, ERFOLG: 1/det_j = the Atiyah–Bott/zeta-determinant fixed-point factor, computed from three independent sources — the equivariant mode ledger with Abel value (1/2, 1/4, 1/2), the zeta/reflection determinant 4·sin²(πj/4) with the unique real positive Quillen section, the δ₁f block constant term 1/det_b — with the v516 chain reproduced number by number under the typed premises TP-REG/TP-Q/TP-NUM/TP-CH; residual [O] = the global BCOV integral beyond the fibre zero-mode factor); and the ε₁ stage is now executed as well (v514, exact sympy/Fraction, 34 checks, CELEST.WP5E.EPS1.01 — the O(−2) bulk-axion slot, verdict B): the slot is a CONSTRUCTION (the equivariant Penrose ledger closes block by block for all d ≤ 6 and all four characters; character series P₀ = 1 + 3t² + 15t⁴ + …, P₁ = P₃ = 2t + 8t³ + …, P₂ = 6t² + 10t⁴ + …; the d = 0 slot has multiplicity (1,0,0,0) — the bulk axion survives the projection; Molien invariant ring = the v492 hypersurface XY = Z⁴ with relation degree 8 = the a₀ weight; twisted minimal content (2t, 6t², 2t) = the Coxeter eigenvalues; graviton control: O(+2) invariant only from fibre degree 4 with multiplicity 3 = {X, Z², Y}), λ̃ = 6 is pinned by three exact ledgers (Okubo (6⟨x,x⟩)² on the 240 glue roots; the measure chain μ-exact with the wrong bookings 3 and 12 excluded; flux single-channel iff k = 1, (κ/c₃)² = 12), and the GH/A₃ back-reaction step re-derives the v493 family and the Coxeter clock from centre geometry (two branches, period lockstep 4πt₀(i−1)(1, i, i²), source charge 4 = |μ₄|, EH asymptotic log exactly 0 — the CPS log is an exceptional-locus statement, multipole rule m ≡ 0 mod 4 with (4,±4) carrying −a₀); conditional on Costello's flat-PT matching [C]; the quantised BCOV coefficient and the twisted channels (32·T₃) stay [O] with the M1–M3 milestones preregistered (the A₃ Ω_N / the twisted KS measure / the a₀ uplift, each with success + kill); and the M1 milestone is now executed as well (v515, exact sympy, 30 checks, CELEST.WP5E.M1.01 — 'the A₃ Ω_N', SUCCESS on the preregistered criterion): the back-reacted Ω_N is closed-form on the A₃ twistor family (Ω_N = Ω₀ + Σ N_p K_p, CPS/Bochner–Martinelli kernels on the four centre twistor lines; the residue form derived with cover factor 4 = |μ₄| and clock phase i; the family closed as XY = Z⁴ + 4t₀²λ²Z² − t₀⁴(1−λ⁴)² with the CY-compatible clock lift Ω → +Ω), all S³/ℤ₄ periods are (2πi)²-integral with the lockstep flux vector N(1,1,1,1) (forced uniform: clock orbit + K₄ connectivity) and clock covariance Π → iΠ, the 12 conifold nodes sit exactly on the 8 eighth roots of unity, and the lens geometry FORCES the source charge 4 = |μ₄| (only N ≡ 0 mod 4 passes); honest fence: integrality alone does not discriminate — the (2πi)² quantisation holds on the forbidden Z⁴ − Z family too; the discriminator is the lockstep phase structure (0/24 vs 8/24) plus the clock forcing; and the M2 and M3 milestones are now executed as well: M2 (v516, exact sympy/Fraction, 23 checks, CELEST.WP5E.M2.01 — 'the twisted KS measure', SUCCESS on the preregistered v514 S8.2 criterion ON THE DECLARED COMPLETION MEASURE, verdict B): the completion contact term contact_j = (Q⁽⁰⁾ − Q⁽ʲ⁾)/det_j carries the exact completion-weight identity w_m = Σ_j(1 − i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4h_m = |μ₄|h_m = −4·ch₂(T_m) — the three sphere axions pair through their OWN McKay ch₂ charges, no free scale, no fit; parameter-free locks (T₅ = 0 for any scale, ratio 4:3 reproduced, T₃ budget forces c = 4 = |μ₄|); every twisted channel becomes the perfect Okubo square 36⟨x,x⟩²/det_j, total 45⟨x,x⟩² = (5/4)×36 = Dedekind × Okubo (the unique quartic-free weighting of the v505 rigidity theorem); both v508 certificates killed (32 → 0, 72 → 0) and the v511 slice ψ = 64 SUPPLIED EXACTLY — no cubic d-channel needed (c_d free = 0); controls: wrong scale, shuffle, SO(16) (the KILL fires there — E₈ doubly special), diag(i,i), ℤ₂/EH anchor at scale 2 = |ℤ₂|; the completion reading is DECLARED [C] (supported by the δ₁ modular-completion finding, not derived from the BCOV integral — that derivation stays [O], δ1d); and M3 (v517, exact sympy, 23 checks, CELEST.WP5E.M3.01 — 'the a₀ uplift', SUCCESS on the preregistered v514 S8.3 criterion): the (4,±4) multipole uplifted to the GLT kernel χ = log P₄ (the log of the v515 family polynomial; null coordinate ⇒ harmonic for any kernel, residue identity 1/r_p matches the V-ledger, flux −4π per centre), and the log-type correction is coupled to the centre count on FOUR scales (asymptotic kernel log 4 = |μ₄| with first seam-fibre correction exactly a₀/η⁴ and exact m-grading; GLT tower p_{4k} = 4(−a₀)^k with the n ≡ 0 mod 4 selection rule; exceptional-locus log χ(0) = log a₀ = 4·log t₀ + i(4φ₀ + π); period response d log Π/d log a₀ = 1/4 = 1/|μ₄| integrating to the clock monodromy i, v493 reproduced) with a₀-rigid ℤ₈ node support and topological (2πi)² fluxes; controls: (4,0) clock-invariant, ℤ₂/EH reads 2 = |ℤ₂| on every dial, k = 3/5 orbits move the coefficient, the forbidden family fails both dials — the KILL (decoupling) does not fire; the GLT dictionary stays [C], the full nonlinear Kähler potential [O]; the v514 fence M1–M3 is FULLY WORKED OFF, the δ₁ chain is decided by v518, the measure question is decided at probe level by v520 (the declared reading wins), the w_m normalisation is derived constructively by v523, and the named remaining target narrows to the GLOBAL BCOV INTEGRAL beyond the fibre zero-mode factor (the ψ = 64 slice itself is delivered by v516; the cubic-GS-term question stays dissolved — v518/v520 do not revive the d-channel); the continuum uplift of the WP5d lattice witnesses is Xu's theorem, cited not claimed) — WP5a–WP5d (both WP5d stages) plus WP5e-α/β/γ/δ₁/δ₂/ε₂/ε₁ plus M1–M3 are landed. SEAM.EQUIV.01 stays [O]; nothing here moves it. A compact thirty-step synthesis of the executed work packages — the narrative arc from the μ₄ clock to the (E₈)₁ boundary shadow, closing with the WOIT α/β₁/β₂/β₃ milestones (v519/v522/v524/v565 — the PT ↔ PT* duality typed: the OS cut and the (2,2) signature forced, the kill branch empty by algebra, the induced member = the Θ_phys carrier), the constructive w_m derivation (v523) and the twist-state kill (v525) — is presented as a dedicated section in Paper 3 (E₈ Audit & Bootstrap); this contract remains the full technical reference (typing fence, kill tests, work-package statements). Interface state 2026-08-03: the index-4 statement carries two exact witnesses — the NS/R grading is the parity character of E₈(Z[i])/(1+i) = F₂⁴, so the Ramond projection is (1+i)-adic at the one ramified edge of the Z[i]-E8 Hecke tower (v722, GNET.RAMIFIED.01), and the Pimsner–Popa/Watatani index is exactly 4 on the CAR ladder with μ₄ derived from the clock and the Ramond sector healed state-preservingly (v726, GNET.PPINDEX.01); the Q-system identification is the registered open half, gate typing unchanged.

THIS IS THE ACTUAL BRIDGE FROM COMPILER TO PHYSICS — everything in CELEST.SEAM.01 is preparation for it. A research contract [O] (ledger row WOIT.OS.TWISTOR.01: Open, research contract), not a claim. The external programme it engages — Woit's Euclidean Twistor Unification (arXiv:2104.05099) — is a NAMED reference frame for the shape of the target, never a confirmation in either direction. INPUT: X₊ = (PT/Γ)₊ (Γ = Γ_ALE ≅ ℤ₄, normalised by the clock); A_hol, the INTERACTING open+closed twistorial algebra (SDYM(E₈) + BCOV — the WP5e-proper object whose free/equivariant skeleton is pinned by v492–v518); ρ, the order-4 clock diag(i,1); Θ, the anti-linear real structure induced by the seam reflection — precision (i), from the α stage (v519): 'induced by the seam reflection' means the seam-circle REFLECTION, not the deck/covering involution — the deck (free by topology, v510) furnishes the (−1)^F Kramers class, the seam-circle reflection furnishes Θ_Fock² = +1; precision (ii): on the RP side the μ₄ marks sit at the BOND MIDPOINTS of the 16-Majorana seam circle (the cut through the sites fails RP exactly); μ_BCOV+SDYM, the interacting functional. TARGET THEOREM: Θ² = 1 and ΘρΘ = ρ⁻¹; the gauge-invariant algebra is reflection-positive; and the OS quotient produces (H, Ω, U(P↑₊), A_Mink) with: a positive Hilbert metric, positive energy, local causality, ONE chiral fermion generation WITHOUT mirror doubling, the TFPT charge lattice, an internal SU(3)×SU(2)×U(1) action, and the (E₈)₁ seam net as an ACTUAL boundary net (not only as a character). KILL TESTS (all seven preregistered): (1) Θ incompatible with the clock; (2) RP fails after gauge fixing; (3) the reconstruction produces a vector-like mirror generation; (4) the Penrose transform reaches only free/self-dual states; (5) the reconstructed net has the right character but the wrong OPE / fails net equivalence; (6) the internal SU(2) remains a spacetime factor; (7) the four μ₄ marks are not incidence-compatibly extendable over spacetime. THE α STAGE — EXECUTED (WOIT.THETA.FREE.01, v519): the real structure EXISTS, and free reflection positivity picks the SAME family — exactly two families of anti-linear structures normalise the clock (family D inverts it exactly with Θ² = +1, Kramers-free, and is the OS conjugation σ_std with real points ℝP³; family A centralises it projectively and is Woit's euclidean ρ_tw, replicated exactly on ℂ⁴), the mark-compatible Θ form a μ₄ torsor, the ℤ₈ spin plane has no phase leaks, Θ_Fock = U_r∘K has Θ_Fock² = 2⁷ (normalised +1) with V ↦ 4096·V⁻¹ while the deck-induced candidate has Θ_t² = (−1)^F (the v510 dichotomy), and free RP holds on the bond cut with no degree truncation ((8,0,0)/(29,0,0)/full N = 8 algebra; η = +i forced; the clock-centralising family fails RP structurally; the anti-chiral state flips the odd sector — the free shadow of kill test 3). KILL TEST 1 therefore does NOT fire at the free/equivariant level — and stays formally LIVE on the interacting algebra A_hol; kill tests (2)–(7) are untouched; no marker moves. THE β₁ STAGE IS EXECUTED TOO (v522, WOIT.BETA1.GSO.01, typed UNDECIDED per the frozen preregistration): the μ₄ clock average violates Hermiticity exactly (witness −i/(8·sin(5π/16)); 745 matching / 96 anti / 0 violations — 'OS-symmetric' is strictly weaker than Hermitian), all 16 seam mirror axes invert the clock (it IS Woit's euclidean rotation — time-like), the gaugeable part of the ℤ₈ tower is exactly the GSO/fermion-parity ℤ₂, and under that corrected typing gauge-fixed RP HOLDS ((29,0,0)/(8,0,0) PD; the site-cut defect (7,9,6) survives; family A stays indefinite (17,12,0)); kill test (2)'s free shadow does NOT fire, contract precision (iii) added, and the clock-equivariant statement moves to β₂. THE β₂ STAGE IS EXECUTED TOO (v524, WOIT.BETA2.OS.01, verdict SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii)): the OS quotient of the free system is EXPLICIT — H_phys nondegenerate and PD at both levels (dim 37 = 29⊕8 at N = 16 deg ≤ 2, min eigenvalue 1.7801e−6 at 40 digits; dim 16 = 8⊕8 = 4² at N = 8 complete half algebra — compact euclidean time reconstructs a thermal/KMS representation, exact certificate sin²(3π/8) − sin(π/8)·sin(5π/8) = 1/2), the Klein–Landau local transfer semigroup is exactly Hermitian on all shrinking domains with the site/bond dichotomy as its positivity pattern (even steps PSD via the exact square identity T(2j) = A*A; the one-step transfer NOT positive — the chirality datum, kill-3 shadow sharpened), the μ₄ clock = T^(N/4) is a positive self-adjoint transfer step with spectral calculus (N = 8 spectrum exactly {1, √2−1} = {1, 1/δ_Silver}) and a reconstructed unitary rotation group U(s) = exp(isH) — per precision (iii) the [C]-operationalisation of 'the clock acting unitarily'; the v522 non-Hermiticity is resolved as exactly the domain/wrap artifact (census (745,96,0), every anti-match a wrap overlap); the pre-declared KMS deviation carries exactly the silver witnesses (C(1)/C(3) = 1+√2 = δ_S, det(G−τ₄) < 0 — no contraction on the compact circle); Θ_phys² = +1 on every sector (Kramers-free), θ_cut∘θ_perp = α_(N/2) exactly; controls: site cut indefinite (the contract kill branch fires there), family A no quotient, anti-chiral (8,8,0); kill tests (1)/(2) strengthened, (3) shadow sharpened, none fires — all seven stay live on A_hol. THE β/γ ROADMAP (named milestones with success and kill criteria): (β1) Θ on the gauge-invariant subalgebra + gauge-fixed RP on the equivariant SDYM(E₈) sector (kill: kill test 2 fires) — executed via v522, UNDECIDED, neither kill fires; (β2) the OS quotient of the free system made explicit (kill: the quotient degenerates) — executed via v524, SUCCESS, neither kill fires, β₃ next — now under the straddle-law constraint: the first genuinely interacting seam toy fires Kill-Test 2 at toy level (v529, straddle law 24/24, typed fence one toy / one interaction class), and the filter, since executed as a selector (v534, SEAM.STRADDLE.CONE.01), keeps exactly ONE member alive — reflection positivity dynamically selects the alignment bit δ = π/2 with positive coupling (the symmetric straddling of the self-mirror member protects RP where every asymmetric member dies; the literal leading-order cone formalization is dead — the protection is nonperturbative; toy-level evidence for a dynamical origin of the bit, not a derivation, no marker moves); (β3) the PT ↔ PT* duality typed against σ_std (kill: the duality forces a clock-centralising structure); (γ) the chirality theorem + the mark incidence (kill: kill tests 3/6/7 fire). SCOPE FENCE (explicit non-claims of the celestial/twistor branch until this closes): both helicities, generic amplitudes, local matter, full Einstein dynamics, EWSB, confinement. SEAM.EQUIV.01 and its route split (MMST/TWISTOR) are stated in their own rows and are not moved by anything here.

The two open non-RH kind-(A) external-math targets are additionally packaged as short, self-contained EXTERNALIZATION CONTRACTS — hand-off documents for outside specialist mathematicians (conformal nets/VOA/AQFT for the seam; determinant lines/η-invariants/index theory for alpha). Each contract carries six parts: (1) the MINIMAL THEOREM STATEMENT — for SEAM.EQUIV.01: the scaling limit of the gapped μ₄-equivariant CAR collar exists in local-net topology, the index-4 simple-current extension functor commutes with this limit, and the OS reconstruction is the holomorphic (E₈)₁ lattice net, broken into four lemmata L1 (uniform energy/nuclearity bounds — honestly typed: no uniform nuclearity estimate exists in the corpus), L2 (convergence of local algebras, the cited Osborne–Stottmeister theorem with the μ₄-equivariant structure retained), L3 (the crossed product commutes with the limit; the finite index-4 Q-system is explicit, v125/v154/v469), L4 (uniqueness of the holomorphic c=8 reconstruction; det K = 1 vs the same-c rival SO(16)₁); for ALPHA.QUILLEN.EXACT.01: T1, the gap-stable continuum limit c₁(det D_finite) → c₁(det_ζ D_seam) under norm-resolvent convergence with the Fermi gap uniformly open over the twist torus (the Dai–Freed section has no zero; finite side computed, v472), and T2, δ_τ(log det_ζ Δ_U(1) + 8b₁c₃⁶ log φ_seam) = 0 = Bismut–Freed curvature = inflow response with the exact corpus coefficients k₀ = |C| = 1, k_Y = 5/3, b₁ = 41/10, c₃ = 1/(8π), exponent −5/4 = −q(D₅); (2) the COMPLETE typed HYPOTHESIS LIST (PROVEN-FINITE with its vN witness / CITED-CLASSICAL / OPEN — seam: 12/5/1; alpha: 10/5/1); (3) the runnable FINITE MODELS in the repo; (4) the HONEST LEAN AXIOM SURFACE — the seam face is a composition audit only (SeamScalingLimit.lean kernel-proves the arithmetic hypotheses by decide, the analytic content is named cited axioms over opaque Props, no sorry; L1–L4 have ZERO Lean content beyond that), and the alpha target has NO Lean formalisation at all, stated plainly; (5) MUST-FAIL CONTROLS — seam: c=8 alone must NOT suffice (the red-team point), a wrong extension index must yield SO(16)₁, the trivial M=3 collar must give no chiral limit, a non-order-4 clock must break the marks, the v286 import firewall; alpha: no experimental α anywhere in the construction, deck/carrier/Chern-level ablations must destroy the CODATA match, M=3 ⇒ C=0 / M=−1 ⇒ C=−1, the {0,3,6} π-power partition; (6) ACCEPTANCE TESTS — for alpha the review's three verbatim: no experimental α input, unique physical fixed point 137.0359992168, ablations destroy the hit. Relative-determinant note (2026-08-29, review wave 4): the correct object is the RELATIVE determinant Q(A) = log[det′ Δ_A / det′ Δ_{A0}] + 8 b₁ c₃⁶ log φ(A); the BFK constant 2^{−4} is A/τ/α-independent at fixed cut number, so δ log 2^{−4} = 0 — no physical compensation needed (consistent with COMPENSATION_INTERNAL). Absolute normalisation is fixed by the reference A0. Both targets stay [O]; the contracts document and externalize, they do not close; any marker move happens in the ledger by the house process. NO RH claim.

The third hand-off document: the prime-front programme's terminal OPEN STATEMENTS packaged self-containedly for external specialists in analytic number theory (large sieve, sampling/frame theory, de Branges spaces, explicit-formula methods). It offers open problems only — it asserts no progress toward the Riemann Hypothesis in either direction, names a document rather than a ledger row, and moves nothing. (1) SELF-CONTAINED FINITE OBJECTS: rung h, modes ω_k = kπ/a with a = ½log h and K = ⌈1.25·h·log h⌉, the von Mangoldt atoms (log q, Λ(q)/√q) as the only arithmetic input, the wall matrix M_h = M_pole + M_arch − M_prime with the prime block LINEAR in two atom transforms per mode (v935), the wall argmin ray d, the census polynomial N(y) (numerator of F(y) = c₀ + Σ(−1)^k c_k y/(y − b_k)), the moment–Laurent form Φ(z) (v924), and the jet mass δ_h = |J_h|²_G exactly (step A, v939). (2) THE THREE MINIMAL OPEN STATEMENTS in the canonical note-DII form: R1 THE TRIPLE — {H1 ∧ H2 ∧ H3}-cofinal, one rung per dyadic block, all three at the same h (H1: no census root with Re y ≥ c*y_t, c* = 1.10–1.15, certified source-pure per rung; H2: census complete-real nonnegative; H3: y_t ≤ 0.155·T_z⁴, certified 26/26 margin ≥ 1.99, refutable), the limsup form only mod the measured defect D = 0.0042; R2 THE LOOP CHARACTERIZATION — census-forall-k, honestly stated as RH-equivalent-in-currency via four independent machine-detected proof-route cycles (v928/v929/v930/v938); external value: a genuinely new independent sign source, or a proof the loop is essential; R3 THE H-PIN — the one λ-uniform edge of the counting pair {L1, WPD} with the Ω-a/Ω-b split and the exact place the floor escapes linearity: the two machine-exhibited maps (eigenvector map and census-root map, v937). (3) COMPLETE TYPED HYPOTHESIS LIST: 11 PROVEN-FINITE rows (theorem PF with the exponent the trace, v931; the rate dictionary a = p/2 − 1, v932; the subsidy-empty pigeonhole, v933; the unconditional Landau/Gonek pricing, v934; the mode-level Landau bridge, v935; the tau-free DK exclusion h ≤ 13 with the exact b*(h) schedule, v936; WPD == H-pin, v937; the exact census semigroup e^{−tT} with T = 4y∂² + 2∂, v938; step A exact, v939; the sub-dof composition chain, v940; the source-free Gram + projective linearity, v941), 7 CITED-CLASSICAL rows (Landau 1912; Gonek 1985/1993 with the RH-conditional Gonek 1984 family flagged never consumed; Montgomery–Vaughan 1974; Ortega-Cerdà–Seip 2002; Nazarov–Turán 1993; Rodgers–Tao 2020 + Polymath 15 as cited ceilings), 1 OPEN row (R1–R3). (4) HONEST MEASURED BLOCK: margins ≥ 1.405 with selector margins 2.14/3.05; the frozen alignment triple (descriptive band (0.38, 0.54), wall lock μ_m = 0.2372·log₁₀ g_min at R² 0.9916, deep excess 5.64–7.58 dex); θ∞ in [0.0766, 0.0977] typed OPEN-NONPERTURBATIVE-VARIATIONAL; the refuter ladder ALWAYS PAIRED (measured 30–33 orders with the proven b*(h) schedule 23.8/21.7/15.7/4.4 at h = 4/5/8/13, none at h ≥ 16). (5) THE KILL ATLAS: eleven named dead route classes (pointwise symbol minorants, ℓ¹ majorants, phase-discarding additive forms, Vieta pinch/power sums, moment/trace caps, Riccati/manifold transport, dBN pinch, global CBJ frame, sub-dof scoping, Carleson-as-floor, naive floor-power composition), each with its one-line death mechanism and round — so external solvers do not rebuild corpses. (6) RUNNABLE FINITE MODELS with exact paths: v931–v941 + the substrate v922–v930, the eleven frozen SPEC-hashed discovery probes (r171–r182), the frozen builder with the four control worlds, the 2×10⁷ verified-ordinate cache and the PT21 horizon. (7) HONEST FORMALIZATION SURFACE: the only prime-front Lean content is the finite spacing/jet algebra; NOTHING of R1–R3 is formalised, stated plainly. (8) MUST-FAIL CONTROLS MF-P1–MF-P6: any solution must fail or lose its constant on Epstein (off-line zeros), Scramble, and Smooth; must consume no zero tables (no-zero ancestry test); clusters/weights/selectors predefined before sign evaluation; and must not consume the four flagged loops (census-forall-k, A₀-triangle, zero-verification-as-hypothesis, RH-conditional second moments). (9) ACCEPTANCE TESTS: an external result counts iff it delivers (a) an explicit all-h all-a bound, (b) a genuinely new sign source that separates the worlds AND independently orients, or (c) a proof that one of R1–R3 is RH-equivalent — which would close the programme's hardness question honestly and is recorded as exactly that, never as progress toward RH. NO RH claim.

A programme section organizing the 4D contracts into ONE constructive route (no marker moves). The working hypothesis: TFPT is not missing twenty independent formulas but ONE growth principle — the unique local, reflection-positive, approximately quantum-Markovian 4D completion of the seam algebra, anomaly-free, with exactly one relevant dimensionful direction (= the v_geo calibration torsor, ANCHOR.VGEO.02/v153/v725 — inherited, not re-opened). Seven conditions are mapped onto contracts: seam compatibility (exact boundary restriction, not group labels), reflection positivity, a local unitary dilation with size-uniform Lieb–Robinson bounds (DYN.UNITARY.DILATION.01), chiral anomaly freedom without mirrors (CHIRAL4D.NOMIRROR.01), only one relevant scale direction, approximate quantum-Markov recovery I(A:C|B) ≤ C₀e^(−dist/ξ) (Fawzi–Renner arXiv:1410.0664; Chen–Rouzé arXiv:2504.02208), and nontriviality (a surviving connected four-point function). THE VERIFIED PIECE: the conditional 4D dimension selector DIMENSION.SELECTOR.4D.01 [C] (v975, 16/16 sympy-exact): under A1 (d > 2, propagating gauge fields), A2 (dimensionless Yang–Mills coupling), A3 (real self-dual/anti-self-dual 2-form sectors), A4 (Weyl chirality, even d), the dimension d = 4 is unique and minimal on d = 2..12 — and overdetermined (A2 alone = {4} via [g_YM] = (4−d)/2; A3 alone = {4} via the explicit 6×6 Hodge star on Λ²(ℝ⁴) with *² = I and eigenvalues ±1 at multiplicities 3/3; A1 & A4 alone = {4,6,8,10,12} — chirality does NOT select 4 by itself); μ₄ and g_car enter NOWHERE ('μ₄ ⇒ 4D' stays forbidden per DIMENSION.UPLIFT.FIREWALL.01), and axiom provenance from {c₃, g_car} is the registered open half. THE FOUR NEW CONTRACTS (all [O]): SEAM.SIMPLECURRENT.GENERATOR.01 — the seam-gap compression: ONE normalized simple-current/spin-field intertwiner (convergence + energy bounds + locality + braiding + Q-system closure) generates the entire 128-dim extension sector, collapsing the v973 residual N1 + N2 + N4 onto one convergence theorem (1+1D in and out; the generator is meanwhile IDENTIFIED at the lattice level, v983 2026-08-28: the glue vector λ = (ω_s, ω_f) with ‖λ‖² = 2, h = 1, order 4, coset root census [52,64,60,64] — the odd fusion powers carry the full 128; the analytic half G1–G4 stays [O]); TFPT4D.LATTICE.ACTION.01 — the explicit finite 4D lattice family S_a = S_Wilson + ψ̄D_GW ψ + S_Φ + S_seam/top with seven machine-checkable finite gates T1–T7 (gauge invariance, positive transfer matrix, exact seam restriction, anomalies incl. global SU(2), index/generations, mirror separation, nonvanishing connected 4-point) — the single object on which nearly all open 4D questions become simultaneously testable; SEAM.DETLINE.UNIFICATION.01 — the determinant-line hypothesis Res_seam det D_4D ≅ det D_seam with connection, whose bulk holonomy must equal the discrete orientation phase: would unify seam extension, chiral anomaly freedom, generation index and CP orientation as projections of one geometric object (the continuum Bismut–Freed identification is exactly the critical missing step); FTRANSFER.GENERATING.01 — all four F_transfer bridges (masses, m_p/m_e, η_B, axion relic) from ONE generating functional W[J] = log Z[J] (the FR.TRANSFER.01 guard stays binding — no upgrade permitted). The dynamics correction: fundamental order is local unitary amplitudes → decoherence → Markov matrix (the v971 kernel embedding is the dephased shadow; the unistochastic/Jarlskog-sign finding is exploration-level motivation only). Gravitation stays strictly downstream in the GRAV.NONCIRCULAR.01 discipline (Jacobson's entanglement equilibrium presupposes a local QFT). Kill criteria are registered so the route may die early; the Yang–Mills mass gap is not defined away. Binding separation: RH and the PRIME.* programmes remain separate — a green RH probe would be neither necessary nor sufficient for the 4D physics.

A typed DECISION (QFT4D.LATTICE.FUNDAMENTAL.01), not an [E] claim and not a marker move: TFPT's PHYSICAL completeness criterion is the finite, local, unitary lattice quantum theory — Hamiltonian route: Gauss-law Hilbert space, hermitian local H, T = e^{−aH} positive by construction, Lieb–Robinson cone — while the exact continuum Osterwalder–Schrader limit (QFT4D.OS.RECON.01) is retyped as MATHEMATICAL REINFORCEMENT, a named strengthening programme, no longer the physical bottleneck. Poincaré invariance is an IR fixed-point property with experimentally bounded irrelevant Lorentz-violating operators. Justification anchors (v989): the Euclidean overlap shortcut is killed at T2 (exact; N_t-exact confirmation: |det D_ov|² Gram PSD at N_t=2, indefinite at N_t=4, det-only λ_min ≈ −0.249; Wilson control PSD everywhere — pinned on overlap time nonlocality), and the Hamiltonian route clears T2 by construction. Display stays honest: QFT4D.OS.RECON.01 unchanged as the math programme. Amendment (2026-08-29): a single finite box is not a world — the fundamental object is the quasilocal consistent family {H_Λ} with τ_t = lim e^{it H_Λ} A e^{−it H_Λ}; continuum (a→0) optional (mathematical reinforcement), thermodynamic limit (|Λ|→∞) and controlled IR universality mandatory. Decision typing UNCHANGED. THE PROMOTE ROUND (suite 979 → 985): v987 executes the OS/dilation ladder (kernel continuation exact, size-uniform free band, congruence interacting family, quantum SWAP d(θ)∼θ^{1.99}; continuous field-level OS stays [O]); v988 executes S3 exact + the measured S1/S2 skeleton + the lemma reduction to cited quasi-free theorems (Shale–Stinespring/Araki/Ruijsenaars) + the MMST identification — reduction, NOT closure; v989 the T1–T7 harness plus the named T2 kill/clearance plus the 1+1D chiral Gauss census (single-exponent Gauss iff q_L ≡ q_R); v990 finite W[J] derivative identities + transduction shadow (seam-coupled mixed derivative ≈ −9.3×10⁻³, decoupled control exactly 0); v991 finite bulk–edge detline shadow (2π·(+1) = winding +1, diff 5.6×10⁻¹⁶); v992 joint-likelihood v1 (χ² = 11.80/dof 9, p = 0.225, ν_eff = 1, 0th percentile of 200 scrambled decoders). No contract closed. WAVE-7 (2026-08-30, v1008): 2+1D scaffold-coherent (K=0 theorem, contractive-root selector, wall/mirror, Z6 assembly); L=3 spaces out of suite. AFTERNOON (2026-08-30, v1011): 3+1D minimal object viable; fully coupled link–wall at minimal scale; Kronecker limitation removed. LATE EVENING (2026-08-30, v1013): mandatory-dynamics leg CLOSED at Hamiltonian-class level (LR + τ_t + A^G + state existence; remaining phase uniqueness, limit gap, IR universality). Decision typing UNCHANGED.

v993 (29/29) runs the FULL rank-8 ADE census (SNF of Cartan) with cyclic ℤ₄ glue on both factors: the unique hit is (D₅, A₃) (D₃ ≅ A₃ aliases collapsed). The D+A architecture of v624 is an OUTPUT of (rank 8 + cyclic ℤ₄), not an INPUT. Kill: D₄⊕D₄ / A₇⊕A₁ fail cyclicity (product 16); ℤ₃ control E₆⊕A₂. Lattice shadow of U² = (−1)^F: [λ]² = [v] exact. Unique finite trace-preserving conditional expectation (module property needed; kernel dim 36/720 without it). AX.P1.01 / AX.P2.01 typing UNCHANGED; equidistribution stays the open [C] of v813; cited-not-proved remain c₋ = 8 and holomorphic uniqueness of (E₈)₁. THREE NEW [O] CONTRACTS: GAUGE.DETLINE.FIXPOINT.01 — all three gauge couplings as unique stationary points of one nonabelian zeta-det/inflow functional (generalizes ALPHA.QUILLEN.EXACT.01; honest: α_s(M_Z) is currently an external input); GRAV.SPIN2.EMERGENCE.01 — massless transversal spin-2 pole from the same spectral determinant (Einstein equation stays downstream/conditional; GRAV.NONCIRCULAR.01 binding); FTRANSFER.SK.RHO0.01 — cosmological transfers need (S, ρ₀), not W[J] alone (typed candidate θ_i = 3π/5, μ₄ orientation picks k = 0; FTRANSFER.GENERATING.01 covers equilibrium only). Dual rest: compiler Rest = v_geo ⊕ G_net ⊕ F_transfer beside Rest_TOE (ten named [O] summands). v986 motivation retyped: Tr I = 3 is loose (Spec(I) = {1,1,1}); operator reading is Q₊ Spec{1,2,3}; texture DATA_CONSTRAINS_TEXTURE; check logic unchanged. No marker upgrades.

Four modules graduate the completeness-wave probes (suite 986 → 990; eight ledger rows updated; NO status-marker upgrades). v994 (11/11) executes 5 of 7 MMST identification criteria [E-measured]: c = 8.005 (16 Majorana copies), conformal edge spectrum [0.506, 1.516, 2.523, 3.524], k = 1, det D₈ = 4 → det E₈ = 1, and the flagship μ₄/GSO character sums reproduce the (E₈)₁ vacuum [1, 0, 248, 0, 4124, 0, 34752] three orders deep. C6 is now WRITTEN OUT in articles/2026-08-28/psi_lambda_convergence_theorem_en.tex (analytic log coefficient 2/π² = 0.20264 vs measured 0.203, 0.18%) — this IS the G1/C6 hand-off; C7 modular invariance stays cited/open. v995 (10/10): all 33 v972 mixing directions killed by KMS alone on finite CAR₈ = M₂₅₆; covariance redundant; 196608 → 0; type-III/continuum stays [O]. v996 (17/17): H0 structural kill of the naive α-grammar extension (SU(2) inverse −151.2, SU(3) −115.9; 64 conventions 0 hits; U(1) control 137.0359992168 survives); detline curvature → 2π exponentially at rate ~ ln 2 (numerical Bismut–Freed shadow). v997 (24/24): R+R² clean (massless TT pole, two helicities, scalaron exact); local a₄ Weyl² truncation necessarily carries a spin-2 ghost — typed; FK SMG toy N=8 unique Spin(7) singlet, gap 14 volume-independent, N=4 2^L contrast, physical edge π/L exact. NU_TEXTURE_CENSUS_NULL (0/1607 + 0/200) is a canonical note on FLAV.NUSCALE.05, not a module. Display markers unchanged.

Four modules graduate the outstanding exact/measured probes (suite 990 → 994; ledger 1166 → 1168: two new rows; NO status-marker upgrades). v998 (14/14): two-edge HS remainder ≤ 2.11 on the frozen plateau; lattice character θ_{E₈}/η⁸ EXACT four orders [1,0,248,0,4124,0,34752]; Θ_{E₈}(τ) = E₄(τ) q-expansion ≥ 8 orders exact (Jacobi vs Eisenstein; C7 arithmetic shadow now exact; net-level C7 stays cited). v999 (14/14): continuous-time dilation — Richardson 1.098×10⁻¹⁰, diag L = Q symbolic, e^Q = B exact, GNS 0, locality 1.355×10⁻²⁰; strong-collision rank 9/81; finite ladder now COMPLETE (open = thermodynamic field limit only). v1000 (26/26): lattice graviton positivity exact, 2 helicities at all 5852 momenta, ω = k − k³/24 exact; SK KMS/FDT ~10⁻¹⁷, ρ₀ contrast 3.550×10⁻³ vs static 10⁻¹⁶, 3π/5 unique in the μ₄ lift [C]. v1001 (14/14): pentagon-class candidate FLAV.NUSCALE.06 [C]/[N] — U_e = I, φ = 288°, θ = 2π/35 LEE 2.7%, max pull 0.557, SHA-16 a4c28732fa687620, Σ = 0.0599 eV, m_β = 9.0 meV, m_ββ ∈ [1.5, 3.8] meV, δ_CP = 287.66°, v270–θ₂₃ 1.85σ TYPED; census 0/1607; NO seesaw closure. Amendments (typed): QFT4D.LATTICE.FUNDAMENTAL.01 quasilocal family {H_Λ} (a single finite box is not a world; continuum optional, thermodynamic limit + IR universality mandatory); v_geo CLOSED METROLOGY (R₊ torsor; display stays [O]); ALPHA.QUILLEN relative determinant (BFK 2⁻⁴ needs no physical compensation). Master contract TFPT.TOE.COMPLETE.01 [O] names AND(T1..T8) vs Validated = Complete AND independent holdouts — not a closure.

Two modules graduate the wave-5 probes (suite 994 → 996; ledger 1168 → 1171: three new rows; NO status-marker upgrades). v1002 (39/39): DET16 rank-one projector on the full 2¹⁶ cluster — Ω†Ω=P₁₆, ΩΩ†=P₀, P_φ hermitian idempotent 2.8×10⁻¹⁸, h_mir {0¹, 1⁶⁵⁵³⁵} gap 1, 45 so(10) Fock commutators 0 (det ρ₁₆=1); hopping gaps 0.90/0.86 at t=0.2. NEW CHIRAL4D.MIRROR.DET16.01 Candidate [C] (open: dynamical gauge fields, domain-wall geometry, 4D volume theorem). Independently the number-preserving Casimir projector is EXCLUDED (census N=8:0, k=2:27, k=3:1463, |W(D₅)|=1920) — recorded on CHIRAL4D.NOMIRROR.01, display stays [O]. v1003 (24/24): charged-sector h=(1,1,1), d=(64,60,64) [E]; Schur-texture NULL 8/8, D4 forces λ₁=λ₃, required K ~ [3536.998, 1768.499, 1/3] matches none of 9 comparators; orientation-doubling lifts the degeneracy generically [E]; scale NULL 12/12, 1-|c/a|=1.885×10⁻⁴ not supplied. NEW FLAV.NU.TEXTURE.MECHANISM.01 [O]: mechanism must be D4-odd AND supply a ~2e-4 even-odd cancellation; pure seam data excluded; NUSCALE.05/.06 unmoved. NEW SEAM.MMST.TYPEIII.CHARGED.01 [O]: ONE scaling-limit theorem Ψ_{λ,N}→Ψ_λ from which B≅(E₈)₁, μ=1, type III₁, unique rotational KMS, unique CE, deck equidistribution and modular invariance follow as corollaries; cited articles/2026-08-29/holomorphic_kms_extension_en.tex (13 pp; KLM + Longo–Tanimoto GIVEN identification). GAUGE.DETLINE.FIXPOINT.01: unique fixed-volume stiffness (contraction −0.632, Dynkin ratio 4.0) BUT thermodynamic step-scaling L=2..8 DIVERGENT (g⋆ oscillates 0.65..1.69); typed hurdle ≥2+1D. v_geo: unit choice closed; dimensionless hierarchies remain predictive obligations.

Two modules graduate the wave-6 probes (suite 996 → 998; ledger 1171 → 1173: two new rows; NO status-marker upgrades). TYPING is binding: CLASSICAL (cite, no claim) — Milnor algebra of x²+y³+z⁵ ≅ ℚ[y,z]/(y²,z⁴) dim 8, spectral numbers = E₈ exponents {1,7,11,13,17,19,23,29}. NEW-IN-CORPUS EXACT [E-finite] (v1004, 40/40): rank clock (2−a)(4−b) sums to h(E₈)=30; S=pqr·μ/8; self-clock iff μ=8; (2,3,5) unique among ordered spherical triples; Galois-Gray 11/7/−1; CP = socle/Frobenius; integral D⁴ bridge basis-dependent. INTERPRETIVE [C]: PG(3,2)=AG(3,2)⊔PG(2,2). NEW SEAM.MILNOR.LOCALRING.01 [O]: canonical geometric identification of the raw seam collar with F₂[y,z]/(y²,z⁴) unproven. v1005 (43/43): Hankel pₙ pₙ₊₂−pₙ₊₁² = 2ⁿ⁺¹ and winding {5/2,1,1} [E-finite]; relative pencil EXACT BUT CIRCULARITY-FLAGGED [C] — unique t=2, λ=7/3, index 25=g_car² SNF (1,1,25), BUT carrier 5 already sits in the column sums of Q₂ and C: NOT a P2 selector; AX.P2.01 unmoved. Klein-four SNF (2,2) after D=2d interpretive [C]. NEW GRAV.WEINBERG.WITTEN.01 [O]: binding firewall before any spin-2 marker move (no microscopic Lorentz-covariant local T_μν; Lorentz, diffeomorphism Ward and spin-2 emerge in the SAME IR limit). Display corrections: Rest_TOE / TFPT.TOE.COMPLETE.01 placed next to the compiler rest; SM completeness retyped to discrete structure; gravity display retyped off 'parameter-free'.

Four modules graduate the wave-7 strands (suite 998 → 1002; ledger 1173: NO new rows; existing contract rows updated; NO status-marker upgrades). v1006 (68/68): five lemmas in-house on SEAM.MMST.TYPEIII.CHARGED.01 [O] — L3 crossed-product, UGF K_G=π²/4 (measured plateau ~1.023), TEL-a N⁻² with exact isometries (A_TEL=5120(1+π/2), envelope ~3.42), integer D5+A3 pairings, Z4 outerness in the limit + finite-inner correction. Residual boxed: TEL-B-EXTERNAL (Hankel C_R; HS remainder sourced 2.105079358 / fit 2.107565497 / v998 bound 2.11, not recomputed) + ALG-EXH (two Buchholz–Verch estimates). Display stays [O]. Cited articles/2026-08-30/mmst_charged_scaling_limit_en.tex (21 pp) + externalization_mmst_handoff_v2_en.html. v1007 (67/67): T1/T2 proved (v1002); T3 Michalakis–Zwolak cited-verified (LTQO, t*>0, gap ≥1/2). Counting n=2,3; n=2 closing scan through t=4; dynamical Z2/Z4 uniquely gapped (full-probe min 0.728854416 pinned). SW 1−α t²+O(t⁴); c_geo/L bounded. 1/192 boxed (ordinary hopping not block-diagonal); BDL boxed. CHIRAL4D.MIRROR.DET16.01 stays Candidate [C]; NOMIRROR unmoved. Cited det16_mirror_gap_theorem_en.tex. v1008 (22/22): 2+1D master-object scaffold-coherent — combinatorial K=0; frozen-link q²~4, K(q=0)=0; unique-contractive |R'|<1; QWZ wall slope ~−0.9989, DET gap ≥1.5 through t=0.6; assembly Z6 (1,2,3,0), clock [0,1,1,2]. L=3 262144 / 129024 out of suite. Lattice-fundamental Decision and GAUGE.DETLINE.FIXPOINT.01 [O] unmoved. v1009 (13/13): unique KMS compression (Klein), Hessian strictly positive, centre dim 1, identity ~8e-17. TYPED V1000_CONSEQUENCE_MISMATCH (compression kills SK response vs frozen contrast 3.550e-3) + CENTER_FLATNESS_PREMISE_FALSE. Canonical formula needs a weaker admissible set. FTRANSFER.SK.RHO0.01 stays [O]. Python-only / Wolfram deferred.

Two modules graduate the afternoon harvest (suite 1002 → 1004; ledger 1173: NO new rows; existing contract rows updated; NO status-marker upgrades). The simplicity campaign finds no smaller axiom core — the simplicity lives in the theorems. v1010 (42/42): derivation matrix remainder min S4=2; anchor (1,1,2) not among 3 declared Milnor maps; φ₀ four novel NULL. Bridge Q CANONICAL: ladder forces sums (9,5,1); C's 5 inherited from R — the v1005 circularity flag is corrected as forced provenance. Bridge W CHOICE-but-conditionally-unique (1078 → 1 under democratic-image + carrier-anchor-kernel); remaining obligation = seam-geometric derivation of those premises. Milnor strong all-structure bridge NONEXISTENT at F₂ (clock 2 vs 4, CP rank 2 vs 4) and at every upstairs home (Z/4, Gaussian k=2/3, affine); only the coarse D+pairing bridge exists (|Aut(X)|=36864, |Aut(Y)|=8). SEAM.MILNOR.LOCALRING.01 stays [O] (canonical status SHARPENED); AX.P2.01 stays an axiom. v1011 (32/32): 3+1D ladder B6–B9 complete at scaffold — viable (Gauss 32768, confinement, exact isotropy, g★≈1.915); tree-fixing 524288→4096; DET-under-coupling; K collapses in the confined phase; charged channels ~2.014× at weak g. BINDING: matching scale of the coupling functional must sit in the deconfined/weak regime. QFT4D.LATTICE.FUNDAMENTAL.01 Decision UNCHANGED (Kronecker limitation removed); GAUGE.DETLINE.FIXPOINT.01 stays [O]. Python-only / Wolfram deferred.

One battery graduates the evening TOE-gate wave (suite 1004 → 1005; ledger 1173: NO new rows; existing contract rows updated; NO status-marker upgrades). v1012 (40/40) executes four fronts. T5: physical QWZ edge c → 1 (0.99993), clustering dichotomy ξ·gap ≈ 1.089 vs power-law exponent 2.034, Lieb–Robinson cone v_LR = 5/3 ≥ c with leakage 0.015, cubic curvature → 1/6 with volume; TYPED SPLIT: gauge holonomy + seam clock are not propagating modes — the common-c test needs dynamical gauge excitations. T8: eight unique ρ₀ candidates; hard sectors kill the SK response (~10⁻³¹); every response-alive set is exactly ρ_KMS even without μ₄ — entropic-proximity selection is VACUOUS at finite level; verdict NO_SET_WORKS; binding: a non-entropic principle (Euclidean-cap / orientation-branch). T6: six pre-declared D4-odd κ candidates, all parity-checked, all NULL (five at 10⁻¹⁴; K₄ = 3.55×10⁻³ is 18.8× too large); 1.885×10⁻⁴ requires the true 4D functional — scaffold-level nu-mechanism bound complete. T7: conserved interaction-complete lattice stress ~10⁻¹⁵, TT positivity exact, sum rules ~10⁻¹⁵, dominant positive-Z pole persists under φ⁴ (gapped); Z trend k1 0.958 / k2 1.033. Missing: TFPT content, k→0 volume scaling, Ward identities. TFPT.TOE.COMPLETE.01, FTRANSFER.SK.RHO0.01, FLAV.NU.TEXTURE.MECHANISM.01 and GRAV.SPIN2.EMERGENCE.01 stay [O]. Python-only / Wolfram deferred.

Two modules graduate the late-evening harvest (suite 1005 → 1007; ledger 1173: NO new rows; existing contract rows updated; NO status-marker upgrades). The thermodynamic-dynamics theorem closes the mandatory T3 dynamics leg at Hamiltonian-class level. v1013 (12/12): uniform Lieb–Robinson bound J=12/5, R=2, z=4, κ=16043/450, v_LR=32086 e/225 ≈ 387.64; norm-convergent τ_t; gauge-invariant quasilocal A^G (Gauss caveat resolved on the invariant subalgebra); existence of ground and β-KMS states. Numeric twin: measured v=2.0 ≪ proved bound; analytic finite-volume bound dominates nested differences at buffers 8/16/32. Remaining: phase uniqueness, limit gap, IR universality. Decision typing UNCHANGED. Cited articles/2026-08-30/tfpt_thermodynamic_dynamics_en.tex/pdf. v1014 (17/17): finite detline restriction isomorphism VERIFIED (c_phase constancy 3.7×10⁻¹⁶, conjugation covariance exact, C=W_bulk=W_seam=+1 / mirror −1); orientation fixes only the conjugate branch (2→1); the residual constant U(1) is the A0 reference normalization — recorded on ALPHA.QUILLEN.EXACT.01. W-bridge: P-anch DERIVED (e1=R⁻¹(1,1,2)^T via the winding lock); P-dem PARTIAL (Z4 average annihilates nontrivial characters); missing object = the character-blind determinant-response map — the same MMST/Quillen externalized leg as TEL-B/ALG-EXH/P1. AX.P2.01 stays an axiom. Historical scope: within the finite W-bridge/compiler lane considered here, the remaining identification was routed through the external MMST/Quillen leg; this did not classify or close the independent physical TOE gates T3–T8. Python-only / Wolfram deferred (engine DEFERRED_NO_ENGINE).

Two modules graduate the Monday-morning harvest (suite 1007 → 1009; ledger 1173: NO new rows; existing contract rows updated; NO status-marker upgrades). v1015 (11/11): character-blind P-dem response DERIVED — r=(1,1,1) exactly at collar sizes 12 and 16, democracy residual 0; mutants split (1,0,0) and (5/4,1,5/4). Together with P-anch (v1014) BOTH W-bridge premises are derived at finite level; the axiom-core remainder is ZERO modulo the externalized MMST identification. AX.P2.01 stays an axiom (finite shadows; continuum identification is the same external leg). T1 note: the structure-postulate route is now fully premise-supported at finite level. v1016 (31/31): R4 seam-modular cap is the unique finite-level non-entropic selector (D_tr=0.1434, SK RMS 3.038×10⁻³, 3π/5 saddle preserved; finite-proxy caveat; FTRANSFER.SK.RHO0.01 stays [O]). TEL-B certified-tail BLOCKED (N² D_N 530→19032, UV-supported remainder); strictly smaller external target A_R<43 with factor-~350 measured headroom; N-uniform CAR nuclearity PROVED (C_β=(67.97, 29.73, 12.15)) as ALG specialist input; ALG-EXH unchanged (SEAM.MMST.TYPEIII.CHARGED.01 stays [O]). DFP volume-uniform gap cited-verified for ℤ₂/ℤ₄ open chains (a=0.0233, a/16=0.00146); dynamical-link leg closed at that level; remaining rotor/wall/3+1D (CHIRAL4D.MIRROR.DET16.01 stays [C]). Historical scope: this routing statement applies to the finite W-bridge/compiler lane only; T3–T8 and a shared 3+1D parent remain independent open obligations. Python-only / Wolfram deferred (engine DEFERRED_NO_ENGINE).

One module graduates the kernel-Loewner positivity certificate (suite 1009 → 1010; ledger 1173 → 1174; new row PRIME.RDAGGER.KERNEL_LOEWNER.01, Numerical/certified float64, not [E]). v1017 (26/26) re-derives rounds r494/r495 with no probe imports: Q_W(h) ≥ 2.1×10⁻³ ‖h‖₂² on supp(h) ⊂ [−0.3, 0.3] (2L = 0.6 < log 2, prime term empty). Float64 enclosed floor 2.122×10⁻³ after a 3× Hilbert–Schmidt tail charge (NOT interval arithmetic). G1 identity vs defining digamma (σ_A(0)=−5.3721834192256654). G2 Loewner after zero-extension. Independent r495: translation identity 6/6 exact over ℚ; doubled-c_L false-world budget −2.188. BOUNDARY: r496 NO_GO(compact-tail@L=0.8) is the named method boundary — not λ_*(L)≥0 in general. No cofinal claim; no RH statement. Python-only / Wolfram deferred (engine DEFERRED_NO_ENGINE).

Two modules graduate the directed E8 readout and the Coxeter–Euler completion (suite 1010 → 1012; ledger 1174 → 1176; two new rows). v1018 (47/47) re-derives round r609 with no probe imports: seven exact E8 readout cells [E] Identity (Seifert/Phi_30; Hamming 1+14y^4+y^8; srg(120,56,28,24); N(n)=240 sigma_3(n) for n<=10; A_P(n)/A_P(1)=tau(n); (Z/30)^x cong C2 x C4; E6 oplus A2 index 3, Smith (1^6,3,3), glue 78/81/81). C7 Gauss-code transform stays OPEN (rem:c7-audit). v1019 (46/46) re-derives r617: exact det(I-xC)=Phi_30, Tr C=-1, U=1 oplus C, Tr U=0; classical Moebius Phi_30; global Z_C and D_E8 as zeta quotients, abs. conv. Re s>1/2. Numerical (X=10^5): D_E8 residual 4.76e-4 at s=0.75, 4.16e-12 at s=1.5. Class: vanishing linear term generic from Tr C=-1; E8 selects only the divisor set of 30. Beurling-generic. Fence (verbatim, no marker upgrade): The trace-free completion is zero-free and pole-free in Re s > 1/2. The splitting into the scalar zeta channel and the Coxeter channel is open and RH-equivalent. No RH claim. NO-GO E8.COXETER.REGULARIZED_SPLIT.NO_GO.01: det_2 cannot isolate 1/zeta(s). Like the Eisenstein bridge, RH-neutral. Python-only / Wolfram deferred (engine DEFERRED_NO_ENGINE).

Typing: research contract [O], registered 2026-08-29 from review wave 4. This row NAMES the AND of eight gates; it does not close any of them and it does not upgrade a marker. Dual rest: the compiler residual Rest = v_geo ⊕ G_net ⊕ F_transfer sits beside Rest_TOE; this contract is the named AND, not a closure of either. THE EIGHT GATES. (T1) structure postulate → P1/P2/compiler (AX.P1.01, AX.P2.01, TFPT.IRREDUCIBLE.01, DIMENSION.SELECTOR.4D.01). (T2) seam = (E₈)₁ proven (SEAM.EQUIV.01, SEAM.EQUIV.MMST.01, SEAM.EQUIV.TWISTOR.01, SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.DETLINE.UNIFICATION.01, SEAM.STATE.RPMIXING.01). (T3) quasilocal local unitary 3+1D Hamiltonian family (QFT4D.LATTICE.FUNDAMENTAL.01, TFPT4D.LATTICE.ACTION.01, DYN.UNITARY.DILATION.01, DYN.MARKOV.EMBED.01). (T4) chiral SM with local measure + uniform mirror gap (CHIRAL4D.NOMIRROR.01). (T5) IR Lorentz + confinement + clustering + nontrivial scattering (QFT4D.OS.RECON.01, SEAM.BULK4D.RECON.01). (T6) all three gauge couplings + neutrino texture internally fixed (ALPHA.QUILLEN.EXACT.01, GAUGE.DETLINE.FIXPOINT.01, FLAV.NUSCALE.01–.06). (T7) quantum massless spin-2 with universal coupling (GRAV.SPIN2.EMERGENCE.01, GRAV.NONCIRCULAR.01, GRAV.WEINBERG.WITTEN.01). (T8) unique initial state + one SK functional generating all readouts (FTRANSFER.SK.RHO0.01, FTRANSFER.GENERATING.01, OBS.TRANSDUCTION.01, PRED.JOINTLIKELIHOOD.01). SEPARATION (binding): TOE_Complete := AND(T1..T8); TOE_Validated := Complete AND independent holdouts passed. Every existing 4D / dilation / detline / SK / flavor / gravity contract is a child of one gate; children do not list this row back. Status: TFPT.TOE.COMPLETE.01 [O]. EVENING (2026-08-30, v1012): T5 four IR witnesses + propagating-mode precondition; T7 interacting stress mechanism; T8 selection-principle vacuity typed (needs a non-entropic selection); T6/nu scaffold-level triple bound complete. HISTORICAL SCOPE (v1013–v1016): the finite Hamiltonian-class and W-bridge/compiler lanes were narrowed; those statements never classified the independent physical completeness gates. ROUND 3 (2026-09-05, v1022–v1025): T1 retained only finite axiom-core/W-bridge support while unconditional provenance and the dimension selector were open; T2 gained interval-certified TV, analytically proved C1/C2a with executable final-constant certificates and the scalar C2b budget, while CF, DG and ALG-EXH were still open at that cut and the former ALG2 Vandermonde implication was refuted; T3 stayed at Hamiltonian-class level without a shared 3+1D parent; T4 had only the finite derivative-filtered quasi-free block; T5 had finite IR witnesses plus the v1020 spectator obstruction; T6 had a finite parent-internal intertwiner with a projective full-Fock lift; T7 had gap/TT locality no-gos; T8 had an arbitrary finite Z5 cap. ROUND 4 (2026-09-05, v1026–v1030): at fixed M=1 and Ny=8, native v1026 with v1022/v1025 proves ||R_N||HS < 2.995906 < 3 for every even N≥16, including the former CF/DG residual for this relaxed norm. v1027 constructs signed CAR only under the DET-singlet premise and fixed classical gauge, not an interacting quantum-link or hard bare-mirror-gap theorem. v1028 gives Gauss residues 3 mod 5 on one site and 0 mod 5 on the open cube only with the specified nine-irrep link truncation, plus a two-dimensional invariant choice in the selected 12D D4 pair space. v1029 requires removal of the global zero-mode block and is not a TFPT embedding. v1030 is conditional on an actual joint-adjoint word frame and tails. ALG-EXH/FE-GEN, all T1–T8 gates, TFPT.TOE.COMPLETE.01 and the shared 3+1D parent remain [O]; no marker moves.

Typing: candidate [C]/[N] (ledger row FLAV.NUSCALE.06); mechanism = the Q₊-to-flavor operator [O]. No seesaw closure; FLAV.NUSCALE.05 unmoved. (v1001). Executed content: U_e = I inventory theorem; misalignment U = U_v9 R_13(θ, φ); pentagon double hit φ = 288° = 4(2π/5) frozen, all three measured angles ≤ 0.56σ (honest max pull 0.557) at θ = 2π/35, unique LEE survivor of nine pre-declared candidates (LEE 2.7%); v3 chain SHA-16 a4c28732fa687620 with Σ = 0.0599 eV, m_β = 9.0 meV, m_ββ ∈ [1.5, 3.8] meV, δ_CP = 287.66°; v270–θ₂₃ tension 1.85σ TYPED; census null 0/1607. Kills: DESI floor on Σ; DUNE δ_CP discriminates 287.7 vs 240; JUNO. Status: Candidate [C]/[N]; no closure. WAVE-5 (v1003): both structural nulls recorded on FLAV.NU.TEXTURE.MECHANISM.01 [O] (D4-odd AND ~2e-4 cancellation); this candidate unmoved.

Typing: candidate [C], registered 2026-08-29 from review wave 5 (v1002). Exact finite-cluster gapping on the full chiral 2¹⁶ Fock space via the number-violating determinant vertex: Ω†Ω=P₁₆, P_φ rank-one hermitian, h_mir gap 1, 45 so(10) Fock commutators 0. Open: dynamical gauge fields, domain-wall geometry, 4D volume theorem — not a 3+1D closure. Does not upgrade CHIRAL4D.NOMIRROR.01; the Casimir-projector kill is recorded on that parent. Status: Candidate [C]. WAVE-7 (2026-08-30, v1007): T1/T2 proved; T3 Michalakis–Zwolak cited-verified (LTQO, t*>0, gap ≥1/2). Counting line n=2,3; n=2 closing scan through t=4; dynamical Z2/Z4 uniquely gapped (full-probe min 0.728854416 pinned). SW 1−α t²+O(t⁴); c_geo/L bounded. 1/192 boxed (ordinary hopping not block-diagonal); BDL boxed (no volume-uniform gap remainder). Display stays Candidate [C]; NOMIRROR unmoved. Cited articles/2026-08-30/det16_mirror_gap_theorem_en.tex. MONDAY MORNING (2026-08-31, v1016): Fröhlich–Pizzo hypotheses cited-verified for ℤ₂/ℤ₄ DET open chains — volume-uniform spectral gap ≥ Δ/2 in the parametric window τ_FP (a=0.0233, a/16=0.00146). Dynamical-link leg closed at that finite-group level. Remaining: rotor links, wall mixing, 3+1D placement. Display stays Candidate [C]. ROUND 3 (v1023): the separate derivative-filtered 2×2 quasi-free block is exact, but the bare b sector is not invariant and the low branch has z=2; no Weyl cone, DET16/DET32 realization, interacting parent, measure or 3+1D theorem follows. DET16 stays [C] and NOMIRROR/T4 stay [O].

Typing: research contract [O], registered 2026-08-29 from review wave 5. Demand: ONE scaling-limit theorem Ψ_{λ,N}→Ψ_λ strongly on the finite-energy core + crossed-product continuity, from which B≅(E₈)₁, μ=1, type III₁, unique rotational KMS, unique conditional expectation, deck equidistribution and modular invariance all follow as corollaries. Children (listed here, not back): SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.STATE.RPMIXING.01 continuum, ALPHA.QUILLEN.EXACT.01 rigidity, AX.P1.01 reading. Cited document articles/2026-08-29/holomorphic_kms_extension_en.tex (13 pp): unconditional rotational-KMS uniqueness via KLM + Longo–Tanimoto GIVEN the identification; P1 = theorem-conditional on seam identification + β_angle=2π. Axiom typing UNCHANGED. Status stays [O]. WAVE-7 (2026-08-30, v1006): five lemmas in-house — L3 crossed-product, UGF K_G=π²/4 (measured plateau ~1.023), TEL-a N⁻² with exact isometries (A_TEL=5120(1+π/2)), integer D5+A3 pairings, Z4 outerness in the limit + finite-inner correction. Residual boxed: TEL-B-EXTERNAL (Hankel C_R; HS remainder sourced 2.105079358 / fit 2.107565497 / v998 bound 2.11) + ALG-EXH (two Buchholz–Verch estimates). Cited mmst_charged_scaling_limit_en.tex (22 pp) + externalization_mmst_handoff_v2_en.html. Display stays [O]. MONDAY MORNING (2026-08-31, v1016): TEL-B certified-tail BLOCKED (N² D_N 530→19032, UV-supported remainder); strictly smaller external target A_R<43 with factor-~350 headroom; N-uniform CAR nuclearity PROVED as ALG specialist compactness input; ALG-EXH unchanged. Display stays [O]. TEL-B REDUCTION (2026-09-04): residual restated as TEL-B-EXTERNAL via cover identity + sawtooth split; (A) lattice piece certified numerically for all N, ||R^sm_N|| ≤ 1.7833 (all-mode BV, one float64 TV constant); (B) explicit piece reduced to Σ|Res_N|² ≤ 0.2769 (measured 0.1550), open items C1 (C⋆ ≤ 0.1525 enclosure), C2a (|φ_N| ≤ 0.51/N), C2b (cell oscillation of r); numerically 2.57 < 3, conditional analytic 2.9495 < 3. The A_R<43 dyadic-increment route is superseded (measured A_R=0.1238 at r645). Standalone note articles/2026-09-04/telb_bound_b_sketch.tex superseded and removed. Not a marker move; display stays [O]. ROUND 3 (v1022/v1025): native Arb/Acb certified TV, C1 and the C2a final constants and checked the analytic scalar C2b budget below 0.400; at that cut, full C2b still depended on CF≤0.139/√N and DG≤0.060/√N, while ALG-EXH was open and the old ALG2 Vandermonde implication was refuted by an exact M2 countermodel. ROUND 4 (v1026): at fixed M=1 and Ny=8, the native CF/DG, one-sided CROSS, validated Fourier-alias and assembly certificates prove ||R_N||HS < 2.995906 < 3 for every even N≥16. The microscopic one-boundary system, ALG-EXH/FE-GEN and the MMST scaling limit remain open; parent status stays [O].

Typing: research contract [O], registered 2026-08-29 from review wave 5 (v1003). Charged-sector h=(1,1,1), d=(64,60,64) [E]. Schur-texture NULL [X]: 8/8 (K,B) fail; D4 forces λ₁=λ₃; required K~[3536.998,1768.499,1/3] matches none of 9 comparators. Orientation-doubling [E]: sgn-J odd sector generically lifts the degeneracy. Scale NULL [X]: 12/12 fail; 1-|c/a|=1.885×10⁻⁴ not supplied; η-branches isospectral. Consequence: the mechanism must be D4-odd AND supply a ~2e-4 even-odd cancellation; pure seam data excluded [X-typed]. FLAV.NUSCALE.05/.06 unmoved; no seesaw closure. EVENING (2026-08-30, v1012): kappa six-fold NULL completes the scaffold bound — mechanism scale strictly beyond frozen finite objects; 1.885×10⁻⁴ requires the true 4D functional. Status stays [O]. ROUND 3 (v1024): a positive finite parent-internal seam/neutrino-pair intertwiner has mixed resolvent 0.104712041885 and conditional gap 0.25, but ordinary D4 on the selected pair operators lifts projectively on full Fock space. It supplies neither a neutrino mass matrix nor the 2×10⁻⁴ cancellation or a 4D functional. T6 stays [O].

Typing: research contract [O], registered 2026-08-28 from review wave 3. EXECUTED UPDATE (v996, completeness wave): the naive H0 grammar extension is a STRUCTURAL KILL — negative b₂/b₃ flip the stationary-root signs (SU(2) inverse −151.2, SU(3) −115.9); 64 conventions 0 hits; U(1) control 137.0359992168 survives all mutants. Exponential detline-curvature → 2π with rate 0.6936 ~ ln 2 is a numerical Bismut–Freed shadow, not the continuum theorem. Naive census-only extension excluded [E]; genuinely nonabelian Casimir/instanton structure required — typed. Demand: all three gauge couplings (g₁, g₂, g₃ / equivalently α, sin²θ_W, α_s) arise as stationary points of ONE nonabelian zeta-det / inflow functional on the determinant line — the nonabelian upgrade of the U(1) face ALPHA.QUILLEN.EXACT.01. Acceptance: unique stationary points, positive Hessian, α_s(M_Z) without measured input, RG from the matching scale reproduces the data, mutants fail. Honest bound: α_s(M_Z) is currently an EXTERNAL INPUT (the QCD matching / lattice input of F_QCD); this contract names the missing first-principles replacement, it does not claim the number is derived today. Kill: a unique stationary point fails to exist; Hessian not positive; mutants (wrong level, wrong inflow multiplicity) still pass; RG from the functional fails to land on the observed couplings. Relation: generalizes ALPHA.QUILLEN.EXACT.01. Honest: α_s(M_Z) remains an external input. WAVE-5 (2026-08-29, exploration probes, not a new module): mechanism executed at FIXED VOLUME (unique fixed point, contraction −0.632, exact q² and SU(2) Dynkin ratio 4.0) BUT preregistered thermodynamic step-scaling L=2..8 is DIVERGENT (g⋆ oscillates 0.65..1.69, |R′|>1 at L=4,5,8). Typed hurdle: the 1+1D toy has no plaquette self-interaction; the real contract needs ≥2+1D. Status stays [O]. WAVE-7 (2026-08-30, v1008): the 2+1D plaquette scaffold is now executed — combinatorial K=0, frozen-link q²~4, unique-contractive |R′|<1 (L2 0.578 → L3 0.936 harvest pins; L=3 Lanczos out of suite). The 1+1D no-plaquette hurdle is lifted at the scaffold level; thermodynamic 4D fixpoint stays [O]. AFTERNOON (2026-08-30, v1011): BINDING — holonomy stiffness collapses in the confined phase; the matching point of the coupling functional must be defined in the deconfined/weak regime; charged channels enhance (~2.014× at weak g) but do not prevent collapse at minimal volume. Display unmoved Open.

Typing: research contract [O], registered 2026-08-30 from review wave 6 (v1004). Demand: a CANONICAL identification between the raw seam collar / E₈ transition bus and the reduced Milnor algebra F₂[y,z]/(y²,z⁴) preserving simultaneously the dual-number action, Frobenius pairing, Gray torsor, deck action and CP. Acceptance: geometric/mechanical (not basis-chosen); rank clock and socle-CP as outputs. Kill: any second inequivalent identification with the same invariants, or failure of μ₄-equivariance. Currently [O] because Milnor algebra + E₈ exponents are classical and the corpus map is unproven. Executed finite algebra [E-finite]: rank clock sums to 30=h(E₈); self-clock iff μ=8; (2,3,5) unique; Galois-Gray; CP=socle/Frobenius; integral D⁴ bridge basis-dependent. PG(3,2) interpretive [C]. Circularity note (v1005, not a third contract; CORRECTED by v1010): the pencil sums are forced provenance (ladder c=2 + n=3 force Q sums (9,5,1); C's 5 inherited from R) — non-circular; W remains conditionally unique 1078→1 given democratic-image + carrier-anchor-kernel; remaining obligation = seam-geometric derivation of those premises. AX.P2.01 unmoved. AFTERNOON (v1010): strong all-structure identification finitely obstructed at F₂ and all upstairs homes; only the coarse D+pairing bridge exists; ring-internal identities (rank clock, socle CP, self-clock) unaffected. LATE EVENING (v1014): W-bridge P-anch DERIVED (e1=R⁻¹a via winding lock); P-dem narrowed to the character-blind determinant-response map (MMST/Quillen externalized leg). AX.P2.01 unmoved. MONDAY MORNING (v1015): P-dem DERIVED (r=(1,1,1); both W-bridge premises finite; axiom-core remainder 0 modulo MMST). AX.P2.01 unmoved. Status stays [O].

Typing: research contract [O], registered 2026-08-30 from review wave 6. Child of TOE gate T7; cross-link GRAV.SPIN2.EMERGENCE.01 (listed here, not back). Demand: the microscopic Hamiltonian family must NOT possess a fundamental Lorentz-covariant local conserved T_μν; Lorentz symmetry, diffeomorphism Ward identities and the spin-2 mode must emerge in the SAME IR limit. Acceptance: positive TT spectral density, exactly two helicities, massless pole, emergent diffeomorphism Ward identity, universal soft coupling, AND an explicit statement of which Weinberg–Witten premise is evaded. Kill: a microscopic covariant local T_μν together with a massless composite spin-2 claim. Binding firewall BEFORE any spin-2 marker move. Status stays [O].

Typing: research contract [O], registered 2026-08-28 from review wave 3. EXECUTED UPDATE (v997, completeness wave): exact Barnes–Rivers quadratic decomposition — R+R² clean (one massless TT pole, two helicities, scalaron at M_scal exact); the LOCAL a₄ Weyl² truncation NECESSARILY carries an opposite-residue spin-2 ghost — typed. Content pinned on the untruncated form factor a(□)=e^{−□/M²}. EXECUTED UPDATE (v1000, review wave 4): quadratic Hamiltonian half — positivity exact, 2 TT helicities at all 5852 momenta (N=6..12), ω = k − k³/24 exact; must-fail: a mass term gaps TT; a wrong-sign kinetic term yields two negative directions. Spectral-action Hessian identification, nonlinear Ward and universal coupling stay [O]. Demand: from the SAME spectral determinant that carries the gauge fixpoints, a massless transversal spin-2 pole with two helicities, universal T_μν coupling, diffeomorphism Ward identities, and positive Hessian / reflection-positive transfer. Relation: the entanglement-equilibrium Einstein equation (v358/v359) stays a DOWNSTREAM / CONDITIONAL readout — it presupposes a local QFT and can never be cited as producing one; GRAV.NONCIRCULAR.01 is BINDING (BW/CHM uses remain assumption-declared). Kill: a massive or longitudinal extra mode; non-universal coupling; failed diffeomorphism Ward; negative Hessian / RP violation on the spin-2 sector. WAVE-6 (2026-08-30): GRAV.WEINBERG.WITTEN.01 is the binding firewall before any spin-2 marker move (no microscopic Lorentz-covariant local T_μν; Lorentz, diffeomorphism Ward and spin-2 emerge in the SAME IR limit). EVENING (2026-08-30, v1012): interacting TT half-step — conservation/positivity/sum-rules/Z-persistence executed; missing TFPT content, k→0 volume scaling, Ward identities. Display stays [O]. ROUND 3 (v1024): a uniform full-parent gap excludes a massless pole and an exact strictly finite-range direct TT projector is obstructed by its direction-dependent k→0 limit. This is a no-go/boundary, not a graviton; no Ward identity or universal coupling follows. T7 stays [O].

Typing: research contract [O], registered 2026-08-28 from review wave 3; mechanism executed 2026-08-29 (v1000). Demand: cosmological transfers (F_relic, F_Boltzmann, and any nonequilibrium 4D readout) need the pair (S, ρ₀), not W[J] alone — the Euclidean-cap / KMS initial state. Typed candidate: the θ_i = 3π/5 saddle S_init = −κ cos(5θ − 3π) as the selection. Arithmetic: stationary points θ = (3+k)π/5; the μ₄ orientation picks k = 0. Relation: FTRANSFER.GENERATING.01 covers EQUILIBRIUM correlators of W[J] only; this contract is the Schwinger–Keldysh completion. Kill: the (S, ρ₀) pair is inconsistent with the W[J] of TFPT4D.LATTICE.ACTION.01; the 3π/5 saddle is not selected by μ₄ orientation (a different k is forced); the Euclidean cap fails KMS. EXECUTED UPDATE (v1000, review wave 4): KMS/FDT on the exact Bohr grid ~10⁻¹⁷; ρ₀-dependence contrast 3.550×10⁻³ versus static 10⁻¹⁶; saddle 5-fold degenerate with 3π/5 unique in the chosen μ₄ lift [C]. No cosmological solve. Status stays [O]. WAVE-7 (2026-08-30, v1009): finite uniqueness closed — constrained minimizer uniquely the normalized KMS compression (Klein), Hessian strictly positive, centre dim 1, identity ~8e-17. TYPED: V1000_CONSEQUENCE_MISMATCH (compression kills the SK response vs frozen contrast 3.550×10⁻³) + CENTER_FLATNESS_PREMISE_FALSE. Canonical formula needs a weaker admissible set. EVENING (2026-08-30, v1012): double diagnosis — hard sectors response-dead, KMS-affine sets selection-vacuous; canonical state requires a different principle (e.g. Euclidean-cap/orientation-branch). MONDAY MORNING (2026-08-31, v1016): R4 seam-modular cap is the unique finite-level non-entropic selector (D_tr=0.1434, SK RMS 3.038×10⁻³, saddle preserved; finite-proxy caveat). Display stays [O]. ROUND 3 (v1024): the finite 12D Z5 cap is gapped but chosen, D4-breaking and zero on a large complement; relative-commutant and Weyl-pair results are algebraic boundaries, not a global rho_0 selector or unique SK functional. T8 stays [O].

The selector-triangle pairings and the v_geo scale anchor are finite, algebraic and falsifiable today; G_net is a deep analytic programme; F_transfer is the downstream interface. The recommended order freezes the frontier status in between.

F_transfer = F_observable ∘ F_threshold ∘ F_RG — standard physics fed TFPT source data — with four interfaces, each a typed RUNNABLE solver with a kill test: F_pole (Koide source→pole, v371; the 53/54 factor is an exact [E] readout, the pole interpretation [C]), F_Boltzmann (η_B via the BDP washout, v372), F_relic (the finite-T axion relic — the spine angle θ_i = 3π/5 = π·N_fam/g_car is the sharper branch, the 170° hilltop over-produces, v373/v211), F_QCD (m_p/m_e via carrier-b₃ running, v374) — folded into a status-typed prediction-observatory CI (v375). A machine guard (v187) keeps all four [C]/[O], never promoted to a primitive [E] compiler prediction (exact sub-parts like 53/54 and b₃ = −7 may be [E]). The functor contract CONTRACT.F.01 (v213) pins four structural axioms: μ₄-deck equivariance (λ₂ = (2/3)⁶ is the deck transfer eigenvalue), Plücker preservation (53 = aᵀ(R+Q)1), positivity/stochasticity (spec T = {1,(2/3)⁶,(1/3)⁶}), and explicit external modules. Dynamically (v303) all four share ONE shape — a gapped, positivity-preserving relaxation to a unique attractor (Perron–Frobenius / Boltzmann H-theorem / RG fixed point), the same shape as the main-branch E₈-mark update; F_pole runs it at the seam rate (2/3)⁶ exactly, the others with honestly-fenced external rates. So F_transfer is the downstream readout of the one discrete→dynamic principle — the predictions stay [C], never compiler outputs. 2026-08-05: the frozen external-clock contract FTRANSFER.CLOCKS.01 is EXECUTED (v777) — the preregistered K1 kill fires exactly as the frozen prior expected (NO-COMMON-CONNECTION: the transported Schwarzians are sympy-exactly {−Δ²/2, −Δ²/2, 0}, so no common continuous clock exists for the four jets; all four dictionary-validity legs pass; the prereg YAML and both data tables were byte-frozen before the first run). The surviving architecture is the FIBERED functor: one shared discrete PGL₂ base (anchor cross-ratio 4/3 exact; unit parabolic deck translation) with the constant seam obstruction cocycle, values exactly {0, ±Δ²/2}; thermal/proper-time clocks {τ, β} vs the RG clock {log μ} split the cosets, the relic channel stays degenerate and unclassified. The jet route of CONTRACT.F.01 is closed at the physical-clock level. 2026-08-06: the named next step is executed and is a THEOREM (FTRANSFER.KMSCOSET.01, v792, KMS-COSET-THEOREM) — the coset carried by a clock chart is a function of its KMS/modular typing datum alone, S = −(ln λ)²/2 with λ the time-1 PGL₂ holonomy multiplier per clock e-fold; the classifier is Schwarzian-free and derivative-free (non-circularity gated on its own source), the blind assignment classifies the four deployed charts exactly as the fibered functor carries them, the unblinding is sympy-exact, and the controls fire (fake KMS caught; affine invariance; the v578 Möbius clock as the positive case) — the executor → groupoid → coset chain is whole. The four observables stay [C]/[O].

The prime/zeta line of the contracts document carries its own dated contract chain. 2026-08-05: the diagonal Gram closure theorem PRIME.GRAM.DIAGONAL.01 (registered 2026-08-04) is CLOSED per its own frozen stakes — an honest negative adjudication, not a marker upgrade. The final cascade: Gates 1/2/4 positive from the diagonal gram round (v759–v762, v765); Gate 3 dead at the corner level (v769: q_f is representation gauge, but the corner increments of the contract's own objects rise beyond X ~ 13 at every gated eps below 1e-1 on the 1.6e7 comb); Gate 5/v764 never executed; the qf offensive's own line — settled-positive levels (v770), no rank-6 representation lift (v771), no fixed-d object at a moving spectral edge (v772: avoided crossing 0.0039, widening entry cadence), cell cocycle domain-only (v773: structure without limit). What survives is typed as theorem-shaped facts: the exact anti-alias theorem (v760), the unconditional paired Abel bound (v761), the canonical dense family (v762), the Kato bundle frame and the settled coupling levels (v770), the Herglotz-certified exact Feshbach reduction (v772), and the domain-preserving Möbius/Redheffer cell cocycle through mode entries (v773). No new variants; the ten-item stop-list stays binding. The handover: PRIME.Z1.OPERATOR.01 stays OPEN [O] and is SHARPENED — construct a self-adjoint geometric bulk operator with a canonical finite-dimensional boundary/threshold structure whose Weyl M-function delivers the qf block and whose relative trace formula reproduces the full Weil formula, constrained by the measured mode-entry cadence (888/992/1108/1276, ΔX widening 1.625 → 2.625, avoided crossing 0.0039), the ram-odd contact direction (cos 0.997), the settled coupling levels (R2 0.225–0.358, R1 0.008–0.079), and the cell-ordered domain-preserving prime transport. Kill criteria stay active (zeros or an RH-equivalent norm assumption = renaming; cadence/level contradictions = dead on arrival). 2026-08-05, executed: the sharpened contract's first execution is the v780 trilogy (PRIME.Z1.COMPACTNESS.01) — the N2 GNS/Jacobi family carries the ram-odd contact (cos up to 0.9971), edge collisions at the source depth and settled couplings natively but NOT the widening cadence (its edge census is regular quadrature filling); the finite boundary triple is exactly Herglotz through all typed transitions but dies as a whitened K = M/2 import (the Gram near-kernel packets are delocalized, cell-mass exactly 0.500 beyond the half-window); with the raw μ-weighted import the variable-edge Herglotz family is bounded (0.936) and equicontinuous (0.807) with summable ~rank-one entry poles at the arithmetic thresholds (c_mass 0.032 ≪ 1) while the moment functionals do not settle (osc 22.1). The measured unification: PRIME.Z1.OPERATOR.01 and PRIME.KMS.INDUCTIVE_STATE.02 share their compactness theorem (carried — Helly/Montel at finite level) and share ONE remaining obstruction: state selection = import-faithful boundary coupling; the merged target is named Z1-COMPACTNESS; both contract rows stay, cross-referenced. The exact cell-cocycle core of the closed Gram route is now also machine-checked in Lean (CellCocycle.lean, 18 declarations — including the bounded-monotone convergence theorem that names the missing uniform Loewner bound precisely). 2026-08-05 (round 20): the positive-protocol round registers PRIME.POSITIVE_DESCENT.01 OPEN [O] on top of the measured v791 facts — the packet GNS state on N[C2] ⊗ N[F2⁴] ⊗ N[μ4] is manifestly positive in exact rationals (the naive linear pushforward is NOT a state: signedness is observer projection), and the GL1 sign sector is bit-identical to the deployed Weil window and its UNIQUE PSD sector of 24 (the breaking tensor factor is the continuum/pole leg, not the registers). The contract demands three objects: (1) sector-adapted continua (the twisted-channel explicit formulas; the f₈-sector continuum is the finite-level falsifier), (2) GL1-sector PSD persistence in the Z1-COMPACTNESS frame — Weil positivity retyped as sector compression of a manifestly positive object, cross-referenced both ways with PRIME.Z1.COMPACTNESS.01 — and (3) the carrier intertwiner (at registration the one non-CP-trivial step). Stop conditions: no fixed-d variants, no re-gating of the closed diagonal-Gram objects; demand (2) failing at any finite depth = DESCENT-DEAD. 2026-08-06 (round 21): all three demanded objects are DELIVERED at finite level — (1) the sector continua exist and are ONE functor (v793: the f₈/χ₄/twist sectors PSD with their own Γ_R-rule continua; the twist conductor 16 by Atkin–Li + the Fricke ward; the conductor datum load-bearing at exactly ln 2), (2) the limit object is identified exactly (v794: the per-sector positivity floor on V_∞ = the Z1-COMPACTNESS demand sector-decorated, anchor 3.882e−6 reproduced; measured trend: no crossing, GL1/f₈/twist power-law falling, χ₄ saturating at ~1.5e−6 — the first measured sector floor), and (3) the carrier intertwiner EXISTS in Stinespring form (v801: Φ = V*πV from the 105 Kraus legs, Choi exact-rational, all covariances exact; the four automorphic channels of one CP map land on the deployed GL1 Weil window at 6.0e−16 and the Γ_R-rule windows; the F1 failure retyped as a negative Choi eigenvalue). The contract stays OPEN for the remaining analytic core: the per-sector positivity floor (GRH-type, unproven) plus the new PRIME.CP.INTERTWINER.01 demands D1–D3 (X-compatible dilation family; normality on the Z1-COMPACTNESS limit object; the limit identification with the critical-line Weil functional — which CONTAINS RH and is not claimed). Also registered 2026-08-06: SEAM.CODE.TYPEII.01 (the boundary universe premise becomes three physical axioms), SEAM.CLIFFORD.MODULAR_S.01 (the metaplectic S-lift; R2 solved, R3 named), CURVE.CODE.OUTERSPIN.01 (decided CANONICAL), GNET.MARTINGALE.LIMIT.01 (limit hypotheses measured; steps 5–7 typed). 2026-08-06 (round 22): eleven further registrations and four dated updates — E8.RAMIFIED.JETCODE.01 [E] (+ E8.AFFINE.NSR.01: the jet-code normal form, non-splitness = the no-origin obstruction; the affine NS/R reconstruction sharpens the ARF.BOUNDARY.CODE.01 attack surface, R1′ unchanged), PRIME.CARRIER.GRAY.01 (the intertwiner’s register chart: deck-covariant with trivial μ₄-cocycle, GL1 channel re-lands on the Weil window at 6.0e−16; demands D1–D3 typed), E8.SYNDROME.ALGEBRA.01 (DEAD as frozen; successor criterion named), HECKE.LOCAL.CLIFFORD.01 (the analytic activation ordering DEAD; positive side-result: χ₈/χ₋₈ complete the Γ_R conductor-rule map over the full mod-8 dual group — noted on PRIME.SECTOR_CONTINUA.01), PRIME.LORENTZ.SPINOR.01 (the spinor reveal: strict α-monotonicity, Kendall 1.000; the 1D monotonicity candidate named), CARRIER.PETERSEN.RADIAL.01 [E/H] (+ TRANSPORT.SIXTHROOT.01: the spectrum is frozen, the basis is not — the named open), CURVE.CODE.DOILY.01 (the (2/3)⁶ six-step target named), CARRIER.CUTCODE.01 [E] (+ CARRIER.MOMENT.INCIDENCE.01: the 210 decorative per the frozen rule), PRIME.KRAUS.DOILY.01 (protocol-grade: the 105 legs a complete context protocol, [B₄₅, B₆₀] = 0 exactly; the σ-invariant-spread falsifier named), FLAVOR.GRAPH.FILTRATION.01 (order-exact budgets, no entry reconstruction — typed fingerprint), and P1.INDEX.KMS.01 registered OPEN [O]: I·β·c₃ = 4·2π·1/(8π) = 1 exact with the Jones index c₃-free and β = 2π independently measured — the identity EXPLAINS the P1 axiom, it does not derive it; the one open bridge is the even modular-response normalization over the I deck sectors (kill: any asymmetric sector offset). Dated updates on ARF.BOUNDARY.CODE.01, PRIME.CP.INTERTWINER.01 (the Gray chart and the Kraus protocol; D1–D3 unchanged), PRIME.SECTOR_CONTINUA.01 and E8.ONEOBJECT.01 (the null-selector addendum). 2026-08-06, round 23: the selection problem of the unified compactness contract is finite-level SOLVED — PRIME.MOSCO.SELECTION.01 registered (Mosco form convergence + Friedrichs minimality on the v762 dense core; moment oscillation 22.08 vs Friedrichs resolvents 0.0004 on identical rungs, cofinal-unique 2.5e−05; the import diagnosis completed at form level — nothing whitened at the core; v816); the positive-descent uniqueness becomes one abstract theorem — TFPT.POSITIVE_DESCENT.MASTER.01 registered (kernel-checked Lean core; both instances measured: G_net 0.267/doubling, prime packet state defects 0.701/doubling ≈ 2^−1/2 with mh₂(p) = −1/15 exact; positivity a SEPARATE hypothesis by control K4; v817); and the sector floor reduces to ONE ratio inequality — PRIME.FLOOR.RATIO.01 registered OPEN [O]: ρ(X) = τ/τ_pnt > 0 with the measured h^−3/2 envelope (constant ≈ 4.85, non-decaying), the direction owned by the density rotation law (symbolic, 100% staircase sign-match), the capture angle-certified frame geometry (cos θ 0.990, scramble-robust), the amplifier carried by the smallest prime powers; kill = the envelope failing at depth or the capture angle collapsing; NO positivity theorem, promotion fenced (v818). Also registered: PRIME.AORB.REFINEMENT.01 (the Kraus falsifier pair decided: spreads σ-broken but family-stable, [E,K] = 0 extends to the 600-dim register, the 39-dim nonabelian commutant closure; v815 — the PRIME.KRAUS.DOILY.01 falsifier retired), K5.SIXSTEP.TRANSPORT.01 (clock-only + the T₁₀ proposal; the TRANSPORT.SIXTHROOT basis-freeze question ANSWERED bit-exactly: T_v221 = B⁶, dated correction on the v808 row), PRIME.PACKET.RM14.01 (RM(1,4)*/CSS [[15,1,3]], Lean companion), PRIME.KRAUS.RM24.01 (+ PLANEFRAMES: σ₃(3) = 28 and a₃ = −4 as plane counts), PRIME.VACUUM35.01 (the E₇ completion 112+21 = 133 as a matrix identity), and the vacuum-route CLOSURE row PRIME.CONTINUUM.UNSHORTEN.01 (+ VACUUM.DILATION: both transcriptions dead, the c* = (2/21)λ_pencil fence quantified, deficits ×3e7/×2e2 — the continuum's completion role exhausted inside T_dep). 2026-08-06, round 24: the floor contract is NARROWED — PRIME.FLOOR.LAGRANGE.01 registered (the sector floor det Â₂ = λτ as an EXACT machine-verified sum of squares over zero+pole rank-one carriers, Lagrange identity with wards ≤ 1.4e−9 on all 14 rungs; the pole the universal non-collinear leg, the moving zero leg on the alias comb; the fixed pair (pole × γ₁) certified strictly positive on 14/14 rungs with the budget tightened a median 9.8 orders by the psd-remainder monotonicity chain; share growing h^{+1.06}; v823) and PRIME.FLOOR.SKELETON.01 registered (the three-piece uniform certified lower-bound skeleton: the analytic fixed-pair limit X_∞(α) = 16απ²·sin(αγ₁)·sinh(α/2)·[bracket] with explicit h₀(α) ≤ 500; the certified top-100 family exhaustion 0.93–0.97 of the floor; the deep tail closed at citation grade for ALL h at the fixed verified horizon T_ver = 3e12 via the product-sup envelope + Abel/RvM explicit constants — growth law h-free (+1.98 → +0.13), validity horizon α* ≈ 11.2; v824). The dated PRIME.FLOOR.RATIO.01 contract-text update states what is closed (the deployed-battery skeleton at citation grade) and what remains (α > α*, the family bound at the sin-nodes, the product-sup Lipschitz certificate, and the V_∞ positivity itself — battery-relative, α-bounded, necessary-side). 2026-08-07, round 25: the contract is DEPTH-HARDENED — its own kill gates were played at full sieve depth X = 18.375–25.5 (comb caps to 1.2e11; the deep uniform-grid frames decouple depth from dimension) and SURVIVED with margins ×5.76–×8.92 growing (min cos²θ = 0.849; the h-law wins; the single pair collapses 40× → 673× while the certified family carries 0.977–0.981 of the floor; v829), and the α* ≈ 11 horizon is REMOVED as a float-convention artifact: under the explicit Higham-linear budget (7×–171× tighter; the deployed v818 convention stays frozen, the linear budget is convention for NEW modules only) the citation-grade family gate closes 6/6 to α = 12.75, and the envelope is now certified-explicit — ρ ≥ ρ_certfam ≥ 4.335·h^{−3/2} on 73/73 battery points, phases cannot conspire (dip floor 0.170) — with the remaining proof blocker NAMED: alias phase correlations, random-phase h^{−1} vs the measured h^{−2.5} tower (v830). Also registered: PRIME.DETECTOR.WINDOW.01 [O], the comb-native window detector of the exclusion strand (v825–v828: certified exclusion ladder to X = 24.81 with Cholesky/Higham + witness-Rayleigh certificates; the hash-preregistered battery v2 uncensors the exclusion floor to Ξ = 0.0816 at slope −1.39; the locator validated OUT-OF-SAMPLE on the disjoint window [60, 120] at 83% detection / 0% false positives / precision 0.086; the capstone census 21 + 4 typed misses = 25 = cache = rounded RvM main term at X = 24.8125, deepest certified rung X = 25.5) — open: the depth-to-width law as theorem, the completeness mechanism, and any reach beyond the Nyquist window (explicitly NOT promised); mandatory typing everywhere: strictly weaker than classical (Turing) verification on every axis. Still [O]; kill criteria unchanged; promotion fenced. 2026-08-07, round 26: the analytic-envelope route of the floor contract is CLOSED at its typed circularity boundary — the round-25 blocker resolves into the boundary itself (v831, ALIAS-CORRELATION-PAIRCORR, the seven preregistered-honest premise-overturning FAILs pattern-gated): the correlation-corrected alias second moment is exact and sympy-proven (τ = (S₂ − S_c)/2 − S_s²/(4P₀) + O(P₀⁻²)), the premise 'the phases carry the gap' is OVERTURNED (the amplitudes carry it: −2.505 = −3.172 + 0.668 exactly; q = S_c/S₂ sign-changing), and the exact Guinand split puts the coherent sum in the prime-comb fluctuation at 0.01× the Poisson square-root scale (smooth −994 / fluctuation +995, cancelling; the comb scramble explodes it 10⁶×) — by Guinand the comb's self-cancellation IS the zero-side floor statement itself, so the required control is even deeper than Montgomery-type pair-correlation input. NO further analytic-envelope variants (stop-list entry per house discipline); the demand moves to the NEW bridge contract PRIME.FLOOR.PAIRCORR.01 [O] — the floor ↔ pair-correlation bridge (forward: an unconditional variance-type bound with its pair-correlation-grade entry point declared, no hidden circularity; backward: instrument calibration only; kill: fluctuation share < 0.6 or scale ratio > 3; the proving direction contains pair-correlation-grade arithmetic, fenced). A boundary, NOT a theorem. NO marker moves; the kills preregistered adjudications. No RH claim. 2026-08-07, round 27: both corner-era routes at that wall are DECIDED — PRIME.CORNER.CHARACTER.01 / PRIME.HJELMSLEV.CPTOWER.01 registered (v835, CORNER-IDENTITY-SYMBOLIC + HJELMSLEV-STRUCTURE-ONLY: the character-corner identity holds as polynomial algebra in free event weights with ĉ_j = −1 exact for all 136 events, consuming only the glue identity Σ Θ_m = 240σ₃; the chain-ring ladder Z[i]/(1+i)^m, m = 1..5, carries a strictly projective CP tower at certified cb defect identically zero with the identity level-exact — but identity and state corner are comb-blind and the level-m motion is the pure register-dilution law 16^(1−m): the wall RELOCATES into the identification step and stays PRIME.FLOOR.PAIRCORR.01; register-only tower lifts stop-listed, the one live door position-dependent Kraus data on the level-m flags — register-side dressings provably cannot carry it, POSITION-KRAUS-TRADEOFF 13/13 probe-level) and PRIME.COMMUTANT.SOS.01 registered CLOSED at registration (v836, COMMUTANT-SOS-INFEASIBLE: the degree-2 SOS ansatz over the canonical five-dim abelian subalgebra of the 39-dim commutant collapses exactly to a rational LP whose unique feasible point is the trivial diagonal rewriting — no cross-sector positive transfer; the rank-3 det form has signature (1,2), forced G = diag(1,−1,−1) with the rational dual certificate q(0,1,0) = −1 < 0, q-negative directions achievable even on the nonneg cone; FENCE-HIT on the positivity branch — the nontrivial version is pair-correlation substance; a second stop-list entry). The bridge contract's demands, kill and close conditions are unchanged. No RH claim. 2026-08-07, round 28: the wall gets its full coordinate system — the corner route's perimeter CLOSES as measured compression-class theorems (v837, DOORS-CLOSED + LEVEL2-CLOSED: the 90-cell class map has no identity∧visibility∧placement cell, all 128 characters read position-blind carrier modes, the quantifier extends to tower levels m ≤ 3; v838, EXPECTATION-CLOSED + POSITION-CARRIER-TRADEOFF: all 5276 subgroup expectations, the full pinching and Stinespring compressions obey the dichotomy, and position-dependent carriers are EXTREMALLY PINNED — ĉ_GL1 = −1 locks the entire C₂ mass, so identity-true carriers read zero on every self-consistent comb; four stop-list entries PRIME.CORNER.OPENDOORS.01 / LEVEL2.01 / EXPECTATION.01 / PRIME.CARRIER.POSITION.01; the structural half kernel-checked in SectorPositiveDescent.lean with IdentificationPositivity the single named hypothesis); the zero side is QUANTIFIED (v839, BRIDGE-FULLY-BEYOND + GUE-SATURATING: the demand in Montgomery F(α)-form with every supply row carrying its conditionality tag — the named minimal missing input is an unconditional F(α, T) ≤ 0.33–1.7 out to α ≈ 3; the demand/GUE ratio saturates at R_∞ = 1.11 and the certified ladder doubles as a calibrated form-factor instrument, F̂ = 0.44 ± 0.14; v840, SATURATION-STRUCTURAL + LOOP-SHORT: every Guinand-admissible variant lands at the plateau with the tight band pinned in the unfolded coordinate, and the bootstrap loop is short — g = 1/(k²R²c_sup), even ideal supply gives 0.655 < 1: the wall's self-conservation IS the saturation); and the route REOPENS with the relational input — PRIME.RELATION.MULT.01 [O] registered (v841, RELATION-CARRIER-EXISTS + EXCESS-NONNEGATIVE: the identification carrier exists — all four gates including the self-consistency null; Λ = μ∗log exact, the h = 2 Epstein x² + 5y² separates at 200.0 with Selberg-class-correct blindness; the identified corner's excess positive on all 67 rungs — the sharpest wall form τ_X = λ_min(structural) + EXCESS) and PRIME.RELATION.SKELETON.01 [O] registered (v842, SKELETON-CERTIFIED: strictly positive certified interval enclosures of τ_X on all 67/67 rungs, the h = 2 fake certified-negative, the horizon α* ≈ 9.1 far beyond the ladder end) — what remains is the INFINITE QUANTIFIER over strictly-positive certified enclosures, sharpened demand: a UNIFORM lower bound on the excess margin. PRIME.FLOOR.PAIRCORR.01 [O] unchanged. No RH claim. 2026-08-07, round 29 (the compact closing round): the margin becomes a DOUBLY-DERIVED typed law — PRIME.MARGIN.LAW.01 registered with the Lean layer FORM.PRIME.EXCESS.SKELETON.01 [F] (v843, MARGIN-RECURSES-THE-WALL, 10 checks with the ONE preregistered-honest FAIL kept and pattern-gated — fit-free h-exponent median −1.341 vs the frozen bar edge −1.35, not refit): τ = e₁(α)·h^(−3/2)·τ_pnt(α) with the certified envelope constant reproduced EXACTLY across two independent coordinate systems (e₁ ∈ [4.855, 24.209] on all 67 rungs, min ≥ 4.335 — the consistency ward on PRIME.FLOOR.RATIO.01's envelope); the tower gives scale, not recursion (ratio defects non-decaying); the excess is a growing cancellation — the wall self-similar at cell level (no per-prime positive control; same-class margin-law re-attacks stop-listed); the compiler connection null (0/96). And the finite-table limit becomes a KERNEL-CHECKED THEOREM: TfptCarrier/ExcessSkeleton.lean proves pointwise_pos_not_uniform (per-rung positivity at every rung does not yield a uniform bound) and the bridge theorem excess_floor consumes UniformMarginBound as the single named hypothesis — the quantifier now sits on the ONE scalar series e₁ ≥ 4.335, and the demanded object is a UNIFORM lower bound on e₁ with its arithmetic entry point declared. Dated closing notes on PRIME.RELATION.SKELETON.01 and PRIME.FLOOR.RATIO.01. And 2026-08-07, round 30 (the consolidation of the v5.4 strategy campaign, v844–v848): the three candidate proof architectures are DECIDED — PRIME.SCHUR.GRAM.01 + PRIME.SPECTRAL.MOTHER.01 (v846, SCHUR-INDEFINITE + SPECTRAL-TV-UNIVERSAL: the manifestly positive relational Gram exists but the corner identity fails in trace AND form by exactly the forced Cauchy–Schwarz diagonal price, 3.1e4–4.5e4 × τ at the density-anchored floor — and the price is GEOMETRY-INDEPENDENT: the unitary spectral mother (J² = I; U_d·U_m = U_dm exact) gains 20–33× at symbol grade but never at Gram grade; harvesting interference is Fejér–Riesz of the total symbol, i.e. the positivity itself), and PRIME.WEDGE.LAGRANGE.01 + PRIME.CELLCONE.TRANSPORT.01 (v847, WEDGE-PARTIAL + CONE-BROKEN + RAY-EDGE-CONFIRMED, the two frozen-honest FAILS kept and pattern-gated: the sign-register lift exists as exact algebra where the naive signed Lagrange provably cannot, but the frame-uniform law fails at ~15% vs the 4.4e−5 floor need — the commutant uniformity wall transported; both completed-cell groupings exit the Lorentz cone on 67/67 rungs at the n = 2 cell with the ray cascade to (5, −3, 4) confirmed and the inverted Epstein signature — the arithmetic sits IN the violations). And the continuum extraction is COMPLETE — PRIME.EXTRACTION.CHAIN.01 [O] registered (v848, EXTRACTION-CHAIN-COMPLETE, 19/19; hypothesis (H) never evaluated): the implication chain cofinal finite positivity ⇒ Weil positivity ⇒ (Weil's criterion) the target is theorem-grade modulo named citations (Weil 1952, Bombieri 2000, Suzuki arXiv:2606.09096, Iwaniec–Kowalski Thm 5.12), with the quantifier reduction: no Mosco compactness, no uniform δ, no diagonal argument in the implication — the pure-box class carries the EXACT Weil value at every finite level, and the arithmetic wall is EXACTLY hypothesis (H) and nothing else. Plus the finite-compiler compressions recorded (MESSAGE.LADDER.01, DOILY.PASCAL.RANK.01, NORMALFORM.CFIN.01 — v844/v845). Dated round-30 closing note on PRIME.RELATION.SKELETON.01 (the extended stop list: diagonal relational mothers; constant wedge laws; unrenormalized small-n cell transports). 2026-08-07, round 31 (the invariance atlas, v849–v855): the wall is proven INVARIANT across four axes — COMPRESSIONS (the nuclear-norm TAX THEOREM closes the whole positive-dilation class with fixed comb coupling: tr P + tr Q ≥ 2‖R‖_* exact with zero-duality-gap certificates on every anchor, BASIS-INVARIANT — the v846 geometry-independence now a corollary; the exact optimum already ≥ 4057.6×τ on every rung, diverging ~h^0.24 against h^−3/2; the measured Schur designs only 13.7–20.4× above it — optimality could not have saved them; and the finite-dimensional spectral-flow index is a REFORMULATION of the endpoint pivot signs: the density endpoint is NOT PSD (n₋ = 5..12, the premise corrected by measurement), all 634 crossings upward and endpoint-determined, the velocity test at ratio 1.00 — distance-to-crossing IS the metric margin divided by the flow velocity — v850, PRIME.PSD.COMPLETION.TAX.01), GEOMETRIES (basis invariance), CRITERIA (Weil = Li = Nyman–Beurling: λ_n > 0 to n = 20 computed with NO zeros, d_N² exact to N = 64, the BD wall constant = 2λ₁ at 4.9e−17, the NB span IS the spectral-mother geometry term by term — one mother {e^v}, integer dilation shifts, Möbius-register weights, the 1/x mirror = the deployed J — yet the Li transfer fails by CONE GEOMETRY, residual 60.6% vs the 5% bar: no coordinate system holds hidden supply) and INPUT CLASSES (statistics = sieve: the demand rewritten EXACTLY in Selberg-hierarchy coordinates, zero bookkeeping loss, and audited against on-range-verified elementary constants — the α ∈ 1–2 band reached in SCOPE (window-free), ZERO coverage in GRADE, best factor 205×; the demand at 99–100% of τ_pnt exceeds the factor-2 gate at truth on every rung — unclosable by ANY upper-bound class; the named sieve object dChain₂, the bilinear chain fluctuation — v855, PRIME.CRITERIA.ATLAS.01 + PRIME.SUPPLY.SELBERG.01). The cone violations resolve into the GRADED KERNEL LAW (the strict census wanders, P₀ ~ X^1.03 at max 244333 vs cap 100, but the depth-10⁻² G1 kernel is n ≤ 73 on ALL 67 rungs, collapsing to {2,3}; the skin depth D(X) = 0.754·X^−0.548 at R² 0.99 with verified X₀(ε) — vanishing-depth skin, not kernel growth; PRIME.CELLCONE.GRADEDKERNEL.01 [O] registered: it bounds DEPTH, not SIGN; the corner cluster expansion closes — exact resummation, position-geometric weights; the causal tube field transports clean, 0/355199, but is self-calibrating — FIELD-STRUCTURAL-ONLY, the four must-break controls kept as frozen FAILS — v851, PRIME.CELLCONE.KERNELFIELD.01 + PRIME.CLUSTER.MULT.01), the relation strand becomes operator-level and geometric (𝓛 = −M[D,Z] = −[D, log Z] = T(Λ) EXACT three ways with log Z rational and the BCH series truncating; the four-comb discipline at operator level — the h = 2 Epstein leak at [6, 14, 21, …] exact, first unramified site 21 = 3×7, REPAIRED by the class average a_A + a_B = 1∗χ₋₂₀; the ideal-level Dedekind Λ_K; the carrier bridge — the deployed μ-pairing IS the first row of 𝓛; typed honestly as classical incidence algebra — v853, PRIME.RELATION.MANGOLDT.01; and multiplicativity IS flatness at machine zero with the Epstein curvature localized at the class-group products and the F₂ Arf-lift obstruction PROVEN — but gate 4 fails typed: the window form is 0-chain-supported, coboundary sensitivity ~3e4, NOT a function of the cohomology class; the Pfaffian has no anchor-independent normalizer — v854, PRIME.RELATION.HODGE.01), and the minimal hypothesis is KERNEL-CHECKED — FORM.PRIME.COFINAL.WEIL.01 [F] registered: TfptCarrier/CofinalWeil.lean (11 declarations, 3415 jobs, axioms clean) proves the ε/2 implication with NO diagonal argument (one PSD certificate per rung covers the whole dense family) and the strict hierarchy uniform ⊊ pointwise ⊊ cofinal (witnesses 1/(m+1) and ±1 on the even ladder) — UniformMarginBound FORMALLY DEMOTED to an over-strong sufficient lemma; the load-bearing chain of PRIME.EXTRACTION.CHAIN.01 consumes EXACTLY (H_cof), cofinal PSD on one pre-fixed preregistration-shaped ladder. THE ONE OBJECT IN FOUR LANGUAGES: the uniform e₁ envelope bound = the form-factor band α ∈ 1–2 = the bilinear chain fluctuation dChain₂ = the comb block's soft direction (the minimizer tracking law at 0.0056 rad; the drift real per the Bonferroni demonstration — no closed-form identification claimed, −4/π typed a coincidence). Dated round-31 notes on PRIME.RELATION.SKELETON.01 (the extended stop list: positive-dilation completions with fixed comb coupling in ANY basis; finite-dimensional index/spectral-flow reformulations; 2-dim corner cluster expansions; elementary upper-bound supply rows against the factor-2 gate), PRIME.FLOOR.PAIRCORR.01 (the pair-type object = dChain₂ = the comb-soft direction), FORM.PRIME.EXCESS.SKELETON.01 (the demotion) and PRIME.EXTRACTION.CHAIN.01 (step 2 kernel-checked; (H) formalized as (H_cof)). Round 32 (2026-08-08, v856–v860) extends the record with the GRADE LAW: two new formal registrations — FORM.PRIME.GRADE.NO_GO.01 [F] (TfptCarrier/GradeNoGo.lean, 10 theorems, axioms clean: a 1-homogeneous target can never be matched exactly by a 2-homogeneous Gram square — the two-scalar ray evaluation, a CLASS closure; the affine trilemma with the exact PSD tax, the background killed too; and the elevator lemma tangent_psd_on_kernel_null — RATES, not amplitudes, the only licensed grade-1 mechanism) and FORM.PRIME.COFINAL_CURRENT.01 [F] (TfptCarrier/CofinalCurrent.lean, 7 theorems, axioms clean: ConnectedTail + PositiveHeadCell + PhaseRecurrence ⇒ (H_cof), composed through the minimal H theorem to Weil nonnegativity — hypothesis 2 measured EMPTY at the deployed frame: a continuation contract, not a discharge) — plus the round-32 E8 audit compressions record (the −1/15 character theorem to 16500; the G31 clock alphabet normal form with the 607-group kill scan; the winding quadratic with the triple lock s = 6) and the dated round-32 notes on PRIME.RELATION.SKELETON.01 (the grade law as the unifying diagnosis — exchange rate 10⁴–10⁵ across the four graveyard instances; the Lévy/conditional-positivity elevator class closed on the deployed sides, the arch digamma band ending at τ* = 6.27; the extended stop list: finite-head phase rescues, amplitude-Gram constructions without grade accounting, Lévy elevators on the deployed sides) and PRIME.FLOOR.PAIRCORR.01 (the pair-type object now constructible zero-free — the connected covariance EVADES the nuclear tax, relapse ratio ≈ 0.3, and is typed an instrument, with the grade gap 2.5–4.1e5 × τ the reason it is not a floor certificate). Round 33 (2026-08-08, v861–v868) gives the wall its OPERATOR FORM: two new registrations — FORM.PRIME.KREIN.DEFECT.01 [F] (TfptCarrier/KreinDefect.lean, 10 theorems, axioms clean: the defect representation Q = ‖B₊f‖² − ‖B₋f‖², contraction ⇔ PSD with the full-rank Douglas converse, SourceContractor the NAMED hypothesis with the circularity warning typed, and krein_cofinal_weil composing contractors on a cofinal ladder to Weil nonnegativity) and PRIME.KREIN.CONTRACTOR.01 [O] (the sharpest demand so far: ONE phase-aware, target-free bound certifying that the explicit closed-form source contractor C = W₋FG₊⁻¹FᴴW₊ — the v866 factorization, warded at 1.4e−14 incl. blind holdouts, with certified defect transfer — is a contraction, equivalently G₋ ⪯ G₊, equivalently K ⪰ 0; with three PROOFS about the tool space as the registration's teeth: no absolute-value bound can succeed — the Perron value ρ(|C|) = 2.4–3.1 > 1 everywhere is the infimum over all absolute Schur tests; no source word of any length reaches C — the monomial closure theorem, miss ≥ 0.874; and no fixed-depth quadrature family certifies uniformly — the depth law m* ~ √cond(G) is intrinsic, no source preconditioner waives it) — plus the round-33 canonicity record (the 210 lattice pinned uniquely by the Euler determinants; the chirality Z₂ proven gauge) and the dated round-33 notes on PRIME.RELATION.SKELETON.01 (the Krein coordinates; the rank-one defect; the extended stop list: source-word searches at all lengths, absolute-value kernel bounds, fixed-depth quadrature without conditioning control, chirality deciders via quadratic readouts) and PRIME.FLOOR.PAIRCORR.01 (the floor demand in Krein coordinates: the certificate must control the PHASES of the pair kernel, not its magnitudes). Round 34 (2026-08-08, v869–v872) names the kernel and preregisters the next test: the contractor's reproducing kernel K₊ is EXACTLY the Christoffel–Darboux kernel of an explicit source measure in x = 2cos(Dτ) (rank-2 displacement collapse with a 10¹³ gap on all rungs incl. blind holdouts; firewalled chain-only reconstruction at ~1e−13; honest boundary typed pre-run: the collapse is window geometry — the controls collapse too — and the arithmetic lives in the source Jacobi chain and the Christoffel weights, O(1) different for the fakes), the defect splits EXACTLY as I − C*C = T₁ + T₂ (the indefinite cross-measure Jacobi geometry plus the PSD Christoffel damping, 1e−12 on all 42 rungs) with the exact global minimizer equal to the soft direction and the wall as two explicit source numbers (kz 9: −0.0328 + 0.0330 = 1.68e−4 = τ; s = κτ over the certified bulk floor) — PRIME.CD.DAMPING.COMPENSATION.01 — while the classical escapes close with typed residues and stop-list entries (Uvarov/Christoffel/Geronimus dead at x_pole = 2cosh(D/2), best: small-negative-mass Geronimus at 3.5–8.1% with no λ(D) law; finite-rank cross-defect corrections dead at Pearson +0.996 linear rank growth; μ₄-offset Clark kernels dead by the equal-phase law), and the Prüfer/Cotlar route is committed as the FROZEN preregistration PRIME.PRUEFER.COMPENSATION.01 (16 fixed phase cells, Cotlar–Stein decision rules and all kill criteria frozen before any deployed-data run, deep holdouts kz 90/116/142/177/243, unfreeze-flag lock; SPEC SHA 4621b899…7440811, FILE SHA 93208a1b…4825d9fd, committed byte-exact and NOT run — dated round-34 notes on the PRIME.KREIN.CONTRACTOR.01 and PRIME.FLOOR.PAIRCORR.01 blocks). Round 35 (2026-08-08, v873) EXECUTES that preregistration — the program's first fully preregistered uniformity test, and it returns COTLAR-GROWING / route dead BY ITS OWN FROZEN RULES: the provenance chain is machine-warded (committed pre-execution in 526ca3eb; the unfreeze flag with its committed audit line; exactly two documented MECHANICAL fixes — the h ≤ 900 battery filter the spec's own text mandates, and the overflow renormalization validated at ≤ 6.6e−4 against a 60-digit mpmath reference — with the FROZEN_SPEC literal SHA byte-identical throughout; executed FILE SHA 15d35b26…5ffb4cc), the predeclared danger geometry is REAL (the frozen cells capture 0.98/0.61/0.94/0.85/0.81 of λ_min(T₁), source-only, without the soft eigenvector) but the local compensation fails (Σε_r = 6.88–10.08), the envelope does not decay (Spearman −0.17..0.00 vs ≤ −0.8, bimodal exactly at the predeclared π-resonance cells d = 7–8), the battery is flat (S_U 5.55–6.30) while the frozen deep holdouts explode (kz 142: S_U 32.07/S_C 58.78; slopes 0.209/0.408 ≥ 0.20, both channels GROWING), the contrast bars pass (Epstein 3927%/224×, scramble 314462%/1.26e6), kills 2 + 5 fire, and RUN 3 is correctly withheld. The blockwise Cotlar–Stein / phase-cell class on Prüfer phases is CLOSED and stop-listed; the surviving demand narrows to a NON-STATIONARY phase bound on the explicit kernel with the π-resonance as the known critical structure and the measured α-not-h growth law as the typed constraint (the explosion tracks kz-depth, not window size: kz 90/116 at h = 1430/1433 stay in band while kz 177 at smaller h = 1219 explodes) — dated round-35 closing note on the PRIME.KREIN.CONTRACTOR.01 block. Preregistration + frozen bars + committed hashes is the standard the program now holds itself to. No RH claim. Round 36 (2026-08-08, v876–v878) CORRECTS it, dated: the deep-holdout data was comb-truncated (ATOM_MAX artifact; complete-comb floors strictly positive — v877, DEEP-ALPHA-ARTIFACT), and under the identically frozen v1 bars the complete-comb sums are BOUNDED (COTLAR-BOUNDED-V2; run 3 unlocked and passed) — the stop-list entry is amended, the α-not-h law retired, and the route reopens as PRIME.PRUEFER.COMPENSATION.02 while v873's booking stands as the record of the v1 execution as measured. The surviving analytic target is registered in embedding coordinates: PRIME.CARLESON.PRIME.01 [O] — the Carleson embedding of the negative arm measure into the positive one at degree h−1 with constant 1 − τ_h, machine-exact reduction (v876). The same round records the three compiler theorems (feedback normal form, winding decoder, global shell theorem; Lean mirrors FlavorFeedback.lean + GaussianShells.lean) and the ledger's first QA fix (FORM.QGEO.03 → FORM.QGEO.04, primary-key violation) with the new integrity guard GATE.LEDGER.01 (v878). No RH claim. Round 37 (2026-08-08/09, v879) CLOSES the partition chapter entirely — the compact closing round of the reopened route: the analytic core is SAVED (multiplication by cos θ is exactly tridiagonal on the odd frame with a single rank-2 boundary defect; the CD telescoping identity at 1.3e−13 on every rung incl. all five complete-comb holdouts; the derived pointwise bound carries the route's FIRST h-uniform source constants, C_int ∈ [1.232, 2.328] from h = 168 to 1445 — entrywise grade, with C_int itself discriminating 1.41/3.59/12.8), but the cell-envelope decay is CANCELLATION-CARRIED (provably not entrywise-derivable — the two frozen-honest FAILs kept and pattern-gated), no predeclared cell accounting reaches below 3.568 (bar 1), Σε_r = 6.9–12.9 is α-uniform on clean complete-comb data, and honest tight wave-packet frames on both natural phase spaces (‖B‖ = ‖C^G‖ exact; the Gabor envelope the first partition to show decay; discrimination 4.985 vs 128.7 vs 9006.6) leave diagonal mass ≤ 18% under ANY pairing with a growing Schur constant (4.985 → 9.222): the cancellation is ATOMICALLY GLOBAL — PRIME.PARTITION.CLOSURE.01, with the dated round-37 notes extending PRIME.CARLESON.PRIME.01 (the certificate must be NON-DECOMPOSITIONAL: eigen-enclosure / Loewner-order / passivity) and closing PRIME.PRUEFER.COMPENSATION.02 as a class (stop-listed: wave-packet/coherent-state partitions; entrywise bounds on the cell envelope); the surviving assets are the tridiagonal identity, the h-uniform derived constants, and their source-law persistence as h → ∞ (the named open object). No RH claim. Rounds 38/39 (2026-08-09, v881/v882) execute exactly that non-decompositional demand and give the wall its complete reduction chain plus its universal source law. Round 38 (v881), the exact operator geometry — four sides of ONE object: the review's literal rank-2 Pick target is REFUTED as stated and replaced by the exact structure, the rank-2 Jacobi displacement [J, Δ] = b_h(e_{h−1}rᵀ − r e_{h−1}ᵀ) with source-only generators (≤ 4.3e−14 on construction rungs AND blind holdouts; the scalar Herglotz carrier exists exactly; the Schur transfer λ_max = 1 − τ exact at 9.5e−13) (PRIME.CD.PICKDEFECT.01); the TESTING/GAUGE IDENTITY E = S(√ν̃ K_CD √ν̃)S — the wall operator is orthogonally equivalent to the plain Carleson Gram of the CD kernel (2.1e−12) with the CLASSICAL Carleson testing functional ν̃_m K_h(y_m, y_m) on the diagonal: the off-diagonal phases are PURE GAUGE, the arithmetic sits in the node-and-weight distribution of the two measures, and the testing margin falls as 1 − T_h ~ h^{−0.70} with the port numerator atom-carried (PRIME.CARLESON.TESTING.01); the PORT SCHUR REDUCTION, exact and non-decompositional — I − E ⪰ 0 ⟺ I − R ⪰ 0 AND I − D_P ⪰ 0 with Haynsworth inertia integer-exact on all rungs and both indefinite controls, and (1 − λ_max(D_P))/τ = 1.00 on ALL five rungs incl. blind holdouts: THE PORT IS THE WALL (13–54 nodes, ~15% of n; bulk margin 420–45000 × τ; cut-robust at 1.0000 ± 1e−4) (PRIME.PORT.SCHUR.01); and the dressed port operator is itself an IIKS-class integrable kernel — [Y, P] AND [Y, D_P] both rank 2 EXACT, the Schur dressing preserves the displacement structure, opening the discrete Riemann–Hilbert route (PRIME.PORT.INTEGRABLE.01). Round 39 (v882), the universal source law: under r = √(n/X) the weighted prime measure uniformizes to Lebesgue dr (Kolmogorov sup 0.0148 → 0.0005 over X = 1e4..1e7) and the last-log-unit edge mass → 1 − e^{−1/2} = 0.393469 (measured 0.3936) — the wall's ~39% port mass IS the classical PNT edge law, with universality typed (Epstein uniformizes too; the arithmetic lives in the fluctuations, scramble breaks hard) (PRIME.SQRT.UNIFORM.01); the port symbol is the Mellin–Cauchy kernel 1/(1 + 2iτ) (max deviation 0.0126 → 0.0004) and the deployed port numerators are predicted WITHOUT FIT by the continuum integral (rel deviation 0.375 → 0.029 with depth — the deviation IS the shrinking arithmetic fluctuation; the SMOOTH PNT model violates the floor at finite depth, so the prime DISCRETENESS is load-bearing) (PRIME.PORT.MELLIN.01); and the port numerators are the EXACT deployed-window prime sums (rel ≤ 1.5e−13 incl. controls) with the criticality budget CLOSED (+1.405 − 1.674 + 0.284 = +0.015 = d log T/d α): the testing criticality T → 1 is arithmetic growth exactly compensated by window geometry + Christoffel — the wall is an ERROR-TERM statement about prime partial sums at the port frequencies (PRIME.PORT.ATOMS.01). The HARDNESS is then decided by measurement (PRIME.ERRORTERM.SCALE.01, DEMAND-CURVE-MEASURED / RH-SCALE-EQUIVALENT): injecting the exact lag signature of an off-critical zero quadruple, ONE quadruple kills the floor on every cell and the kill localizes THROUGH THE PORT BLOCK (Haynsworth 0 bulk + 1 port); the critical amplitude obeys A* ~ √τ/δ² and in ENERGY units the demand curve lies on the τ law EXACTLY (ratios 1.00–1.10) — the wall margin IS injected perturbation energy at RH strength, NO unconditional slack: the round-38/39 reduction chain is an exact reformulation, not a shortcut (at threshold the wall detects energy, not coherence). Five new open contracts carry the demands: PRIME.PORT.LIMIT.01 [O] (a fixed-space limit theorem for the dressed port family; measured: Schur-compressed operator-norm convergence at slope −2.80, criticality approach from below, atom-at-edge class), PRIME.PORT.SCALAR.01 [O] (the wall as ONE scalar inequality σ_h ≥ 0 per rung with a phase-free windowed-prime leading term; σ ≡ 1/[(I−E)^{−1}]_{m*m*} exact at 6.2e−11; the one-sidedness is the demand and carries full RH weight), PRIME.PORT.COCYCLE.01 [O] (the fixed 12×12 port window carries the wall exactly on all 41 rungs; the closed-form limit is the demand), PRIME.CASE.SUMRULE.01 [O] (prove the Case C0/C1 sum rule for the deployed family ⇒ the unconditional testing bound T_h ≤ 1, the diagonal half of the wall; the coherent off-diagonal lift stays RH-hard), and PRIME.PORT.RIEMANNHILBERT.01 [O] (the discrete 2×2 IIKS Riemann–Hilbert problem of the dressed port family is WELL-POSED — resolvent closure verified at 1.2e−12; nonlinear steepest descent is the program, with the wall as the absence of a pole crossing at s = 1). Rounds 40/41 (2026-08-09, v883–v886) open the flow corridor: the determinant chain lands — sign τ_h = sign σ_h = the wall with τ_h := det(I−D_P), machine-exact at 4.8e−13 in log space — together with the PARAMETRIX DECISION (the Euler-product comb is GLOBALLY rigid: the prime-power lattice with smooth masses τ = −78..−1706 and even exact local PNT mass sums −78..−5537 are orders worse than the plain continuum against the true comb +1.7e−4..+6.7e−7, and the zone refinement kills BOTH ways — every smoothing-based parametrix is dead, small parameters live only in the flow/deformation direction); the FIRST RIGOROUS POSITIVITY STATEMENT of the program (v884): σ_h > 0 PROVEN on kz 9/12/13 by exact integer Bareiss/LDL Sylvester certificates on the Q = 10²⁰ grid (certified floors λ_min ≥ 3.327e−4; the Epstein control refused by the identical machinery at pivot index 10; proven MODULO the declared conservative transcendental-evaluation error model, with the ball-arithmetic closure and the 42-rung rollout the named follow-ups); and the flow/induction anatomy (v885): degree-2 Lax closure of the gauge-fixed IIKS generator flow (isomonodromy-compatible, a structural precondition — the arithmetic stays in the value), NO monotone one-prime induction in any insertion order (last sign crossing u*/U = 0.991–0.999; edge-first needs 100% of the atoms; the pure-Arch start catastrophically subcritical) — positivity is a property of the COMPLETE comb, and the conditioned flow coordinate is the named open object (PRIME.PORT.LAX2.01; since adjudicated LAX1-H-EXACT in round 225 — the true minimal degree in the closing direction is one, and the closing direction is h, not s; v955). Two new open contracts registered: PRIME.PORT.LEADING.SIGN.01 [O] and PRIME.PORT.TAIL.01 [O] (the head part delivered on three rungs by v884). Update 2026-08-24 (v955/v956, rounds 224–226 and 228–231): the PRIME.PORT.TAU.01 demand is EXECUTED at the finite-identity level (TAU-IIKS-EXACT — the wall determinant is the exact IIKS Fredholm tau function on the actual builders; the finite theorem set carved out as PRIME.PORT.TAU.FINITE.IIKS.01 [E], the sign question registered as PRIME.PORT.TAU.NOPOLE.COFINAL.01 [O], the umbrella stays [O] for the fully symbolic arbitrary-h statement); the signed-Toda dictionary τ = D_n(μ−ν)/D_n(μ) is exact with positivity WALL-EQUIVALENT; and the half-filling / free-moment geometry is registered as PRIME.FREEMOMENT.JFRACTION.01 [E] + PRIME.JACOBI.DUAL.REVERSAL.01 [E] (the h-free L-gauge midpoint connection) with the wall itself standing alone as PRIME.FREEMOMENT.POSITIVEPREFIX.01 [O]. No RH claim. Update 2026-08-24 (v958, rounds 244–253): the bordered-RHP / tau-readout theorem set is registered as PRIME.PORT.RHP.BORDERED.READOUT.01 [E] — the bordered Hankel end-object (bordered PSD = wall + budget) has an exact Riemann–Hilbert dictionary with the budget a CD-kernel functional of the terminal Y_n data alone; the border is a Schlesinger rank-1 insertion over a canonical 2x2 RHP with a one-dimensional budget cocycle (the irreducible-3x3 steepest-descent campaign dropped without replacement); the centering congruence, the σ° dictionary, the dual-norm identity and the tail-kernel compression are exact (dps 160 through the full depth); the three error-evaluation formulas and the contour R_1 are exact; and the fiber target is the exact augmented tau quotient D = τ^aug/τ with the pole layers classified (rank-1 border removable, D-layer essentially singular). The campaign continues as PRIME.PORT.RHP.FULLSOURCE.BASEFIBER.01 [O] at the post-round-255 measured state (OUTER-MODEL-FAILS; OFFDIAG-EXTENSIVE with the compactness inversion — scramble collapses to 2 eigendirections, MAIN needs 28–30; ORIENTATION-LOWDIM(1) — the base flip is a one-bit 0.2-decade selection event; measurement rounds 250/254/255 stay experiments-side). No RH claim. Update 2026-08-25 (v959, rounds 256–259): the coupled-tau / terminal-budget theorem set is registered as PRIME.PORT.RHP.COUPLEDTAU.TERMINAL.01 [E] — the positive-prefix firewall makes MAIN the only positive-prefix world (pmax = 184 = N; controls INDEFINITE-CONTINUATION at 21/25/27; two r254 headlines downgraded on record as base contamination); the pair (τ, τ^aug) closes under the exact two-term recursion a_n = c_n²h_n, b_n = −(c_nF_n)², equivalently D_{n+1} = D_n − F_n²/h_n, with the bilinear tau form (c_nF_n)²τ_n² derived and gated — the base alone carries the sign, the border only nonnegative magnitude; the Schur budget telescope reduces the entire fiber positivity to the ONE terminal inequality q_N = ρ_{N−1}/(5/7) < 1 (the 5/7 typed FLOOR-IMPORTED, derivation open; the measured driver is the rank-perfect F-h covariance +1.000 — the ratio is the object); the frozen micro-falsifier is passed blind at the coefficient-field level while the parametrix half stays open with a named, measured obstruction (a resummation gap, not a selection gap; level crossing and one-swap statistics refuted — r255's ORIENTATION-LOWDIM(1) revised on record; the mass-majorant class dead 0/42). The campaign contract is carried at the post-round-259 state per the r256 causal decision (base/fiber separation is artificial — the object is the indivisible full-source pair) and re-localized onto its two named terminal edges, registered as successor contracts: PRIME.PORT.COUPLEDTAU.TERMINAL_CROSSRATIO.01 [O] (the last fiber edge = a positive tau cross-ratio: prove h_{N−1}/F_{N−1}² > 7/5 on the cofinal ladder, binding the ratio) and PRIME.PORT.FULLSOURCE.PREFIX_RESUMMATION.01 [O] (the last base edge = a globally oriented prefix resummation: the determinant as a signed partition sum, no saddle dominance, no k-swap truncation); rounds 260–278 have since executed on them and are promoted in wave 4 (see the next update). No RH claim. Update 2026-08-25 (wave 4: v960/v961, rounds 260–278): the terminal-surface closure is registered as PRIME.PORT.COUPLEDTAU.SURFACE_CLOSURE.01 [E] — THE 42-RUNG SURFACE CENSUS q_N < 1 IS CERTIFIED ON ALL 42 RUNGS as a finite fact (35 cheap rungs via the r260/r263 two-branch theorem with both mains closing WITHOUT cancellation and the exception set exactly {kz15, kz20, kz22, kz36, kz38, kz39, kz52}; six exceptions via the sealed phase bounds — edge truncation and block alternation, no detector fires; kz15 exact-finite via the r270 outward-rounded interval certificate, dps 640, end width 1.5e-92, margin +0.02680, dps-halving ward), with the universal pair theorem at H1–H4 proved (Lean rh/lean/RH/PairBound.lean) and H5 — the margin |Z_local| + ε < √(5/7) — the SINGLE open window-dependent hypothesis; the cofinal front is typed precisely (r272: BOUND-COARSENESS, the truth margin rises with N — the bound loses cancellation, not the world; the needed mechanism is non-adjacent/global at address c3 with δ' > 0.21 of available 0.45; r273: PERTURBATION-INSENSITIVE + FIREWALL-MAP — the wall, not the cancellation rate, is what is arithmetically special about MAIN; r275: the KYP/state-space vehicle excluded by an exact structural double obstruction). The midpoint-orientation dictionary is registered as PRIME.PORT.RHP.MIDPOINT.ORIENTATION_DICTIONARY.01 [E] — the base Casoratian IS the pivot chain (c' = 1), the h-free midpoint form IS the node polynomial (provably orientation-free), the augmented telescope D_{n+1} = B − W^aug/W^base is exact, and the blind Maslov census delivers the GO: rule R2 = Jacobi interlacing/reality passes 42/42 with controls firing exactly at flip+1 (one-way, not h-equivalent) while the raw atom-Sturm census is honestly REFUTED as the winding quantity. Two new open contracts: PRIME.PORT.RHP.MIDPOINT.ORIENTED_THEOREM.01 [O] (the contraposition — an independent index obstruction forbidding the R2 break before half-filling on MAIN; rounds 279–281 since executed and consumed in wave 5, see the next update) and PRIME.PORT.WALL.METRIC_FIREWALL.01 [O] (the global metric firewall: the wall is graded-continuous, support exactness is the most wall-critical property, the exact Hellmann–Feynman gradients make the small-primes-loaded u-profile predictive, but the stability law is perturbative-only). The surface closure is a census + certificate result, NOT a cofinal theorem — the window quantifier stays; mincut base 4 / refined 5 unchanged. No RH claim. Update 2026-08-25 (wave 5: v962, rounds 279–281): the half-filling pinning theory is registered as PRIME.WALL.HALFFILLING_PINNING_THEORY.01 [E] — four named theorems ((T1) moment counting: the free pivots are exactly h_0..h_{N_w−1}, half-filling IS the end of the free moment space — 'why half-filling' answered by counting; (T2) crossing budget: #(h<0) = S_− exactly, Jacobi/Sylvester, world-blind; (T3) two-sided parity: node-sign pattern, gap parity and census bilanz, h-blind at every degree with the 87376-case exhaustion; (T4) main window reduction: the ENTIRE open statement of the wall is minC ≥ N_w, exactly equivalent to ∀ n < N_w: h_n > 0) plus four named refutations (no universal O(1) pinning — exact, unbounded-offset one-negative family; no extremality — the w9 crossing is liftable 184 → 185 past half-filling; no generic Maslov obstruction — 3 exact rational counterexamples; no simple offset law — max |sp| 0.273, all world-blind). Rounds 279–281 are consumed on ORIENTED_THEOREM.01 [O] (theorem share promoted, the center precisified to the budget localization), the north star is reformulated on BASEFIBER/METRIC_FIREWALL — why is the signed prime moment form quasi-definite up to the maximally free order? — and two new open contracts register the successor lanes: PRIME.PORT.REPRESENTATION.CONTEST.01 [O] and PRIME.PORT.RHP.FULLSOURCE.QUASIDEFINITENESS.01 [O] (in flight at this cut, not consumed, with the reviewer forbidden lists). In Lean the hole is now fog-free: free_window_positivity (rh/lean/RH/Window.lean) is the central sorry in base coordinates (via T4 the base half of the master theorem), T1/T4 are proved for real, T2 is stated, and the exact one-negative instance is a permanent counterexample guard. No RH claim. Update 2026-08-25 (wave 6: v963, rounds 282–285): the L* reduction dictionary is registered as PRIME.LSTAR.REDUCTION_DICTIONARY.01 [E] — the r283 A2 chain as exact gates (mu-frame congruence minor_k(D_mu − G) == D_k(mutilde); frame contraction h > 0 through the window ⟺ lambda_max(E_m) < 1; crossing exactly at minC + 1; pigeonhole ceiling minC ≤ S_+ re-proved; capacity-as-counting refuted by the rank-one pair — the deciding values are metric, 1.25e-13 vs 1.25e+2) establishes THE CANONICAL FORM OF THE OPEN CENTER, lemma L*: for every real polynomial p with deg p < N_w, ∫p²dnu < ∫p²dmu (equivalently lambda_max(E_{N_w}) < 1) — a two-measure moment problem instead of a determinant cascade, registered as the standalone contract PRIME.LSTAR.SUBORDINATION.01 [O] with the external problem document rh/problem/lstar_problem.tex. The r282 four-language elimination lands as named negative gates (CONTEST_ALL_DEAD — SOS iff empty negative register, Kasteleyn orientation iff S_− = 0 by full 2^S exhaustion, Hamiltonian-PSD == h > 0 bookkeeping, dual-pair sync by theorem; the common deep reason: every classical positivity language forces positivity exactly for the positive measure class, and MAIN is signed), the r285 decomposition bookkeeping is exact (lambda_max = maxdiag·(1 + assist) with the sign-exact budget equivalence), and the typed measurements pin the anatomy: MAIN's wall is a near-single-atom Christoffel event (n_DIAG = 187 vs crossing 185; all controls die collectively), the binding shallow-u ARCH edge grows sub-classically (p = 0.38 — any (D) proof must be a discrete bound), MAIN's wall assist is the extreme ensemble low outlier (pct 0.00), and the round delivers the first two positively MAIN-separating detectors of the program (assist-at-crossing 0.0195 vs dead 1.69..2.99; random-sign z = −3.15 destructive vs dead +4.95..+12.44). Honest and open: the family margin decays ~3 orders (1.68e-4 at the flagship down to 1.4175e-7 at z = 233); the r286 margin-scaling round was in flight at this cut and is consumed in wave 7 (v964: resolved harmless). The predecessor contracts REPRESENTATION.CONTEST.01 and FULLSOURCE.QUASIDEFINITENESS.01 are consumed; in Lean the canonical form is stated (lstar_subordination, the wave-6 sorry) and the direction L* ⟹ free-window positivity is proved (lstar_implies_free_window). No RH claim. Update 2026-08-25 (wave 7: v964, rounds 286–289): the L* coherence census is registered as PRIME.LSTAR.COHERENCE_CENSUS.01 [E] (v964_lstar_coherence_census.py; the four probes byte-exact in their sealed smoke stage). The DCXX margin warning is resolved HARMLESS: 15 new anchors N_w 942–1218, all margins mp-sign-safe positive (min +1.806e-8), the O(1) census offset survives beyond the cap, and the flattening power law (alpha ~ 3.05, driver c_w → 1) tracks the local loading speed — no counterexample, no acute falsification threat. The generic L2 half bows to a named classical theorem: the exact van der Corput inequality at H = ceil(sqrt(m)) delivers delta' = +0.309 > 0.21 world-blind (6/7 exceptions + 38/42 rungs; F1 discrepancy dead; only the kz15 razor blocks 7/7, exact-finite per r270) — registered as PRIME.PORT.L2.VDC_LEMMA.01 [O] (remaining input: the chain origin of the P-variance scaling). The destructive coherence has a named carrier class (antiphase next-nearest ARCH-ARCH pairs, z_v = −3.149, total control reversal, finest alignments below phase resolution), and the diophantine route is excluded (r289 METRIC_ONLY: the rational twin — every tent center replaced by a rational at position cost ≤ 2.1e-9, every exact log-relation destroyed — keeps the full signature identical; metric coherence threshold 1e-3..3e-3 of the local gap; Baker ~7900x too weak and unnecessary). The firewall reads the fraction profile metrically, not its arithmetic; the precise open front is the profile functional (r290 in flight, not consumed). No RH claim. The register-gapcode disenchantment row (v886, GAPCODE-MEASURED) is booked as an honest NEGATIVE/limit result: the 210-register is literally the first four parity checks of the sieve (hard floor, 0 violations in 5.76e6 pairs) and the code IS the sieve (the zero-parameter wheel–Cramér null explains R² = 0.99839; the excess 4% and shrinking; nothing moves with c₃ or φ₀) — the register's uniqueness remains the compiler-side arithmetic forcing rad|W(E₈)| = 7#. NO RH claim; no marker moves. Rounds 42–49 (2026-08-09, v887–v891) are the great consolidation. The certificate rollout COMPLETES (v887, PRIME.PORT.CERTIFIED.LADDER.02, CERTIFIED-LADDER-COMPLETE): σ_h > 0 is PROVEN on ALL 42 reachable rungs h = 142..878 of the deployed ladder — exact integer Bareiss/LDL Sylvester certificates on the head rungs (v884 + the parent rollout's tier 1), validated-precision mpmath Cholesky on the tail (dps 120 re-run at dps 200, every pivot ≥ 10⁶ × the accumulated rounding bound at both precisions; the two deadline-skipped rungs h = 859/878 closed with floors ≥ 8.352e−6 / ≥ 9.187e−6); the Epstein control REFUSED at pivot index 10 by the identical machinery; proven MODULO the declared conservative transcendental-evaluation error model — end-to-end ball arithmetic and the Lean composition of the certificate chain are the named next steps, the h → ∞ tail untouched and staying with the registered port contracts. The FOUR ROUTE DECISIONS of the sum-rule program land (v889, PRIME.PORT.DIAGSEP.01 + PRIME.CASE.ZONESPLIT.01 + PRIME.CASE.PNTGAMMA.01 + PRIME.CASE.SIGNEDHOMOTOPY.01): the wall dies 100% through coherent off-diagonal accumulation (at the wall's death point every diagonal testing entry stays below 1, max T_m 0.94–0.99; separation ratio ρ_sep ∈ [1.99, ∞) GROWING with depth — the diagonal is not RH-sensitive and stays a candidate for analytic investment), the critical zone is FROZEN at θ* = 0.700 (outside testing margin uniformly positive on all 42 rungs, deep-half infimum +0.0214, sharp — 0.667 fails; sublabels honest: OUTLIERS-DANGEROUS, INSIDE-LAW = c/log²), the PNT-smooth world VIOLATES the port testing margin on every rung (PNT-INSUFFICIENT: min γ⁽²⁾ from −0.96 to −7.8e−3 — no classical zero-free-region-strength input can close the diagonal by smooth comparison; the dominant rescue piece is INT(+), the MASK-MASS INTERACTION, neither the support pattern nor the mass fluctuation alone), and the signed homotopy kernel is INDEFINITE-ARITHMETIC (KERNEL-NSD on both frozen rungs): the sum-rule route is retyped CONDITIONAL on a pair-correlation-class input. The SURVIVING POSITIVITY ARCHITECTURE is measured (v890, PRIME.PORT.HIROTA.01 + PRIME.PORT.SFLOW.01 + PRIME.PORT.TAU.MOEBIUS.01): FLAG POSITIVITY (Sylvester) of the section family — every nested LEADING principal minor of I − C_h positive on all 37 full-window rungs (strictly stronger than the wall scalar; typing corrected per the round-51 review — classical total positivity of ALL minors is NOT claimed and untested), the Desnanot–Jacobi bilinear identity exact on every rung, section size and s, the across-rung Hirota closure typed HIROTA-OPEN honestly (the IIKS derivation stays the named contract PRIME.PORT.PAINLEVE.01); the pole-free s-corridor with the exact organizing identity s*_h = 1/λ_max(C_h), i.e. s*_h − 1 = τ_h/(1 − τ_h) — THE WALL MARGIN IS THE POLE DISTANCE of the integrable s-flow (measured h-slope −2.90; the Epstein and scramble controls pull their pole inside); and the multi-factor τ anatomy: the truth ladder keeps EVERY determinant factor off −1 (31/31 full-window steps) while the frame-surviving smooth-mass world crosses factors on 22 of 28 steps — the one-scalar reduction is honestly CLOSED (BRIDGE-DIFFUSE): positivity inheritance, if it exists, is a multi-factor/total-positivity statement, not a scalar cocycle. And the Moebius/carrier-invariance route is honestly KILLED with mechanisms (v891, PRIME.PORT.MOEBIUS.CRFIREWALL.01 + GAUGEFW.01 + CENSUS.01 — the verdicts are kills and recorded as such): the fit-free cross-ratios are dead (CR-DEAD; the predecessor's celebrated 0.0015 residual was MANUFACTURED by the three-point PSL(2,ℝ) pinning), no source-frozen gauge is raw-invariant (GAUGE-MADE; the scalar cocycle LAMBDA-FLAT; the Jacobi projectivization JACOBI-DEAD), and the six-world census shows the frame-dead scramble world beating truth on the bare Moebius bars — rank-2 window KINEMATICS, not arithmetic dynamics, with the arithmetic separating AT THE FRAME (window subcriticality: truth 41/41 alive vs 0/28..0/42 for every control); the sole surviving remnant is the deep-core 8-node cross-ratio coherence only the true prime masses carry (4.3e−4 vs 2.7e−2, report-only). The compiler-side row of the same promotion is v888, the finite Pfaffian/K₆ signature (the doily as the support geometry of a six-slot fermionic Pfaffian with the canonical sign character χ(i) = (−1)^(i+1), computed, not assumed; the self-hosting counting theorem C(g+1,2) = g!! forcing g_car = 5 uniquely with (g−2)!! = 3 = N_fam for free; the flavor hexagon as the Aut(C_fin) ≅ C₆ orbit with λ_rec = (2/3)⁶; the mod-30 clock distinguished; the operative-Coxeter-30 reading honestly killed — the counting theorem [E], the Wick-compiler premise [O]). NO RH claim; no marker moves. Rounds 50–53 (2026-08-09, v892–v896) assemble the closure architecture. The exact hermitian congruence lands (v892, PRIME.PORT.RELCONG.01): A_{h+1} = A_h^{1/2}(I + H_h)A_h^{1/2} EXACT (6.5e−14, H exactly hermitian) with the inheritance margin η_h = 1 + λ_min(H_h) NON-DECAYING (min 0.0050, median 0.29, slope +0.108 while the wall margin τ collapses at −2.74) — the open inheritance inequality is bounded-margin-shaped, not collapsing; ρ(W⁻¹ΔC) was a MISLEADING statistic (strongly non-normal, ‖M‖/ρ up to 26), the hermitian H is the honest carrier, and the mini-theorem is verified: base PD + η_h > 0 for all h ⇒ the whole ladder (Sylvester congruence). The flag-chain induction (PRIME.PORT.PIVOTFACTOR.01): the 12 LDLᵀ pivots of A_h = I − C_h factor rung-to-rung as d_{k,h+1} = d_{k,h}(1 + μ_{k,h}) with EVERY factor positive — all 12 flag quotients Q_k > 0 on all 31 truth steps (the soft-flag minimum 2.06e−14, SIGN-DECIDABLE at 6.4e9× the eigenvalue noise floor under the Cauchy-interlacing guard), the smooth world violating at the BULK flags first — the shortest induction shape: base (v884/v887) + min_k Q_k > 0 ⇒ the whole ladder by pure algebra. The Rouché route is honestly killed (PRIME.PORT.EULER.ROUCHE.01, DEAD): sup_Γ ‖A⁻¹Δ‖ ≥ 1 on 22/31 truth steps including off-cap (max 63.4) — the two-sided contour-norm bound is the WRONG theorem shape for inheritance on this ladder, consistent with the one-sided avoidance law, while the argument-principle machinery itself verifies exactly. And THE WALL IS THE FIXED 8×8 SCHUR CORE (PRIME.PORT.DEEPCORE.SCHUR.01): on the full wall operator the block split at the fixed deep-core aliases {2,…,16} gives Haynsworth-exact inertia and λ_min(S_h)·w_core/τ_h = 1 ± 8.4e−8 with soft-mode core mass w_core ≥ 0.999937 on all 41 full-core rungs — the RH-critical object is a FIXED 8×8 family, not a growing operator, conditional only on the TAU-RELATIVE exterior bound (λ_min(R)/τ trendless at 210–2200 while the absolute exterior margin shrinks h^{−2.865}). The margin sources are explained (v893, PRIME.PORT.ETASOURCE.01 + PRIME.PORT.RELFLAG.01): SCALE-MATCHED — in the dangerous direction the increment and the operator collapse TOGETHER (slopes −3.716 vs −3.456, residual correlation 0.974, 94% shared variance), so the non-decay of η is EXPLAINED: numerator and denominator are sections of ONE arithmetic object, with only the O(1) scatter of the ratio open; the relative laws d₁₂ = c·τ (trendless — the kz-21 outlier diagnosed in the round-53 sandbox as a COORDINATE-ARTIFACT, the kz-19 mechanism repeating, corrected spread 124 → 15: SOFTFLAG TAU-TIED) and λ_min(R) ≥ 210·τ; COMPRESSIONS-DISTINCT typed honestly (the port bulk floor is an ABSOLUTE floor ~1e−2 while the core exterior is tau-tied — different statements at two compressions); and THE PRINTED THEOREM SKELETON — (i) base certified (v884/v887), (ii) R ≥ 210τ trendless, (iii) core ↔ τ at seven digits, (iv) η > 0 non-decaying — leaves exactly ONE unconditionally open statement: the τ-sign inheritance, reorganized from collapsing-margin form (Q₁₂ ~ 2e−14) into BOUNDED-MARGIN form (c, c′/c, c_R, η — all O(1)). The conditional diagonal contract is made concrete (v894, PRIME.CASE.PAIRCORR.CONTRACT.01 [O]; the route stays CONDITIONAL per v889): the first-order homotopy gain regroups EXACTLY (4.5e−15) into the prime-side form Σ 2Λ(n)/√n·K_{h,m}(log n) − PNT integral with the explicit BAND-LIMITED node kernel (n90 = 7–26 modes, support ~90% of the log window — NOT short-interval concentrated), the full LaTeX contract statement is frozen in-probe (H₀ = 151, θ* = 0.700; IF the signed inequality holds on the critical zone THEN T_h ≤ 1 there), the finite shadow is green (all 79 (rung, alias) margins positive, min +2.3e−8), the endpoint bracket fails globally (142/227) but deep small-a cells pass monotonically, and the inner-zone accounting localizes the irreducibly-hard part to a NON-SHRINKING band (~20% of aliases, 38–56% of ν-mass) — the demand: state-and-prove the band's weighted pair inequality, or accept conditionality. The collectivity theorems land (v895, PRIME.PORT.FACTORAVOID.01 + PRIME.PORT.DEEPCORE.01): the norm-bound theorem shape does NOT exist (ρ(W⁻¹ΔC) ≥ 1 on 17/31 truth steps but always via the harmless μ > +1 side) — the true avoidance law is ONE-SIDED, max(−min μ) = 0.9950 < 1 on all 31 steps, which IS PD inheritance itself; the geometry/atom split is EXACTLY degenerate (the deployed atom cutoff is slaved to the tent-support edge — NO separable atom channel: the increment is the collective window re-test of the full comb); and the deep core IS the port core (the 8 deepest common nodes are the FIXED even aliases a_m = π²m², Bessel coordinates, to 0.1%) with ALL FOUR surgical modifications killing the certificate-level cross-ratio coherence — edge-only smoothing, interior-only, prime-power echoes removed, and even the wrong-Λ world changing only the factor k on the k ≥ 2 atoms: THE SIGNAL IS THE ENTIRE MULTIPLICATIVE VON MANGOLDT COMB, the global rigidity of v883 at the finest coordinate. The compiler-side row of the same promotion is v896, the Wick functor arc (SEAM.CFIN.WICKFUNCTOR.01 [O]): the six compiler roles exist in the deployed seam (sector law, grading, C₆ intertwining exact) but the vacuum kernel is channel-diagonal; the scalar obstruction is PROVED (the C₆ 2-cycle {4,5} forces a duad zero; both relaxation witnesses constructed); the block construction (commutant dimension 33) carries 15/15 blocks and 15/15 block Wick monomials with the canonical sign law — and the decisive fact is SEAM-DIAGONAL: the deployed seam has zero cross-blocks, so the value level awaits a physical channel-mixing mechanism; the [O] premise unmoved. Rounds 54–56 (v897–v900) deliver the reviewer's 'immediate' list: the certificate base becomes INTERVAL-RIGOROUS (v897, PRIME.PORT.BALLLADDER.01: all 42 rungs under rigorous mpmath.iv interval shifts, 15 exact-rational + 27 validated-precision, the informal eps_c error model RETIRED, Epstein refused at pivot 10; only the Lean composition remains named); the demanded channel-mixing state is CONSTRUCTED as a candidate (v898, SEAM.CFIN.KMSMIX.01 + SCHURMIX.01: the C₆-covariant KMS state passes all block-functor gates, the exact Schur elimination generates all 10 carrier duads from the bare diagonal state, the frozen 15-signature table is the registered prediction, RP-THETA-OPEN named; the [O] premise unmoved); the conditional pair contract becomes a NORM SQUARE in the frequency weights (v899, PRIME.PORT.CHRISTOFFEL.RATIO.01 + PRIME.CASE.KERNEL.SOS.01 + PRIME.CASE.EDGEDEFECT.01: the exact pivot identity 1/d₁₂ = 1 + v⋆K_σ(y⋆) with the honesty fence λ_min(I−G) = τ exact; the one top-edge tent killed exactly by the periodic full-weight fold, 79/79 modified margins positive — the hypothesis itself stays conditional); and the normalized core update gets its exact two-dimensional anatomy with the honest negatives registered as region boundary conditions (v900, PRIME.PORT.NORMALIZED.CORE.01 + PRIME.PORT.GRAPH.REGION.01). NO RH claim; no marker moves.

Promotion of discovery rounds r494/r495 as v1017_kernel_loewner_positivity.py (26/26; suite 1009 → 1010; ledger 1173 → 1174). Re-derived (no probe imports). SCOPE: supp(h) ⊂ [−0.3, 0.3], 2L = 0.6 < log 2 so the classical prime term is empty. FLOAT64 FLOOR (not interval, not [E]): Q_W(h) ≥ 2.1×10⁻³ ‖h‖₂², equivalently λ_*(0.3) ≥ 2.122×10⁻³ (claimed c=2.1×10⁻³). The x-space Weil form agrees with the defining digamma at the calibration gate (σ_A(0)=−5.3721834192256654). Loewner after zero-extension; quintic C² cutoff books κ_w. Finite-section: 401-dim Legendre of a degree-48 Chebyshev surrogate, Bernstein HS enclosure, exact tail charged 3×. Independent r495: translation identity 6/6 exact over ℚ with strictly positive boundary-strip mass; doubled-c_L budget −2.188 (false-world). BOUNDARY: r496 NO_GO(kernel-Loewner-compact-tail@L=0.8) — the compact-tail method does not scale past the prime-free zone; this row does NOT claim λ_*(L)≥0 for general L. NOT evidence for or against the Riemann Hypothesis.

Promotion of discovery rounds r609/r617 as v1018_e8_directed_readout.py (47/47) and v1019_coxeter_euler_completion.py (46/46; suite 1010 → 1012; ledger 1174 → 1176). Re-derived (no probe imports). v1018: seven exact cells [E] Identity — Seifert/Phi_30, Hamming 1+14y^4+y^8, srg(120,56,28,24), N(n)=240 sigma_3(n) for n<=10, A_P/A_P(1)=tau(n), (Z/30)^x cong C2 x C4, E6 oplus A2 glue 78/81/81. C7 Gauss-code transform stays OPEN (rem:c7-audit). v1019: Coxeter–Euler completion — det(I-xC)=Phi_30, Tr C=-1; classical Moebius; U=1 oplus C, Tr U=0; Z_C and D_E8 zeta quotients, abs. conv. Re s>1/2. Numerical (X=10^5): D_E8 residual 4.76e-4 at s=0.75, 4.16e-12 at s=1.5. Class: vanishing linear term generic from Tr C=-1; E8 selects only the divisor set of 30. Beurling-generic. Fence (verbatim): The trace-free completion is zero-free and pole-free in Re s > 1/2. The splitting into the scalar zeta channel and the Coxeter channel is open and RH-equivalent. No RH claim. NO-GO E8.COXETER.REGULARIZED_SPLIT.NO_GO.01: det_2 cannot isolate 1/zeta(s). Like the Eisenstein bridge, RH-neutral as a finite identity.

A research contract [O] engaging Penrose's Conformal Cyclic Cosmology as a named reference frame — never a confirmation in either direction; the cyclic reading of origin_theory stays [C] regardless. The certified kinematic base is CCC.SEAM.KINEMATICS.01 [E] (v957, six discovery probes embedded byte-exact, 28+29+18+21+14+7 gates): the reciprocal gauge ΩΩ̌ = −1 inside the proven D₄ stabiliser; conformal-factor rigidity (2D needs the reciprocal ℤ₂, on the 3D lens crossover the deck alone kills all moduli — TFPT's candidate answer to CCC's open unique-conformal-factor problem, v_geo staying pure unit calibration); the entropy reset as an explicit Stinespring reduced channel; the kinematic 2D→3D→4D uplift (seam sphere = Hopf base, crossover = S³/ℤ₄ = the lens boundary of the A₃ ALE, 4D bridge = the cone with the inversion as conformal aeon swap, Lorentzian shadow Einstein with a spacelike S³ crossover); the KMS closure T = e^{−H_mod} with β_angle = 2π = 1/(4c₃) = Gibbons–Hawking on the fibre; the holonomy dictionary (seam strings carry exactly the GSO 2-torsion −1); the derived uniqueness half of the v534 straddle selector; and the frozen Gate-6 kernel (sharp causal top-hat disc, θ_max ≈ 1.16°, feeding the preregistered search experiments/ccc-crossover-disc). Demands: D1 the interacting seam algebra ON the lens crossover with RP protected on the mid-gap cut class (= WOIT.OS.TWISTOR.01 γ in the crossover geometry); D2 the aeon-transfer channel as a field-level Stinespring isometry; D3 the cosmology fork decided (Starobinsky r = 12/N² ∈ [0.0033, 0.0048] vs crossover epoch — within reach of σ(r) ~ 10⁻³ experiments); D4 the preregistered disc search executed — EXECUTED 2026-08-24 with a robust null on the Planck PR3 SMICA map (first data contact; freeze intact 3/3 hashes, frozen-kernel guards 5/5 before data contact; map SHA-256 pinned, seed 20260824, reruns bit-identical): p_global = 0.673, p_counts = 0.446, BH-q_min = 0.673 against the frozen q < 0.01 threshold; 171 candidates with no sign excess (83/88); injection recovery 100% at 200 µK — a well-powered, real null; kill criteria K1–K6 all NA (they fire only on a resolved relic), replication legs not required for a null; no kill fired, no type change — the contract stays [O] via D1–D3, the cyclic reading stays [C], and the compiler core is untouched (the frozen kernel was output of the certified kinematics, not input; results machine-readable in experiments/ccc-crossover-disc/results/results.json). Kill criteria frozen, including the forbidden identification of μ₄ marks with Hawking-point counts.

Eight new contract IDs implement the review diagnosis 'a chiral 1+1D seam net does not imply a local, interacting 3+1D quantum world'. DIMENSION.UPLIFT.FIREWALL.01 (standing rule, in force): no 1+1D theorem closes a 3+1D claim; every contract closure states the spacetime dimension of its hypotheses and its conclusion — even a fully proved SEAM.EQUIV.01 is a rigorous boundary building block, not the 4D theory, and the anomaly-inflow bulk is never to be silently equated with physical spacetime. SEAM.BULK4D.RECON.01 [O] makes the seam-to-bulk theorem explicit: 4D locality/microlocality, Poincaré covariance with positive energy, spin-statistics + CPT, both helicities, cluster decomposition, a nontrivial S-matrix, and a unique seam-bulk operator dictionary. The dynamics split DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01 separates the three meanings of dynamics (relaxation Tⁿ, dissipative semigroup e^{t log T}, unitary e^{−itH}): the finite kernel half is executed [E] in v971 — Q = log T of the seam transfer kernel is an exact classical Markov generator (row sums symbolically zero; off-diagonals exactly ln(9/8), 2ln3, 2ln3 > 0; uniformization certificate ⇒ e^{tQ} positivity-preserving for all t ≥ 0; negative control: eigenvalue −1/10 gives det = −1/200 < 0, provably not embeddable) — while the local, size-consistent unitary dilation with a Lieb–Robinson bound and OS continuation stays [O] — its DISCRETE collision/QCA leg is meanwhile executed exactly (v984, 2026-08-28: the collision step V = C(U_B⊗I) is unitary, the Stinespring identity Φ(ρ) = Σ_j P_j U_B ρ U_B† P_j holds symbolically, diag Φ = Bp and six fresh ancillas give B⁶ = T exactly on a radius-1 collision band; the continuous Hamiltonian/OS legs remain the contract; review wave 4, v999: the finite ladder is now COMPLETE through continuous time — Richardson 1.098e-10, diag L = Q symbolic, e^Q = B exact, GNS 0, locality 1.355e-20; strong-collision rank 9/81; open = thermodynamic field limit only); binding precision: the shared F_transfer relaxation shape is a universal contraction class, not one physical clock. QFT4D.OS.RECON.01 [O] demands the genuine 4D Euclidean lattice OS package (reflection positivity, Euclidean covariance, clustering, uniform bounds, continuum limit, reconstruction), with the binding phrasing rule that the v381 all-orders leg is a local perturbative construction under the stated EG/BRST hypotheses — no confinement, mass gap, asymptotic charged states or full S-matrix follows. CHIRAL4D.NOMIRROR.01 [O] demands the explicit Ginsparg–Wilson/overlap chiral lattice theorem (local gauge-invariant measure, anomaly freedom incl. the Witten SU(2) anomaly, no mirrors, correct index/charges, stable continuum limit; Mastropietro 2023 as the state-of-the-art calibration). GRAV.NONCIRCULAR.01 (standing rule, in force): Bisognano–Wichmann is a theorem within an already-local Poincaré-covariant QFT, never a generator of Lorentz spacetime from a modular flow — every BW/CHM use declares assumption-vs-result, and the entanglement-equilibrium Einstein derivation is typed conditional on the 4D package. OBS.TRANSDUCTION.01: internal eigenvalue + nonvanishing projection B·P_r ≠ 0 + physical coupling = observable signature; without the middle arrow neither a non-observation falsifies nor an observation confirms (the ACT+Planck birefringence proximity stays coincidence-level pending the shared-action proof). PRED.JOINTLIKELIHOOD.01 [O]: the evidence is reorganized from hit-counting into overdetermined relation bundles (flavor sum rule; r = 3(1−n_s)², α_s = −r/6; one normalized axion action; character-resolved transfer) with the demand of a joint likelihood carrying the atom-induced covariance, effective degrees of freedom, a prespecified null space and a genuine holdout of future data. The transport-lift wave (v976/v977) executes the lift-structure half of the dilation contract: the deployed Kraus dilation K_ij = √T_ij |i⟩⟨j| is provably entanglement breaking (measure-and-prepare, quantum capacity 0, C₀(T) = 0) — any dilation satisfying D1–D4 must be a genuinely different object; the Birkhoff fibre of the single step B is exactly a one-parameter line t ∈ [0, 1/18] (hidden coordinate = the sign character, ŵ(sgn) = 6t; the triangle loop current is an exact eigen-observable Ψ_t(A) = 6t·A — one step, one readout, no ancilla; on the contrast qubit the Choi law λ_min = −3t/2 puts the deployed spectrum exactly on the entanglement-breaking boundary because 2/3 + 1/3 = 1); and B is unistochastic — an exact SU(3) lift {U, U*} with Jarlskog J = ±1/27, the 5-12-13 Wilson plaquette code ((−5+12i)/13, Gaussian norms {10, 13, 130, 169}), the center bridge disc χ_A = 65 = det(A−I)² + (det A/2)² = 4² + 7² to the v530 atom matrix, and a census-unique full-code point at the deployed (2/3, 1/3). Same classical data, three inequivalent quantum dynamics; registered as TRANSFER.HIDDEN.CIRCULATION.01 and TRANSFER.COHERENT.WILSON.01 (executed halves [E]; fibre-point/branch selection, the defect–Birkhoff forcing functor and the center–transport intertwiner stay [O]); the PMNS near-miss (240.2551° vs 240°) stays a negative control.