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 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). 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 milestones (v519/v522/v524), 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).

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; (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 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.