Original ledger status
CELEST.WP5E.MEASURE.01
THE WP5E BCOV MEASURE QUESTION DECIDED AT PROBE LEVEL (2026-07-22; delta-1e + delta-1f consolidated in the v518 style, one module, 39 checks, ~20 s; ERFOLG-A on the preregistered decision layer): which of the two exact, mutually contradictory measures on PT/Z4 is the true BCOV measure -- (A) the DECLARED completion reading (v516: unphased sector trace, w_m = 4 h_m, supplies psi = 64) or (B) the DERIVED chiral measure (v518: multiplier character chi_4 on Gamma_1(4); all three testers fail)? ANSWER: single-valuedness of the physical one-loop lattice factor is DERIVED from two independent constructive sources, not postulated, and the completion reading (A) wins. (1) THE INVARIANT SUBSPACE (delta-1e D2): dim_Q {v : rho(T) v = v, rho(S) v = v} = 8 = 4 x 2 in the dressed 16-component Weil system (exact rational nullspace); EVERY kernel vector lies in the Q(zeta_8)-span of {e_H, e_H'} -- the two Lagrangian gluings, both theta = E4, level-1 quartic = Q^(0) = the unphased trace; strict trivial-character solutions at physical weight (m, k) = (0, 0): ZERO for every dressing (11 combinations, both orientations). (2) SOURCE 1 -- THE F-LEMMA (delta-1f A1): the only strict chiral families are chi_4 (dims (3,3)) and chi_10 (dims (1,1)), both with nontrivial T-character EXACTLY; the canonical column-matched chi_4 member's total block sum obeys G(gamma tau) = chi_4(gamma) G(tau) pointwise (certificate 3.9e-16 over two fresh tau, nonvacuous |G| >= 59.6); EXACT change of variables: fundamental-domain independence forces int = 0 for EVERY chiral integrand -- under TP-1 + TP-2 the chiral route can never source psi = 64: the v518 route was never a well-defined nonvanishing moduli integral (the kill is SHARPENED, its unfolded values are convention bookkeeping). (3) SOURCE 2 -- THE QUILLEN PAIRING (delta-1f A2): |t conj(t) - 1| < 8.3e-40 on all 15 pairs and both generators (measured unitarity); |chi_4|^2 = 1 exactly vs one-sided chi_4^2 = e(2/3) != 1 (T-fixed: 640 != 0 mod 960, 15/15 defective); the doubled 256-dim hol x antihol Weil system closes STRICTLY at trivial character and physical weight (nullspaces (28, 17) >= 11), contains the unphased diagonal (~2e-15) AND the physical columns w_b (x) conj(w_b) (sigma 4.9e-16/8.3e-16); negative control hol (x) hol: EMPTY nullspace (0, 0). (4) CONSISTENCY CLOSURE (delta-1f A3): the forced unphased numerator inside the v518 scaffold reproduces sum_m V prop (1, 2, 1, 0, 0) = <x,x>^2 EXACTLY on every level n <= 8 (levelwise Okubo/4-design); J-weighted spreads ~5e-41, T5/T3 fractions ~7e-42, zero negative-exponent cells; psi(skeleton) = +0.2302 = -psi(contact) -- the J-weighted mirror image of psi(A_fix) = +64 / psi(contact) = -64; linearity 4.6e-41: the circle to v516 is CLOSED. (5) D3 -- THE Z2/EH ANCHOR (delta-1e): only the declared reading hits the anchor (9<x,x>^2 = (1/4) x 36<x,x>^2, psi(A_2) = -8, scale tooth c = 1/2 = |Z2| h^(A1) unique); ALL THREE derived Z2 instantiations fail the anchor testers (spreads 1.12/0.895/0.516, psi sign wrong). (6) D1 -- COLUMN CANONICALISATION (delta-1e): the physical AB column sum_m i^(bm) e_(m,m) is contained EXACTLY in the chi_4 family (sigma 1.8e-16/1.7e-16, one scalar per orbit -- canonicalising the (N1, N2) freedom); the canonical member STILL fails every tester (sharpened kill). NEGATIVE CONTROLS: SO(16)/D8 (T5 = 20/T3 = -40 exact, mu_2-only supply), wrong form (|Gauss|^2 = 64 != 16, S^2 = C breaks), wrong weight (transport dev 0.78 at exponent 2), shuffled weights (T5 = -14/T3 = 36), planted family detected (1.5e-16), hol (x) hol empty. [C] TYPED PREMISES (the mandatory fence): TP-1 (the twisted one-loop contribution is an F-independent moduli-space integral), TP-2 (it is nonzero -- it must source psi = 64), TP-3 (the v518 kernel-family weight convention), TP-4 (BCOV F1 is Quillen/Ray-Singer: the one-loop factor pairs hol x conj(hol)). [O] the constructive BCOV derivation of the w_m normalisation itself (the residual open item) -- since executed and DERIVED at probe level by v523 (CELEST.WP5E.WM.01: Atiyah-Bott mode ledger + zeta/Quillen determinant + consistency chain, typed premises TP-REG/TP-Q/TP-NUM/TP-CH); the residual [O] narrows to the GLOBAL BCOV integral on PT/Z4 beyond the fibre zero-mode factor; SEAM.EQUIV.TWISTOR.01 stays Open. Discovery provenance: delta-1e (28/28) and delta-1f (23/23) probes in experiments/tfpt-discovery/ (2026-07-22). NO marker moves anywhere.
Recorded status: DECIDED at probe level for the declared reading ([E] exact Weil/Q(zeta_8) algebra, exact invariant subspace, characters + 1/960 grid, ledgers, levelwise 4-design, Z2 anchor arithmetic, change-of-variables corollary, controls; numeric documented: transports 28+ digits, SVD memberships 1e-8/1e-3, certificates fresh tau, HM kernels 30+ digits; [C] the typed premises TP-1..TP-4; [O] the constructive BCOV derivation of w_m -- since DERIVED at probe level by v523, narrowing the [O] to the global BCOV integral beyond the fibre zero-mode factor; NO marker moves)
Dependencies, status detail and source
Canonical status: DECIDED (ERFOLG-A at probe level): single-valuedness is derived from two independent constructive sources (F-independence + Quillen pairing) under the typed premises TP-1..TP-4; the v516 completion reading wins, the v518 kill is sharpened; residual [O]: the w_m normalisation is since DERIVED at probe level by v523 (1/det_j = the Atiyah-Bott/zeta-determinant fixed-point factor, three independent sources); what remains open is the global BCOV integral beyond the fibre zero-mode factor
Dependencies: CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.TWISTOR.01; v502; v505; v508; v511; v514; v515; v516; v517; v518
Scripts: v520_celestial_wp5e_measure_decision.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 587Original ledger status
SEAM.BIT.RPBLIND.01
THE RP/THETA ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-22; one module, 25 checks, ~25 s; an honest, decided NEGATIVE result in the v508 style): does free reflection positivity (v519 RP) or anti-linear Theta existence (with the v519 side conditions) BREAK for delta != pi/2 on the deformed mark family M(delta) = {+-1, +-e^(i delta)} -- which would DERIVE the v512 alignment bit from OS positivity? NO: the entire free RP/Theta battery is SIDE-BLIND, hereby documented as the EIGHTH side-blind test on the v512 scoreboard (7 -> 8); the bit REMAINS genuine discrete input. (1) CENSUS (exact solvesets, symbolic delta): for EVERY delta exactly the two mark-SWAPPING reflections Theta_(+-e^(i delta)) exist (axes delta/2, delta/2 + pi/2; all 20 cut/mark incidence solvesets EMPTY); mark-FIXING reflections exist exactly at delta = pi/2 (solveset cos delta = 0 = {pi/2}, lost immediately at pi/2 - eps); the v510/v512 counterwitness {+-1, +-(3+4i)/5} carries the swap pair exactly and is NOT excluded. (2) RP IS delta-BLIND: bond-cut Gram inertias (8, 0, 0) PD for all tested delta at N = 16, even deg <= 2 sector (29, 0, 0); the full sorted 40-digit spectra are IDENTICAL across all axes (deviation 0.0) -- the ENTIRE free-RP spectral datum carries ZERO delta information; the N = 16 odd-m failure (site axes, inertia (3,3,1), det = 0) is a lattice-PLACEMENT artifact: at N = 32 ALL m = 1..7 (delta = m pi/8) have mark-compatible BOND axes with PD inertia (16, 0, 0); continuum: the OS kernel in axis-adapted coordinates is EXACTLY 1/sin((s+t)/2) -- the axis position drops out identically (Cauchy-Stieltjes factorisation PD); the counterwitness PASSES free RP (6-point Gram (6, 0, 0)). (3) THETA EXISTENCE IS delta-BLIND: Theta^2 = +1, deck normalisation and Fock implementability (U^2 = +2^7/2^8 > 0, exact Cl(16)) hold for every delta; the ONLY delta-sensitive clause of the v519 battery (Theta rho Theta = rho^-1) is for delta != pi/2 not violated but NOT FORMULABLE (a mark-compatible order-4 rotation exists iff delta = pi/2) -- it PRESUPPOSES the bit instead of deriving it; same for the clock-tower clause. (4) THE BATTERY HAS TEETH AT EVERY delta: RP separates the two real-structure FAMILIES (family A/antipode: zero diagonal, indefinite (4, 4, 0); chirality-eta pinning: anti-chiral state (0, 8, 0) ND) -- but never the SIDES within family D. (5) PRECONDITION CONTROLS: hexagonal marks not concyclic (|b_hex| = 2 - sqrt(3) != 1, no seam circle -- rejected before positivity is asked); silver marks all real (deck not free -- excluded by topology); lifting audit: B (pullback) = index relabelling (delta-blind by construction), B' (stretched sampling) fails the pi/2 negative control (not the chiral vacuum -- discarded). [C] FACE #13 of the v512 equivalence web: the group generated by the admissible OS reflections is V4 for every delta < pi/2 and closes to D4 exactly at delta = pi/2 (Theta_i o Theta_1 = the clock) -- a typed REFORMULATION of the bit (12 -> 13 faces (since 13 -> 15 by v528 facets #14/#15)), not a derivation from positivity. [O] HONEST GAP: marks decorating the STATE (defect/twist insertions, interacting A_hol) are outside the free class = exactly v519's [O] scope -- there, and only there, could positivity still see the bit; since DECIDED by v525 (SEAM.BIT.TWISTBLIND.01): the mark-decorated free-plus-twist state class (sigma gauge, Kadanoff-Ceva 4-twist insertions, mu4/Bogoliubov defects -- everything Wick-computable) is side-blind too, the NINTH side-blind test (8 -> 9); the free-plus-twist class is EXHAUSTED, the remaining door is a genuinely interacting A_hol with non-Pfaffian-reducible OS data. VERDICT: KILL exactly as preregistered. Discovery provenance: seam_alignment_bit_rp_selector_probe.py (25/25) in experiments/tfpt-discovery/ (2026-07-22). NO marker moves.
Recorded status: Formal/Identity [E] (exact solveset censuses, exact Gram entries, exact Cl(16) implementers, 40-digit gap-certified inertia spectra, continuum axis elimination, precondition controls) + [C] (face #13 = a reformulation of the bit) + [O] (mark-decorated states / interacting A_hol); the bit stays the one [C] carrier input; NO marker moves
Dependencies, status detail and source
Canonical status: KILL (honest negative, preregistered): free RP and Theta existence are side-blind on the whole M(delta) family -- the eighth side-blind test on the v512 scoreboard (7 -> 8), face #13 added [C] (12 -> 13; since 13 -> 15 by v528); the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; [O] gap: mark-decorated/interacting states -- the mark-decorated (free-plus-twist) half since decided side-blind by v525 (the ninth side-blind test, 8 -> 9); what remains is the genuinely interacting A_hol
Dependencies: SEAM.TAU.FLAG.01; SEAM.BIT.FREEDOM.01; SEAM.BIT.ORIGIN.01; SEAM.CLOCK.RIGIDITY.01; WOIT.THETA.FREE.01; v506; v507; v510; v512; v519
Scripts: v521_seam_bit_rp_blind.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 588Original ledger status
WOIT.BETA1.GSO.01
THE WOIT-BETA1 MILESTONE EXECUTED (2026-07-22; one module, 16 checks, ~5 s; typed result, verdict UNDECIDED per the frozen preregistration -- 'the clock is time-like, GSO is the gauge datum'): contract clause beta_1 ('Theta on the gauge-invariant subalgebra + gauge-fixed RP on the equivariant SDYM(E8) sector'; kill test (2): 'RP fails after gauge fixing') executed on the free/equivariant seam skeleton. FINDING: the preregistered [C-1] clock-tower reading of 'gauge' is structurally the WRONG operationalisation. (1) HERMITICITY WITNESS (the mechanism): the mu4 clock average violates Hermiticity EXACTLY -- the one-step insertion T_1 = <theta(e_a), alpha_S(e_b)> has entry -i/(8 sin(5 pi/16)) where the conjugate transpose demands +i/(8 sin(5 pi/16)); the pairing is complex-SYMMETRIC (745 entries Hermitian-matching, 96 anti-matching, 0 violations): 'OS-symmetric' is STRICTLY WEAKER than Hermitian -- 'positivity after gauge fixing' is not well-posed for the clock reading. (2) TIME-LIKE TYPING: ALL 16 dihedral reflection axes of the NS seam circle INVERT the clock lift (R S R^-1 = S^-1 exactly), NONE commutes -- the mu4 clock IS Woit's euclidean rotation (the time translation itself); the theta-compatible (gaugeable) part of the Z8 tower is EXACTLY its 2-torsion {1, (-1)^F} (Hermiticity census over all powers; alpha^4 = the full wrap = the 2 pi rotation of the seam = fermion parity, lattice spin-statistics). (3) POSITIVE PART -- GSO-FIXED RP HOLDS EXACTLY: N = 16 even deg <= 2 parity-projected bond-cut Gram (29, 0, 0) PD (min eigenvalue 1.78e-6 at 40 digits); N = 8 complete half algebra: the projected 16x16 Gram kills all odd rows/columns exactly and its even block is (8, 0, 0) PD (3.35e-3) with NO degree truncation; the site-cut defect SURVIVES gauge fixing (inertia (7, 9, 6)) -- the RP bond placement is gauge-invariant information; family A keeps failing ((17, 12, 0) indefinite vs family D's (29, 0, 0)); Kramers: Theta_t^2 = id on A^G (the (-1)^F class does not penetrate the even subalgebra), Theta_Fock restricts with Theta^2 = +1; Ramond control: the wrap +1 'true Z4' lift fails state invariance -- the NS/Z8 tower is forced. (4) KILL-TEST BOOKKEEPING: kill test (1) stays discharged also gauge-invariantly (Theta^2 = +1 on A^G, Kramers class trivial; RP separates the families on the invariant sector); kill test (2)'s free shadow does NOT fire (no legitimate Hermitian gauge-fixed form has a negative direction); both stay formally live on the interacting algebra A_hol. (5) WRONG-PROJECTION CONTROLS: the invariant-dimension chain parity 120 > deck 64 > clock 32 is strict, but Hermiticity of the projected form singles out PARITY alone (deck and clock averages non-Hermitian): projecting by the finer 'gauge' groups is structurally ill-posed pre-quotient. TRANSPARENCY (documented in full): the first frozen run scored 6/13 -- the preregistered clock-reading checks failed exactly as the mechanism predicts, and the preregistered deg-2 clock-invariant dimension 30 was a combinatorial error (correct orbit census: 28 free shift-4 quadruples + 4 halved antipodal doublets = 32); the preregistration text is unchanged, the verdict follows the frozen [C-3] logic (Hermiticity failure => structural-failure branch => UNDECIDED). [C] CONTRACT PRECISION (iii) (prose, no marker): 'gauge-invariant subalgebra' at the free level means the GSO/fermion-parity Z2 -- the only theta-compatible part of the mu4 tower (the free-fermion shadow of the E8 glue: (E8)_1 = even NS of SO(16)_1 + R spinor); the clock is the euclidean rotation itself (timelike), its equivariant statement moves to beta2 (OS quotient first, then the clock as reconstructed transfer operator). [O] beta1 PROPER stays open (the clock-equivariant statement needs the beta2 OS quotient); both kill tests live on A_hol; WOIT.OS.TWISTOR.01 stays [O]. Discovery provenance: woit_os_beta1_gauge_invariant_theta_probe.py (16/16) in experiments/tfpt-discovery/ (2026-07-22). NO marker moves.
Recorded status: UNDECIDED per the frozen preregistration ([E] exact Hermiticity witness + censuses, time-like reflection census, GSO 2-torsion identification, 40-digit gap-certified GSO-fixed RP certificates, exact Cl(16) Kramers restriction, Ramond/wrong-projection/site-cut/family-A controls; [C] contract precision (iii) -- prose only; [O] beta1 proper via beta2, kill tests live on A_hol); NO marker moves
Dependencies, status detail and source
Canonical status: UNDECIDED (typed, per the frozen preregistration): the [C-1] clock-tower reading of 'gauge' fails Hermiticity structurally (the mu4 clock is euclidean-time-like); the gaugeable part is exactly the GSO/fermion-parity Z2, under which gauge-fixed RP HOLDS ((29,0,0)/(8,0,0) PD); kill tests (1) and (2) do NOT fire at the free level; contract precision (iii) added (prose); beta1 proper re-routed via beta2; WOIT.OS.TWISTOR.01 stays Open
Dependencies: WOIT.OS.TWISTOR.01; WOIT.THETA.FREE.01; SEAM.BIT.RPBLIND.01; SEAM.CLOCK.RIGIDITY.01; v510; v519
Scripts: v522_woit_beta1_gso_gauge.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 589Original ledger status
CELEST.WP5E.WM.01
THE CONSTRUCTIVE w_m DERIVATION EXECUTED (2026-07-23; the residual [O] of v516/v520, one module, 26 checks, ~1 s; verdict ERFOLG per the frozen preregistration): is the completion normalisation 1/det_j the standard Atiyah-Bott/holomorphic-Lefschetz fixed-point weight AND the Quillen-factorised zeta determinant of the twisted fibre Laplacian -- i.e. COMPUTED rather than declared? YES, from three independent sources. (1) ATIYAH-BOTT (route i): the equivariant mode ledger of the fibre C^2 -- c_n = sum_{a+b=n} i^{j(a-b)} -- equals the closed form 1/((1-q i^j)(1-q i^{-j})) exactly in Q(i) for ALL n <= 120; the closed form is REGULAR at q = 1 (the twisted sectors carry no volume pole) with Abel value (1/2, 1/4, 1/2) = 1/det_j, det_j = det(1-g^j) = (2, 4, 2); the (C,2) Cesaro means converge in exact arithmetic; the fixed-point factor SPLITS OFF EXACTLY at every truncation level d in {7, 12, 25}, for the phased (skeleton) AND the v520-forced unphased (completion) trace alike -- the Abel-limit contact_j = (Q^(0) - Q^(j))/det_j is the v516 contact vector COMPUTED, not declared. (2) ZETA/QUILLEN (routes ii/iii): det_zeta of the g^j-twisted circle Laplacian (eigenvalues (n + j/4)^2) = 4 sin^2(pi j/4) = det_j EXACTLY (Lerch + reflection formula symbolically; Hurwitz certificates ~1e-41); the Quillen split gives det Delta = det_j^2 with |det dbar| = det_j and the REAL POSITIVE holomorphic section unique via the SU(2) conjugation pairing; the delta-1f f1f3 modular block at the (0, b) nodes carries the exact constant term 1/det_b (deviations <= 5.2e-28) -- the v520 transport machinery carries the AB zero-mode weight verbatim. (3) CONSISTENCY CHAIN: the derived weight reproduces the v516 chain NUMBER BY NUMBER -- w_m = sum_j (1-i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4h_m = |mu4| h_m = -4 ch2(T_m); T5 = 0 at every scale; h_2 : h_1 = 4 : 3; the T3 budget 32-8c forces c = 4 = |mu4| uniquely (leftovers 24/16/8/0/-8); per-sector Okubo squares (18, 9, 18)<x,x>^2; total 45<x,x>^2 = (5/4) x 36<x,x>^2; Phi_T3: 32 -> 0, Phi_P: 72 -> 0; psi(A_fix) = +64, psi(contact) = -64. (4) NEGATIVE CONTROLS: 1/det^2 gives w' = (0, 5/8, 1, 5/8) with ratio 8:5, leftovers (T5, T3) = (2, 12) and a Quillen contradiction (det^4 vs measured det^2); 1/|1-i^j| gives w''_1 = 1+sqrt2 notin Q with T5/T3 leftovers exact in Q(sqrt2); the Z2/Eguchi-Hanson anchor PASSES with the same derivation (Abel = zeta = det(1-g) = 4, w = 1/2 = |Z2| h^{A1}, 9<x,x>^2 = (1/4) x 36, both scale teeth clear only at c = 2 = |Z2|); the SO(16)/D8 KILL fires (T5 = 20, T3 = -40); diag(i,i) breaks the zeta = AB identity ITSELF (real (2,4,2) vs complex (2i,4,-2i), no real Quillen section, w_1 != w_3); k = 3, 5 orbifolds: w_m = m(k-m)/2 = k h_m exactly in Q[x]/Phi_k, Dedekind (k^2-1)/12, product k^2 -- the weights wander correctly with the centre count, only k = 4 = |mu4| carries the E8-glue chain. [C] TYPED PREMISES (the mandatory fence): TP-REG (Abel/Cesaro/zeta regularisation IS the definition of the equivariant character), TP-Q (Quillen structure of BCOV F1 = v520 TP-4), TP-NUM (unphased numerator = the v520 ERFOLG-A decision layer under its TP-1..TP-4), TP-CH (the insertion channel (0, j) computes the box-channel weight). [O] the GLOBAL BCOV integral on PT/Z4 beyond the fibre zero-mode factor (the tau-integrated dressing lives in the v518/v520 scaffold); the resolved-ALE route (v514/v517) not built; SEAM.EQUIV.TWISTOR.01 untouched. Discovery provenance: celestial_seam_wp5e_wm_bcov_derivation_probe.py (26/26) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves anywhere.
Recorded status: Formal/Identity [E] (exact Q(i)/Q(sqrt2)/cyclotomic mode ledgers, Abel values, tensor-trace splitting, reflection-formula zeta determinants, Quillen arithmetic, delta-1f block constant terms, the full v516 chain, all controls -- sympy/Fraction exact, Wolfram-mirrored; numeric documented: Hurwitz/Lerch and stripped block limits at 40 digits) + [C] (the typed premises TP-REG/TP-Q/TP-NUM/TP-CH) + [O] (the global BCOV integral beyond the fibre zero-mode factor)
Dependencies, status detail and source
Canonical status: ERFOLG (the w_m normalisation DERIVED at probe level): 1/det_j is 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 sin^2(pi j/4) with the unique real Quillen section; the delta-1f block constant term 1/det_b) and the v516 chain closes number by number (w = 4h, c = 4 = |mu4|, squares (18, 9, 18), total 45<x,x>^2, psi +-64); all negative controls behave (Z2/EH anchor passes at c = 2 = |Z2|, so16 kill fires, diag(i,i) breaks the zeta = AB identity, k = 3/5 weights wander correctly); typed premises TP-REG/TP-Q/TP-NUM/TP-CH; the residual [O] narrows to the global BCOV integral beyond the fibre zero-mode factor; no marker moves
Dependencies: CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.MEASURE.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.TWISTOR.01; v505; v514; v516; v517; v518; v520
Scripts: v523_celestial_wp5e_wm_derived.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 590Original ledger status
WOIT.BETA2.OS.01
THE WOIT-BETA2 MILESTONE EXECUTED (2026-07-23; one module, 20 checks, ~5 s; verdict SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii)): contract clause beta_2 ('the OS quotient of the free system made explicit -- success: (H, Omega) constructed from the v519 bond-cut form with the clock acting unitarily; kill: the quotient degenerates (zero or indefinite completion)') executed. (1) H_phys EXPLICIT: N = 16 (deg <= 2): the 37x37 bond-cut OS Gram is exactly Hermitian, parity-block-diagonal, inertia (37, 0, 0) PD (min eigenvalue 1.7801e-6 at 40 digits), null space {0}, dim 37 = 29 (+) 8; N = 8 (complete half algebra, no degree truncation): (16, 0, 0) PD (min 3.3471e-3), dim 16 = 8 (+) 8 = 4^2 -- compact euclidean time reconstructs a THERMAL (KMS) representation; exact certificate sin^2(3pi/8) - sin(pi/8) sin(5pi/8) = 1/2. (2) TRANSFER SEMIGROUP (Klein-Landau): tau_k = omega(theta(a) alpha_k(b)) exactly Hermitian on every shrinking domain D_k (k = 1..7 at N = 16, dims 29, 22, 16, 11, 7, 4, 2), chain identities exact, vacuum fixed exactly; the positivity pattern IS the v519 site/bond dichotomy: even k PSD via the exact square identity T(2j) = A_j*A_j ((22,0,0)/(11,0,0)/(4,0,0)), odd k indefinite with exactly zero one-particle diagonal ((10,12,7)/(5,6,5)/(2,2,3)) -- the one-step transfer is NOT positive (the free chirality/staggering datum, kill-test-3 shadow sharpened), its even powers ARE. (3) THE CLOCK = T^{N/4}: N = 16: tau_4 PD (11, 0, 0) (min 6.6821e-5), compressed spectrum [0.0194517, 1.64144] with vacuum eigenvalue exactly 1, spectral projections certified ~1e-40; N = 8: compressed spectrum EXACTLY {1, sqrt(2)-1} = {1, 1/delta_Silver} in both parity sectors -- the silver-midpoint axes of the v519 mu4 torsor return as the exact clock-transfer eigenvalue; the reconstructed rotation group U(s) = exp(isH) is unitary with the group law (~1e-40) -- per precision (iii) the [C]-operationalisation of 'the clock acting unitarily'. (4) v522 RESOLUTION: the clock-insertion census (745, 96, 0) reproduced; EVERY anti-matching entry is a wrap overlap and every overlap-free entry matches -- the pre-quotient non-Hermiticity is EXACTLY the domain/wrap artifact; restricted to the quotient domain the same insertion IS tau_4 entrywise: what dissolves in beta2 is the ill-posedness of clock positivity (the clock now has spectral calculus); what remains time-like is the euclidean-rotation character itself. (5) KMS DEVIATION (pre-declared, exactly the declared witnesses): NO contraction on the compact circle -- the edge mode expands by C(1)/C(3) = 1 + sqrt(2) = delta_S exactly (N = 8), det(G - tau_4) < 0 on the odd one-particle block (N = 16, lambda_max = 1.6414 > 1): a typed KMS finding, not a beta2 failure. (6) GSO/THETA: fermion parity descends G-unitarily (H_even (+) H_odd exact); theta_cut and the deck candidate do NOT act on H_phys (support censuses -- theta_cut IS the metric); the PERPENDICULAR torsor mirror descends anti-unitarily (eta_perp in {+-i}), Theta_phys^2 = +1 on EVERY sector incl. odd (the quotient is KRAMERS-FREE), time-reverses the semigroup, and theta_cut o theta_perp = alpha_{N/2} exactly (the torsor closes onto the deck). (7) CONTROLS: site cut indefinite ((3,3,1)/(2,2,4)) -- the contract kill branch fires for the site placement; family A (4,4,0) no quotient; anti-chiral state (8,8,0) -- quotient existence itself selects the chiral orientation; wrong semigroup direction non-Hermitian off-domain (census (58, 6, 0), all mismatches wrap-overlap), Hermitian on the mirrored domain. KILL-TEST BOOKKEEPING: (1), (2) strengthened, (3) shadow sharpened, none fires; (4)-(7) untouched; all seven stay formally live on A_hol. TRANSPARENCY: run 1 scored 18/20 -- a sympy simplify failure on the TRUE product formula sin(7pi/16) - sin(5pi/16) = 2 cos(3pi/8) sin(pi/16), fixed by a Laurent-polynomial certificate; no criterion, tolerance or expectation changed. [C] FENCE: 'the clock acting unitarily' operationalised per precision (iii) as the reconstructed transfer/rotation structure. [O] beta3 (the PT <-> PT* duality vs sigma_std) is the next milestone; WOIT.OS.TWISTOR.01 stays [O]. Discovery provenance: woit_os_beta2_os_quotient_probe.py (20/20) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves. [2026-08-01 XXVI: the reconstructed net of this module now carries the free gamma slice -- v608 (mirror exclusion sector-exact, multiplicity-free generation, mark transport); see WOIT.GAMMA.FREE.01.]
Recorded status: SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii) ([E] exact Hermiticity/semigroup/square identities, exact clock spectrum {1, sqrt(2)-1}, exact wrap-artifact resolution and censuses, 40-digit gap-certified inertia/spectral certificates; [C] the precision-(iii) operationalisation of 'the clock acting unitarily'; [O] beta3 next, all seven kill tests live on A_hol); NO marker moves
Dependencies, status detail and source
Canonical status: SUCCESS ([C]-typed per precision (iii)): the OS quotient of the free system is explicit -- H_phys PD and nondegenerate at both levels (37 = 29+8; 16 = 4^2 thermal/KMS), the Klein-Landau transfer semigroup exactly Hermitian with the site/bond dichotomy as its positivity pattern, the mu4 clock = T^{N/4} positive with spectral calculus (N = 8 spectrum exactly {1, sqrt(2)-1}) and a reconstructed unitary rotation group; the v522 non-Hermiticity is exactly the wrap artifact; the pre-declared KMS deviation carries exactly the silver witnesses; Theta_phys^2 = +1 Kramers-free; no kill fires, all seven stay live on A_hol; beta3 next; WOIT.OS.TWISTOR.01 stays Open
Dependencies: WOIT.OS.TWISTOR.01; WOIT.THETA.FREE.01; WOIT.BETA1.GSO.01; SEAM.BIT.RPBLIND.01; v510; v519; v522
Scripts: v524_woit_beta2_os_quotient.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 591Original ledger status
SEAM.BIT.TWISTBLIND.01
THE TWIST-STATE ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-23; one module, 20 checks, ~80 s; an honest, decided NEGATIVE result in the v508 style -- the NINTH side-blind test on the v512 scoreboard, 8 -> 9): do mark-decorated STATES (Kadanoff-Ceva twist/defect insertions, sigma-gauge arc decorations, mu4/Bogoliubov bond defects -- the v521 [O] gap, everything Pfaffian/Wick-computable) make RP side-sensitive on M(delta) = {+-1, +-e^(i delta)}? NO. (1) ALL LIFTINGS WELL-DEFINED AND BLIND: (a) sigma-gauge (Z2): sigma o r = sigma on every swap axis makes the twisted Gram a diagonal unitary congruence D M D -- spectra IDENTICAL to untwisted (dev 0.0); (b) Kadanoff-Ceva 4-twist insertion omega(D .)/omega(D): well-defined on the whole N = 32 ladder (omega(D) real nonzero, deck-consistent; the N = 16 odd-m degeneration -- omega(D) = 0 at m = 1, imaginary at m = 3 -- is exactly the C(even) = 0 checkerboard artifact); its RP SPECTRA are the FIRST free-class data of the program that depend on delta (min shift 0.242, pairwise up to 1.05 -- the mark-anchored strings break the v521 rotation-equivalence mechanism), but the INERTIA is (16, 0, 0) PD with the SAME eta = +i for EVERY m = 1..7 incl. pi/2 +- pi/8, both swap axes, even sector (29, 0, 0) -- the decoration sees delta, the positivity does not; (c) the mu4 defect at beta = pi/2 is PURE PLANE GAUGE (one state up to gauge, signed permutation = extended monomial class, RP-invisible like (a)); (c') the genuine Bogoliubov defect at beta = pi/4: the sign pattern becomes a real datum and Theta-compatibility selects EXACTLY 2 of 16 patterns (the crossed pattern forced by the NS wrap signs; the naive alternating pattern FAILS), the winner is pure and genuinely non-monomial (|C(even)| up to 0.45) -- still PD everywhere, spectra again IDENTICAL. STRUCTURE THEOREM (empirical, mechanism exact): the defect planes never straddle a cut bond (marks avoid the cuts), so O block-decomposes across the cut and the Theta precondition turns every twisted Gram into an orthogonal congruence U M U^T -- EVERY Theta-compatible quasi-free mark decoration is RP-spectrally INVISIBLE: the quasi-free class cannot even carry delta into its RP datum; only the insertion FUNCTIONALS do, and there positivity stays blind. (2) SUB-RESULTS: the total defect energy E_def = 1.2752872 for EVERY m (40-digit spread 4e-40) -- delta-blind; the 4-twist Casimir ln|omega(D)| measures delta smoothly (-0.890 .. -1.348) but is EXACTLY mirror-symmetric under m <-> 8-m (dev 1.15e-40) -- the delta <-> pi-delta equivariance makes pi/2 the symmetric point of every invariant readout: a family gauge, never a side selector; the twisted parity <Gamma>_tw = +1 for every m (the (-1)^F/Kramers class untouched by every decoration). (3) TWO BIT-PRESUPPOSING pi/2 STRUCTURES (the harvest): the eta flip +i -> -i on the mark-fixing axes (sigma o r = -sigma, odd sector exactly negated, even sector unchanged); the twist frustration of the mark-fixing mirror (theta maps D_short <-> D_long; the theta-closed symmetrized insertion is Hermitian but INDEFINITE (4, 4, 0) for both eta -- the lattice shadow of the Ising twist field's mirror-oddness) -- both formulable ONLY on the fixing axes existing iff delta = pi/2: they PRESUPPOSE the bit (v512 facet class), no selector. (4) NEGATIVE CONTROLS: the twist-free limit reproduces v519/v521 exactly (dev 0.0); the site cut keeps failing in every decorated state; the v512 counterwitness delta_cw = atan(4/3) is ARC-EQUIVALENT at N = 16 to the blind member delta = pi/4 (identical decorated state, integer incidence) and carries no lattice mark-compatible reflection -- no decorated-state selector can exclude it without excluding a blind member; a single twist string is ODD, omega(D) = 0 identically (twists exist only in mark PAIRS); the deck-breaking two-twist decoration is defective -- the deck-paired FOUR-twist decoration is the minimal well-defined one. VERDICT: KILL exactly as preregistered -- the NINTH side-blind test (8 -> 9); the free-plus-twist class (everything Wick-computable) is EXHAUSTED: only a genuinely INTERACTING A_hol whose OS data are NOT Pfaffian-reducible to the chiral vacuum could still see the bit. The alignment bit remains genuine discrete input. Discovery provenance: seam_alignment_bit_twist_state_probe.py (20/20) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves.
Recorded status: Formal/Identity [E] (Pfaffian-exact insertion machinery cross-validated three ways, exact integer incidence frame, exact congruence mechanisms, 40-digit gap-certified inertia/spectrum/energy/parity certificates) + [C] (each lifting is a construction choice, all tested) + [O] (the genuinely interacting A_hol with non-Pfaffian-reducible OS data); the bit stays the one [C] carrier input; NO marker moves
Dependencies, status detail and source
Canonical status: KILL (honest negative, preregistered): every well-defined mark-decorated state functional in the free-plus-twist class keeps RP positive on the always-existing cuts along the whole M(delta) ladder -- the NINTH side-blind test on the v512 scoreboard (8 -> 9); quasi-free decorations are RP-spectrally invisible (exact congruence mechanism), insertion spectra and the 4-twist Casimir measure delta but never reach the positivity verdict, the only pi/2-exclusive structures presuppose the bit; the free-plus-twist class is EXHAUSTED -- the interacting half is since decided by v529 (SEAM.INT.FKTOY.01): the TENTH side-blind test (9 -> 10) on genuinely non-Wick dynamics, while Kill-Test-2 fires at toy level (RP breaks for every g > 0; straddle law); the alignment bit remains genuine discrete input
Dependencies: SEAM.BIT.RPBLIND.01; SEAM.TAU.FLAG.01; SEAM.BIT.FREEDOM.01; WOIT.THETA.FREE.01; v510; v512; v519; v521
Scripts: v525_seam_bit_twist_blind.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 592Original ledger status
SEAM.THERMAL.KMS.01
THE THERMAL SEAM: KMS -> NARIAI/BH BRIDGE (2026-07-23; one module, 22 checks, ~8.4 s; verdict SUCCESS): the reconstructed free OS quotient of the 16-Majorana NS seam circle is KMS, and its temperature normalisation CLOSES onto the Nariai/BH chain as the THIRD LEG of c3. (1) beta MEASURED, NOT ASSUMED: the circle kernel C(d)=(2/N)/sin(pi d/N) has exactly one finite thermal-mode representation with detailed balance; N=8: one real frequency omega=arcsinh(2^{-3/4}), weight ratio kappa=q^{-8} EXACTLY => beta=8=N (Q-polynomial identity Q^2-(2+sqrt2)Q+1=0); N=16: both mode pairs real, pairing exponent exactly (N/2)+1=9 => beta=16=N; anchor Pi(u_i-2)=sqrt2 = Pi sinh omega_i * 2^{7/4} pin at both levels; wrong beta {N/2,N/4,2N} excluded (gaps 0.0937/0.3126/0.0108; N/2 witness C(1)-C(3)=sqrt2*C(3) != 0 exact). (2) T_seam=1/N per clock step; in angle units (step=2pi/N, v519 pin): beta_angle=2pi EXACT, T_seam=1/(2pi)=4 c3 -- N-independent. (3) MODULAR HAMILTONIAN CLOSED: rho_OS faithful, spectrum p={(1+-nu1)(1+-nu2)/4} with nu1=cos(pi/24), nu2=cos(7pi/24) exact; K=eps1 n1+eps2 n2 with eps1=2 ln cot(pi/48), eps2=2 ln cot(7pi/48); full Tomita structure (KMS-beta=1 on all 256 pairs, residual 2.5e-38, J Delta J = Delta^{-1}). (4) THE c3 CLOSURE (class-1 selection in the frozen anti-numerology lattice, exact r=1): beta_angle=2pi=1/(4 c3) -- T_seam=4 c3 is the Bisognano-Wichmann/Hawking normalisation from v208; chain: T_H=c3/M=1/(8pi M) (the axiom IS the Hawking coefficient, here from the seam KMS), SdS 1/(4pi)=2 c3, Nariai T_N=4 c3 sqrt(Lambda), v104 cross-link 2H/T_N=4pi=1/(2 c3) exact. [C]-fence: reading "seam euclidean circle = thermal circle of the reconstructed horizon dynamics" -- temperature as THIRD LEG of c3 beside geometry and anomaly. (5) ENTROPY: S(8)=0.52187, S(16)=0.63510, S(32)=0.75006 nats; DeltaS/ln2 -> 1/6 = c_chi/3 monotonically (chiral c=1/2 log law confirmed); HONESTLY FAILED: v129 horizon fractions {1/3,2/3} and v190 floor do NOT transfer (S/S_max=0.376/0.229, not N-stable) -- temperature bridge closes, entropy-fraction bridge does not. [C-5] typed non-gating: naive clock reading fails ({1,sqrt2-1} are NOT e^{-Delta K} ratios; gaps 0.0496/0.1710), Tomita flow != transfer flow (0.45-0.67); exact replacement: sqrt2-1 = C(3)/C(1) = 1/(2 cosh 2 omega - 1) -- the silver eigenvalue is a thermal kernel ratio. (6) NEGATIVE CONTROLS: site (2,2,4) no state; family A (4,4,0); anti-chiral (8,8,0); NON-COMPACT: Stieltjes => kappa=0, beta=inf, T=0 -- the temperature hangs exactly on compactness of the euclidean circle. Discovery provenance: seam_thermal_kms_nariai_bridge_probe.py (22/22). NO marker moves.
Recorded status: SUCCESS ([E] exact sympy/cyclotomic + 40-digit Tomita certificates; [C] bridge reading typed; [C-5] non-gating clock-vs-modular findings); NO marker moves
Dependencies, status detail and source
Canonical status: SUCCESS: beta MEASURED = N at both levels; T_seam = 4 c3 = Bisognano-Wichmann/Hawking normalisation; modular Hamiltonian closed; c3 third leg class-1 selected; entropy log-law confirms, horizon fractions do NOT transfer; non-compact => T=0; no marker moves
Dependencies: WOIT.BETA2.OS.01; WOIT.OS.TWISTOR.01; v58; v104; v208; v519; v524
Scripts: v526_seam_thermal_kms_nariai_bridge.py
Location: tfpt_3;tfpt_research_contracts;tfpt_horizon_readouts;origin_theory;tfpt_1
Original CSV, line 593Original ledger status
SEAM.CLOCK.SILVER.01
THE SILVER CLOCK EIGENVALUE EXPLAINED AND DEMYSTIFIED (2026-07-23; one module, 22 checks, ~10 s; double verdict, anti-numerology style): STRUCTURE = SUCCESS (closed-form origin of {1, sqrt2-1}); CONNECTION = KILL (frozen-registry readout census, 0 hits). (1) STRUCTURE SUCCESS: {1, sqrt2-1} closed -- diagonal Hankel pencil at N=8, tan(pi/8)=C(3)/C(1), doubling = exact second quantisation, carrier = silver-midpoint axes of the mu4 torsor, gap = arcsinh(1)=gd^{-1}(pi/4). (2) LATTICE DATUM, NOT CONTINUUM: N-scaling (N=8..24) shows pure N=8/16 Majorana lattice datum; positive clock only for N==0 mod 8; golden family as N=10 control. (3) CONNECTION KILL: preregistered 11466-candidate census over the 16 frozen numbers: 0 hits above null expectation; placebos (golden ratio, plastic number) comparable -- NO readout connection. Honest negative in the v100/v513 style. (4) Cross-link to v526 replacement identity: sqrt2-1 as thermal kernel ratio C(3)/C(1)=1/(2 cosh 2 omega - 1). Discovery provenance: seam_clock_silver_spectrum_probe.py (22/22). NO marker moves.
Recorded status: STRUCTURE SUCCESS + CONNECTION KILL ([E] exact sympy Hankel/trig + 40-digit census); NO marker moves
Dependencies, status detail and source
Canonical status: STRUCTURE SUCCESS (closed-form origin of {1,sqrt2-1} via Hankel pencil / tan(pi/8) / second quantisation / silver-midpoint carrier / arcsinh(1) gap) + CONNECTION KILL (11466-candidate census: 0 hits above null; placebos comparable); lattice datum not continuum; no marker moves
Dependencies: WOIT.BETA2.OS.01; SEAM.THERMAL.KMS.01; SEAM.TAU.FLAG.01; v519; v524; v526
Scripts: v527_seam_clock_silver_spectrum.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 594Original ledger status
SEAM.BIT.TWISTCLASS.01
THE ALIGNMENT BIT AS AN EXACT MEASURABLE TWIST-CLASS CHOICE (2026-07-23; one module, 18 checks, ~46 s; verdict SUCCESS -- the physical definition): the alignment bit is the choice of which twist class nature realizes, read out by the order parameter O. (1) FACET #14 (eta-flip <=> delta=pi/2): both directions exact (sigma o r = -sigma on all four fixing axes with eta jump +i->-i; off pi/2 on EVERY axis sigma o r = +sigma; CARDINALITY LEMMA: sigma o f = -sigma forces |A+| = |A-| => 4m = 32-4m <=> m=4; g-class census over all 224 axes: flip class exactly at {15,31} for m=4). (2) FACET #15 (twist-frustration <=> delta=pi/2): theta exchanges D_short <-> D_long exactly, minimal theta-closed insertion unique, Gram indefinite (4,4,0)/(8,8,0) exactly at pi/2; off reducible and PD; same cardinality lemma locks; side finding omega(D_s)=omega(D_l) (complement-string identity, 40-digit). (3) ORDER PARAMETER: O = flip-axis fraction = 1/2 at m=4, exactly 0 else (whole ladder + counterwitness + 2-mark anchor); class alternation (-,+,-,+) around the torsor = nontrivial Z2 character of the Z8 clock-tower shadow; gauge-robust under sigma global flip, admissible site redress, mu4 overlay in all variants, string orientation; rejected candidates with teeth (sign omega(D), spectral shift, v510 index). (4) UNIFICATION THEOREM: eta-flip = frustration = flag-transitivity are ONE Z2 invariant (same arc system, A+ = supp(D_short)); the v510 Kramers class is ANOTHER (constant on the family, exact Cl(16)) -- Kramers = POSITION half (derived), twist class = MODULUS half (the input). v512 web grows 13 -> 15 facets. [C] MEASUREMENT SKETCH (principle only): defect transport around the axis torsor accumulates the eta holonomy = relative pi phase iff bit set -- the bit is in principle interferometrically readable. Honest fence: the bit remains formal input -- a definition is not a derivation. Discovery provenance: seam_bit_twist_class_definition_probe.py (18/18). NO marker moves.
Recorded status: SUCCESS ([E] exact integer/symbolic + 40-digit certificates; [C] measurement sketch principle-only); the bit remains formal input; NO marker moves
Dependencies, status detail and source
Canonical status: SUCCESS: the bit is PHYSICALLY DEFINED as the twist-class choice (facets #14/#15 both directions; O=1/2 at m=4; unification with flag-transitivity; Kramers typed as POSITION half); [C] interferometric measurement sketch; bit remains formal input; v512 web 13->15; no marker moves
Dependencies: SEAM.TAU.FLAG.01; SEAM.BIT.RPBLIND.01; SEAM.BIT.TWISTBLIND.01; SEAM.BIT.FREEDOM.01; v510; v512; v521; v525
Scripts: v528_seam_bit_twist_class_definition.py
Location: tfpt_3;tfpt_research_contracts;introduction
Original CSV, line 595Original ledger status
SEAM.INT.FKTOY.01
THE MINIMAL INTERACTING FIDKOWSKI-KITAEV SEAM TOY (2026-07-23; one module, 24 checks, ~97 s; triple-verdicted -- the FIRST firing Kill-Test-2 shadow). F1 = KILL, F2 = KILL, F3 = ERFOLG. (1) F1 = KILL (THE MOST IMPORTANT PART): Theta exists exactly on the interacting model (U_r^2=2^8, Theta^2=+1, clock-tower inversion conj_V·V=4096, [Theta,H_g]=0 exact, Theta Omega_g = Omega_g) -- Kill-Test 1 does NOT fire; BUT Kill-Test 2 FIRES AT TOY LEVEL: RP breaks in the interacting ground state for every g>0 -- inertia ladder (37,0,0) at g=0 -> (33,4,0) at g=1/4,1/2 -> (31,6,0) at g=1 -> (29,8,0) at g=2 (most negative EW -4.5e-2, seven orders above threshold); Gibbs beta=2 exact same ladder; g=-1: (19,18,0). MECHANISM: interference (neither crossing nor half-local alone breaks -- each (37,0,0)); STRADDLE LAW (24/24): RP fails exactly on quartet-straddled cuts, stays PD on quartet-avoiding. MANDATORY FENCE: ONE toy, ONE interaction class, [C] flat-band parent -- narrows the Woit route (every A_hol must protect RP against exactly this mechanism), does not close it; WOIT.OS.TWISTOR.01 stays Open, but the contract MUST document the firing toy shadow as a named threat (Kill-Test-2 paragraph + the straddle law as a concrete hurdle for beta3/gamma). (2) F2 = KILL: the TENTH side-blind test (9->10), the first with genuinely non-Wick-computable dynamics -- the interaction sees delta massively (spectral spread 1.32, gaps 0.31-1.66, overlaps 0.869-0.962), but the mark-axis mirror Theta_15 maps H(m)->H(8-m) EXACTLY (Fraction identity); all side data mirror-equal (8e-15/7e-16/5e-15); Theta_7 for m=1<->7 obstructed by exactly two NS wrap signs; counterwitness anchors to identical dynamics as m=2. Door narrows: only dynamics that break mirror covariance in BOTH torsor orbits. (3) F3 = ERFOLG: grading exact ([H_q,(-1)^F]=0, <Gamma>=+1 incl. g=100); Z8 backbone: Utilde^2=256 Gamma=(-1)^F nonsplit, V^2=256 Utilde (the clock tower IS the root of the deck), Theta inverts the tower; FK anchor single quartet {-1,+1}x128, m=4 at g->inf binomial ladder {16,64,96,64,16}; OS quotient at g>0 constructive on the pi/2 model (Gram (37,0,0), tau_4 PD (11,0,0), vacuum fixed). (4) CONTROLS: Theta-incompatible quartic makes Gram non-Hermitian (0.46 vs 1e-16); site (3,3,1). Discovery provenance: seam_interacting_toy_fk_probe.py (24/24). NO marker moves. UPDATED 2026-08-27 (v972): the straddle law is REFINED to the ODD-SPLIT LAW -- the Jaffe-Pedrocchi sufficient condition, made decidable in v972 (unique crossing matrix B; 'B Hermitian AND -B PSD' a finite check), predicted RP survival on CENTER-straddled cuts (m = 4 model, axes 7/15, 2+2 mirror split) and direct measurement CONFIRMED it ((37,0,0) at g = 0.5/1/2); a straddled cut kills RP iff the split is odd (1+3). The confusion matrix vs measured RP is perfect over 35 cells (23/12/0/0) and the mu4-covariant quartic class (dim 464) is EMPTY on the basis (SEAM.INT.ODDSPLIT.01). The fence (one toy, one interaction class, [C] flat-band parent) is unchanged and inherited by the refinement.
Recorded status: F1=KILL / F2=KILL / F3=ERFOLG ([E] exact Fraction/Clifford + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves
Dependencies, status detail and source
Canonical status: F1=KILL (Kill-Test-2 fires at toy level: RP breaks for every g>0; straddle law 24/24; Kill-Test-1 does NOT fire); F2=KILL (tenth side-blind test 9->10); F3=ERFOLG (grading+Z8+FK+OS quotient); [C] fence one toy/one class -- narrows WOIT route, does not close it; no marker moves
Dependencies: WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; SEAM.BIT.TWISTBLIND.01; SEAM.BIT.TWISTCLASS.01; SEAM.TAU.FLAG.01; SEAM.EQUIV.TWISTOR.01; v510; v512; v519; v524; v525
Scripts: v529_seam_interacting_toy_fk.py
Location: tfpt_3;tfpt_research_contracts;introduction
Original CSV, line 596Original ledger status
SEAM.STRADDLE.CONE.01
THE RP CONE ON THE INTERACTING FK QUARTETS -- THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT (2026-07-24; one module, 15 checks, ~7 s; double-verdicted; the named v534 candidate of the 2026-07-23 review round executed). V1 = KILL, V2 = ERFOLG. (1) V1 = KILL (the literal contract formalization): independent couplings lambda_q on the four mark quartets of M(delta), leading OS-Gram correction dG via first-order PT (exact reduced resolvent of the gapped flat-band parent; Hermitian to 1e-15, central-difference regression 2e-8) -- the soft-block cone K_RP = Fix(G_delta) cap {lambda: G^lead >= 0 on every admissible cut} is EMPTY for every member and both signs: the linear-pencil formalization cannot carry the selection. Recoverable leading-order content: on the STRADDLED cuts the drift sign pattern is exact -- pi/2 has POSITIVE drift for s=+ (+1.4e-4 on both straddled clock axes) and strongly negative for s=- (-3.7e-2); the asymmetric members have it REVERSED (m=2 s=+: -1.9e-2; s=-: +1.1e-4). (2) V2 = ERFOLG (THE SELECTION LAW, the central datum): among ALL well-posed members x coupling signs of the equivariant FK family exactly ONE combination keeps reflection positivity on every admissible cut over the entire grid g in {1/32..8}: delta = pi/2 WITH POSITIVE COUPLING -- all four Grams PD (37,0,0) including the v529-UNTESTED straddled clock axes 7/15, minimum eigenvalue LIFTED from the free boundary 1.78e-6 up to 5.5e-5 near g=1/4 (the pi/2 interaction pushes the Gram AWAY from the RP boundary); m=2/6 with s=+ violate RP already at g=1/32, with s=- from g=1/8. The v529 straddle law REFINES: asymmetric straddling kills RP, the symmetric straddling of the self-mirror member protects it. (3) EXACT GEOMETRY: delta = pi/2 is the UNIQUE symmetric-straddle member -- stabilizer = full clock+mirror group (rot {0,4,8,12}, refl {3,7,11,15} = FOUR admissible cuts, straddled {7,15}), quartets PARTITION the 16-circle, every straddling quartet reflection-CLOSED with exact sign +1; m=2/6 asymmetric (two cuts, one straddled); odd m no bond cut (typed v521/v525 artifact); Fix(G_delta) 1-dim throughout -- uniform ray on m=2..6, NS-wrap-TWISTED signed ray on the tight members m=1,7. (4) TYPING + CONTROLS: leading order NECESSARY (negative straddled drift kills at g=1/32) but NOT SUFFICIENT (m=2/6 s=- carry positive drift yet die at 1/8; only pi/2 extends -- the protection is NONPERTURBATIVE); every avoiding cut PD for every member/sign/g; Gibbs beta=2 reproduces the pattern on all four pi/2 cuts both signs; non-equivariant lambda=e_0 breaks well-posedness (dev 0.11 -- Fix does real work); clock-pair spectra identical to 4.4e-15; v529 B3 anchors reproduced. TYPED CROSS-LINK (no claim): the RP-selected member m=4 is exactly the carrier of the v528 twist-class order parameter O=1/2 -- dynamical selector and kinematic definition point at the SAME member. MANDATORY FENCE: ONE toy, ONE interaction class, [C] flat-band parent, deg<=2 OS bases, finite grid -- toy-level evidence FOR the bit's dynamical origin, NOT a derivation; nothing about the continuum A_hol is claimed. Transparency: run-1 preregistered verdict logic conflated formalization and substance (UNENTSCHIEDEN, mismatch typed); run-2 split V1/V2 with no tolerance change and no number changed -- note kept verbatim in the probe.
Recorded status: V1=KILL / V2=ERFOLG ([E] exact integer/Fraction census + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves
Dependencies, status detail and source
Canonical status: V1=KILL (the literal leading-order cone formalization is empty everywhere); V2=ERFOLG (THE SELECTION LAW: RP holds for exactly ONE member x sign -- delta=pi/2 with positive coupling; asymmetric members die; straddle law refined: symmetric straddling protects); first dynamical selection of the alignment bit at toy level; [C] fence one toy/one class; no marker moves
Dependencies: SEAM.INT.FKTOY.01; SEAM.BIT.TWISTCLASS.01; WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; SEAM.BIT.TWISTBLIND.01; v510; v519; v524; v528; v529
Scripts: v534_seam_straddle_cone.py
Location: tfpt_3;tfpt_research_contracts;introduction
Original CSV, line 597Original ledger status
DIAMOND.CENTER.QUOTIENT.01
THE CENTER QUOTIENT COMPILER (2026-07-23; external review round, all identities machine-confirmed before promotion; 14 checks, <1 s, sympy exact): the Sheet-Diamond center C = M(1,0) (v95) carries the fixed primitive line Cv = v with v = (-1,1,0), and the induced operator on the quotient lattice Z^3/Zv (unimodular basis P = (v,e1,e3), P^-1 C P = [[1,4,2],[0,8,2],[0,5,3]]) is EXACTLY the atom matrix A = [[8,2],[5,3]] = [[rank E8,|Z2|],[g_car,N_fam]] -- the four discrete atoms form ONE integer quotient operator. [E] INVARIANTS: tr A = 11, det A = 14 = det C, disc chi_A = 65 = 5*13, perm A = 34 = p5(a) (anchor 5th power sum), prod A_ij = 240 = |R(E8)|, det(A-I) = 4 = |mu4|. [E] SELF-CODE: the row sums C.1 = (7,11,13) = (det A/|Z2|, tr A, disc(chi_A)/g_car) EXACTLY -- the 3-dim center encodes the spectral invariants of its own 2-dim quotient; together with the fixed eigenvalue 1 this gives (1,7,11,13) = the positive CP-pair representatives of Exp(E8) = (Z/30)^x under m ~ 30-m (the CP-halved Coxeter clock; complements COX.CLOCK.01/v223). [E] RESOLVENT FACTORISATION: det(C+kI) = (k+1) det(A+kI) identically -- the v414 ladder 14 -> 52 -> 120 acquires its inner structure: (k+1) = (1,2,3,4) = (N_Phi,|Z2|,N_fam,|mu4|) times the quotient ladder det(A+kI) = (14,26,40,56) with [C] readings (dim G2, dim V26(F4), |R(D5)|, dim V56(E7)), first differences (12,14,16) = (dim g_SM, dim G2, dim S^+), and the new endpoint det(C+3I) = 224 = 248-24 = dim E8 - dim A4. [E] HONEST UNIQUENESS (corrects the review's naive claim): eigenvalue 1 is NOT unique to C -- K and Q also satisfy det(M-I) = 0 (R,L,F,J give 6,-6,4,4); but the K quotient [[14,8],[-11,-6]] (tr 8, det 4, disc 48 not divisible by 5) and the Q quotient [[3,1],[3,2]] (tr 5, det 3, det/|Z2| not integer) are NOT the atom matrix and CANNOT self-code -- C is unique in the CONJUNCTION fixed line + atom quotient + CP self-code among the seven named diamond operators. [O] the full selector-stratum ablation (all integer selectors with det R = 8, minors (2,3,5)) stays open future work. Discovery provenance: center_quotient_coxeter_modular_disc7_probe.py (76/76) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves.
Recorded status: Identity [E] (exact integer linear algebra: fixed line, unimodular quotient, self-coding row sums, resolvent factorisation, honest uniqueness controls -- sympy exact, Wolfram-mirrored) + [C] (the Lie-dimension readings of the quotient ladder, audit-typed like v414) + [O] (full selector-stratum ablation)
Dependencies, status detail and source
Canonical status: [E] the center quotient A = [[8,2],[5,3]] (atoms), self-code (7,11,13), CP code (1,7,11,13), factorisation det(C+kI) = (k+1)det(A+kI); [C] Lie readings; [O] stratum ablation; no marker moves
Dependencies: DIAMOND.CENTER.01; DIAMOND.CENTER.RESOLVENT.01; COX.CLOCK.01; v95; v223; v414
Scripts: v530_center_quotient_compiler.py
Location: tfpt_2
Original CSV, line 598Original ledger status
COX.STAGEA.TENSOR.01
COXETER STAGE A CLOSED ON THE PRIMITIVE-CHARACTER SPACE (2026-07-23; 15 checks, <1 s, sympy exact): the tfpt_1 two-stage Coxeter audit asked for a natural order-30 operator with characteristic polynomial Phi_30 on the even-flip atlas OR its 8-dimensional primitive-character space. The explicit integer operator T30 = Comp(Phi_5) (x) Comp(Phi_6) (the v418 carrier clock tensor the family/CP hexagon, 8x8) delivers the character-space alternative: [E] T30^30 = I with T30^k != I for 1 <= k < 30 (exact order 30) and chi_T30 = Phi_30 = x^8+x^7-x^5-x^4-x^3+x+1 exactly; CRT mechanism gcd(5,6) = 1: the eigenvalues are (primitive 5th) x (primitive 6th) = exactly the eight primitive 30th roots -- the v315/COX.COUPLE.01 group split Z/30 = Z/5 x Z/6 realised as ONE integer operator (carrier clock x family clock = Coxeter clock). [E] RAMANUJAN TRACE TOMOGRAPHY: tr(T30^k) = c_30(k) for ALL k = 1..30 with the multiplicative factorisation c_30 = c_5 c_6; signed divisor table (-1,1,2,4,-2,-4,-8,8) at k = (1,2,3,5,6,10,15,30); atom readout (|tr T^3|,|tr T^5|,|tr T^15|) = (2,4,8) = (|Z2|,|mu4|,rank E8) -- eight integer traces type the Coxeter clock without diagonalisation or metrization (a cheap kill test for flip-operator candidates). [E] HONEST KILL SCOPE: Comp(Phi_15) PASSES the unsigned triple (Phi_30(x) = Phi_15(-x)) -- the discriminator is the SIGNED table (c_15(1) = +1 vs c_30(1) = -1); the other degree-8 candidates Phi_16/Phi_20/Phi_24 die already on the triple (traces 0,0,0). [E] COPRIMALITY CONTROLS: C6 (x) C6 has order 3 (not 36) with eigenvalue 1, C5 (x) C5 order 5 (not 25) -- CRT is load-bearing. [O] WHAT STAYS OPEN (no upgrade claimed): a canonical intertwiner from the concrete even-flip atlas (240 = 160+80) onto this primitive space (COX.FLIP.INTERTWINER), and Stage B (norm-2, E8-profile, Weyl-closure metrization); the tfpt_1 Stage A prose is sharpened accordingly, the atlas route itself stays [O]. Discovery provenance: center_quotient_coxeter_modular_disc7_probe.py (76/76) in experiments/tfpt-discovery/ (2026-07-23).
Recorded status: Identity [E] (exact order/charpoly/trace arithmetic + honest kill-scope + coprimality controls -- sympy exact, Wolfram-mirrored) + [C] (the identification with the E8 Coxeter clock, as v223/v314) + [O] (the flip-atlas intertwiner COX.FLIP.INTERTWINER; Stage B metrization)
Dependencies, status detail and source
Canonical status: [E] Stage A answered on the 8-dim primitive-character alternative: T30 = C_Phi5 (x) C_Phi6, exact order 30, chi = Phi_30, traces = c_30(k) = c_5 c_6; [O] flip-atlas intertwiner + Stage B stay open; no marker moves beyond the Stage A prose sharpening
Dependencies: COX.CLOCK.01; COX.COUPLE.01; v223; v418; v55
Scripts: v531_coxeter_tensor_stage_a.py
Location: tfpt_1
Original CSV, line 599Original ledger status
E8.DEGREE.MODULAR.01
THE E8 DUAL-DEGREE MODULAR CHECKSUM 744 + THE PRIME-TOTATIVE FINGERPRINT (2026-07-23; AUDIT-TYPED under the no-free-pattern rule -- feeds no derivation, kills no alternative alone, registered with its own negative controls; 11 checks, ~2 s, sympy exact): [E] the E8 invariant degrees (2,8,12,14,18,20,24,30) (v66) pair dually d_i + d_{9-i} = 32 = h+2; the four dual products (2*30, 8*24, 12*20, 14*18) = (60,192,240,252) satisfy SIMULTANEOUSLY sum = 744 = 3*248 = 3 dim E8, product = 696729600 = |W(E8)|, gcd = 12 = dim g_SM, and normalised (5,16,20,21) = (g_car, dim S^+, det L, N_fam*7). [E] MODULAR ANCHOR: 744 recomputed from scratch as the constant coefficient of the modular j-function, j = E4^3/Delta = q^-1 + 744 + 196884 q + ... (the cube of the (E8)_1 character, v496) -- a finite-to-affine checksum from the finite invariant degrees to the first regular coefficient of chi^3 = j. [E] NEGATIVE CONTROL (the checksum is NOT E8-exclusive -- the mandatory fence): D16 (same h = 30, rank 16) passes with dual-product sum 1488 = 3*496 = 2*744, exactly the heterotic dimension equality 496 = dim(E8xE8) = dim SO(32) (the tfpt_1 audit box); the checksum measures the common rank-16/Coxeter-30 heterotic structure. The non-heterotic controls ALL fail the 3*dim rule (half-pair convention): A8 100/240, D8 200/360, E6 117/234, E7 316/399, F4 72/156, G2 12/42. [E, audit] PRIME-TOTATIVE FINGERPRINT: {2,3,5} u (Exp(E8) minus {1}) = {2,3,5,7,11,13,17,19,23,29} = ALL primes below 30; every totative of 30 except 1 is prime; and 30 is the LARGEST integer with this property (exact scan to 10^4; full list {1,2,3,4,6,8,12,18,24,30}) -- h(E8) = 30 = |Z2| N_fam g_car is the maximal prime-totative Coxeter number. Complements the prime-facet arithmetic (COXETER.PRIME2.01, ARITH.HULL.01, ARITH.TRICHOTOMY.01) at the fingerprint level; per the no-free-pattern rule NONE of this becomes load-bearing. Discovery provenance: center_quotient_coxeter_modular_disc7_probe.py (76/76) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves.
Recorded status: Identity [E, audit-only] (exact integer/q-series arithmetic incl. the j-series recomputation and all controls -- sympy exact, Wolfram-mirrored); explicitly NON-exclusive (D16 control passes); the fingerprint feeds no derivation (no-free-pattern rule honoured)
Dependencies, status detail and source
Canonical status: [E, audit] dual-degree checksum: (60,192,240,252) -> sum 744 = 3*248 (= j constant coefficient, recomputed), prod |W(E8)|, gcd 12, /12 = (5,16,20,21); D16 control 1488 = 3*496 (NOT E8-exclusive); primes-below-30 totative fingerprint with maximality scan; audit-only, no marker moves
Dependencies: E8.DEG.01 (v66); CELEST.WP4.01 (v496); COXETER.PRIME2.01; ARITH.HULL.01
Scripts: v532_e8_degree_modular_checksum.py
Location: tfpt_3;tfpt_1
Original CSV, line 600Original ledger status
FTR.DISC7.NORM.01
THE SHEET TRANSFER IS A NORM LINE OF DISCRIMINANT -7 (2026-07-23; 12 checks, <1 s, sympy exact): the branch-preserving F_transfer path J -> K -> C -> F = M(1, -2..1) (FTR.PATH.01/v224, v412) carries the determinant D(t) = det M(1,t) = 4t^2 + 14t + 14 = ((4t+7)^2 + 7)/4 = N_{Q(sqrt-7)/Q}(alpha_t) with alpha_t = (4t+7+sqrt(-7))/2. [E] INTEGRALITY: -7 = 1 mod 4 and 4t+7 odd => alpha_t lies in the maximal order Z[(1+sqrt(-7))/2] for every integer t. [E] TRANSLATION ORBIT: alpha_{t+1} = alpha_t + 2 = alpha_t + |Z2| -- the whole discrete transfer path is ONE arithmetic translation orbit with norms (2,4,14,32) = (det J, det K, det C, det F) = (|Z2|, |mu4|, dim G2, det F). [E] CONSTANT DISCRIMINANT: the characteristic polynomial x^2 - (4t+7)x + D(t) of alpha_t has discriminant EXACTLY -7 for every t; vertex t = -7/4 with D_min = 7/4 > 0 (the branch-preserving path has no real zero); curvature D'' = 8 = rank E8 and sqrt(-disc) = sqrt(7) -- the sheet coefficients (8,7) reappear as (curvature, fixed quadratic discriminant), the scalaron 7 as arithmetic discriminant [C readings]. [E, audit] -7 = 1 mod 8 => 2 SPLITS in Q(sqrt-7) (class number 1, Heegner field) -- the J endpoint norm 2 = |Z2| is realised by the split prime above 2. [E] NEGATIVE CONTROLS: the winding axis det M(s,0) = 6s+8 is LINEAR (no norm form) and the anchor block det B(1,t) = 3t^2+21t+28 has POSITIVE discriminant 105 (real roots) -- only the sheet determinant is a complex norm line. [C]/[O] THE ARITHMETIC F_TRANSFER FRAME (the new solution perspective): the discrete data of the transfer path live in ONE quadratic order of discriminant -7; the preregistered next test is whether the four external transfer solvers (Koide, eta_B, axion, m_p/m_e) act on alpha_t by a COMMON fractional-linear action ('one functor, four interfaces' as an algebraic contract), with the kill criterion 'four incompatible arithmetic actions'; GATE.FTRANSFER unchanged, the external solver stays external. Discovery provenance: center_quotient_coxeter_modular_disc7_probe.py (76/76) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves. [2026-08-01 XXIV, cross-reference audit: the preregistered 'common fractional-linear action' test is EXECUTED on its discrete half -- v571: the four discrete kernels lie on the alpha_t translation orbit and the cross-ratio 4/3 is Moebius-forced (y_F = 53 fit-free); v575: the continuous export is uniflow-degenerate (closure onto the single v425 flow); v578: each external instance is projective IN ITS OWN CLOCK and the joint obstruction is exactly the clock anchor -- so the residual of this preregistration is the same external-anchor-jet export that CONTRACT.F.01 fences; no independent open remains here.] [2026-08-02 XLI: the preregistered PGL2-action test EXECUTED in its literal group form by v632 -- ONE common parabolic action on the discrete half (exact intertwining with the base translation; CR = 4/3; the F corner 53 Moebius-forced), uniflow degeneration on the native continuous half (g_Boltzmann = g_pole identically, g_QCD exactly conjugate to the base translation, relic trivial); the kill criterion 'four incompatible arithmetic actions' is NOT met; see FTR.PGL2.01.]
Recorded status: Identity [E] (exact norm/integrality/translation/discriminant arithmetic + negative controls -- sympy exact, Wolfram-mirrored) + [E, audit] (split prime 2, Heegner class number) + [C]/[O] (the arithmetic F_transfer frame: common Moebius action of the four solvers = preregistered next test; GATE.FTRANSFER unchanged)
Dependencies, status detail and source
Canonical status: [E] the sheet path J->K->C->F is one translation orbit alpha_{t+1} = alpha_t + 2 in Z[(1+sqrt(-7))/2] with norms (2,4,14,32) and constant discriminant -7; [C]/[O] common-solver Moebius action = preregistered next test; no marker moves
Dependencies: FTR.PATH.01; DIAMOND.SHEET.SOURCE.J.01 (v412); DIAMOND.SHEET.CALCULUS.01 (v413); v224
Scripts: v533_ftransfer_disc7_norm.py
Location: tfpt_2;tfpt_research_contracts
Original CSV, line 601Original ledger status
CP.CHANNEL.IDENT.01
THE CP CHANNEL / INVARIANT IDENTITIES (2026-07-29; one module, 25 checks, ~1 s; promotion of the exact cores of discovery T177 (contract CP.INVARIANT, probe cp_invariant_probe.py, 49/49, verdict DEGENERATE) -- THE CP MIRROR AS ALGEBRA: the prime-front toolkit (gauge-degree bookkeeping under declared group actions) turned on the four CP ledger rows REDTEAM.D.01 / E8.CHAN.01 / CP.MOD.01 / DUAL.FRAME.01; every statement is a NARROWING of an existing reading, executed in the same change, with NO marker moves and NO CP derivation claimed. CONTENT: (1) THE HEXAGONAL CHANNEL IDENTITY -- on the CM unit rho = e^{i pi/3} (CP.MOD.01) the E8 split 248 = 120 + 128 (E8.CHAN.01/v227) has an EXACT fiber realisation: sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly; the degrees mod 6 are four 0s and four 2s, 1 + rho^2 = rho) and sum_k rho^{m_k} = 4 (arg = 0 exactly), with the parity typing forced by integer parity -- all degrees EVEN (phase channel SHEET-EVEN under the sheet flip rho -> rho^4 = -rho), all exponents ODD (magnitude channel SHEET-ODD); CONSEQUENCE: the sheet-even phase-channel angle cannot distinguish quark from lepton (it carries pi/3, not the CP.MU6.01 sheet split); mutation controls: the identity breaks on the non-CM unit e^{i pi/5} and on a mutated degree list (30 -> 31), reality breaks on a mutated exponent list (29 -> 30); HONEST CAVEAT wired as a check: reality of the exponent sum alone is NOT hexagon-specific (the exponent residues are conjugation-closed mod 10 too) -- only the degree half (= 4 rho) is; (2) ZERO PHASE IN THE MAGNITUDE DATA + THE BRANCH-ORDER LAW (the REDTEAM.D.01 narrowing): arg(prod c) = 0 EXACTLY on both TFPT sectors (lepton triple (16/7, 4/3, 7/6), product 32/9; up-quark triple (1/2, 34/41, 4/13)) -- the CP residual is not hidden in the product -- and the mu3 branch group is EXACTLY the kernel of the magnitude data because its order divides N_fam = 3 (w^{3j} = 1; a mu4 branch already shifts the product phase by -pi/2, mutation): the residual is a FIBER datum, not a magnitude datum; (3) TIER-1 EMPTINESS BY THE BLINDNESS THEOREM: both complex kernels commute with conjugation (conj sum rho^{d_k} = 4 conj rho exactly; Im det(1, d, conj(rho) n) = -Im det(1, d, rho n) exactly), so EVERY pi/3-carrier is kappa-odd and invariant + odd forces Im F = 0: strict invariance under all four T177 groups is EMPTY on pi/3-carriers, per algebra and as preregistered; (4) THE FRAME REMOVAL (the DUAL.FRAME.01 narrowing): det(1, d, n) = 21 = N_fam * scalaron and Im det(1, d, rho n) = 21 sin(pi/3) exactly (v225 rebuilt); the orientation functional is homogeneous of DEGREE +1 in the frame normalisation (Im det(1, d, rho(t n)) = t 21 sin(pi/3) symbolically), so the NUMBER 21 sin(pi/3) is FRAME data; dividing by the oriented volume removes the frame IDENTICALLY (Im(rho v)/v = Im rho symbolically for every real v != 0): the invariant core is the fiber datum Im(rho) = sin(pi/3), the sign a declared orientation; sheet control Im det(1, d, rho^4 n) = -21 sin(pi/3); mutation: n' = (5, -8, 6) gives det = 39/2 != 21; (5) THE TWO TIER-2 CHARACTERS + THE JARLSKOG ANCHOR: P2 = arg(sum rho^{d_k}) carries (chi(kappa), chi(sigma)) = (-1, +1) and V5 = Im(rho det)/det carries (-1, -1), both verified as character HOMOMORPHISMS on the full four-element group (16 products) -- TWO INEQUIVALENT invariants carry the same value pi/3 (the DEGENERATE verdict as algebra) and NEITHER couples to the frame; the classical anchor: the TFPT CKM rebuild (s12 = lambda_C, s23 = phi0/(1+lambda_C), s13 = lambda_C^3/3, frozen delta = pi/3 + 3 lambda_C^2 per REG.FREEZE.01) is unitary to 1.1e-41 and gives J = 3.327021e-5 = the v88 lattice value; J passes rephasing invariance (incl. the mu3 branch group) and CP-oddness and fails ONLY the pi/3-carrier test (its phase content is delta, not pi/3) -- the benchmark VALIDATES the criterion instead of the value, and the full delta has NO character under the parity involution (a CP-even correction on a CP-odd angle: the CP.MOD.01 scope narrowing). NAMED LIMITS AS LOAD-BEARING CONTENT: (i) NARROWINGS ONLY -- no marker of any pre-existing contract moves, the CP residual is NOT closed, the word 'derived' appears nowhere, REG.FREEZE.01 and the 3-vs-2 lambda_C^2 coefficient question are untouched; (ii) R1 STAYS OPEN: whether a frame-coupled, scale-free, character-covariant pi/3-carrier can exist at all (the T177 obstruction: the (1, d, n) frame has only ONE oriented volume to normalise against); R2 STAYS OPEN: which of the two Tier-2 characters is physical -- the sheet-odd (orientation) reading reproduces CP.MU6.01's quark/lepton split, the sheet-even (channel) reading cannot: a structural preference, NOT a derivation; (iii) the D4 deck column of T177 is a DECLARED MODEL and is not promoted (only the model-free statements are). HONEST FENCES: no RH statement anywhere (finite exact statements about roots of unity, 3x3 determinants and one 3x3 unitary matrix); Jarlskog 1985, Wolfenstein 1983, Weyl 1946 named CLASSICAL as addresses. Discovery: T177 (experiments/tfpt-discovery/cp_invariant_probe.py, 49/49, 0.2 s, verdict DEGENERATE). UPDATE (2026-07-30, T178/v564, CP.FIBER.PIN.01): R1 is DECIDED -- the natural (metric-free) class is fiber-only BY THEOREM (one bracket generator), the metric class couples but is NON-CANONICAL (a continuum of normaliser-relative values) -- and R2 is SELECTED conditional on the classical anchor (the Jarlskog character tuple (-1,-1,-1) matches the sheet-odd orientation class only); the single-sine lemma types this row's DEGENERATE verdict as FORCED on crystallographic fibers. Markers unchanged.
Recorded status: Identity [E] (exact identities and certified numerics with mutation controls -- the hexagonal channel identity sum rho^{d_k} = 4 rho / sum rho^{m_k} = 4 sympy-exact with the sheet-even/odd parity typing, arg(prod c) = 0 exactly on both magnitude sectors with the branch-order law, Tier-1 emptiness by the conjugation-commutation theorem, the frame removal Im(rho det)/det = Im rho exact with the degree +1 account, the two inequivalent Tier-2 characters as verified homomorphisms, and the Jarlskog anchor J = 3.327021e-5 = v88 at unitarity 1.1e-41) -- NARROWINGS of four existing ledger readings only; no marker moves; R1/R2 typed OPEN
Dependencies, status detail and source
Canonical status: [E] sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly, sheet-EVEN) and sum_k rho^{m_k} = 4 (arg = 0 exactly, sheet-ODD) on the hexagonal CM unit -- the E8 channel typing has an exact fiber realisation and the phase channel is sheet-blind; arg(prod c) = 0 exactly on both TFPT sectors (the CP residual is a FIBER datum, not a magnitude datum); Tier-1 invariance EMPTY per algebra (every pi/3-carrier is kappa-odd); Im(rho det)/det = Im rho = sin(pi/3) exactly (the orientation reading is degree +1 in the frame normalisation, 21 sin(pi/3) is frame data, the sign a declared orientation); two inequivalent Tier-2 characters (-1,+1) vs (-1,-1) carry the same pi/3 (DEGENERATE), neither frame-coupled; Jarlskog anchor J = 3.327021e-5 = v88 passes (a)-(c), fails only the pi/3-carrier test. Four ledger rows narrowed, no marker moves; R1/R2 OPEN.
Dependencies: REDTEAM.D.01; E8.CHAN.01; CP.MOD.01; DUAL.FRAME.01; CP.MU6.01; FLAV.CP.01; REG.FREEZE.01; v88; v220; v225; v227; T177
Scripts: v561_cp_channel_identities.py
Location: tfpt_5_redteam
Original CSV, line 602Original ledger status
CP.FIBER.PIN.01
THE FRAME DOOR OF THE CP MIRROR, DECIDED (2026-07-30; T178, contract FRAME.CARRIER, probe cp_frame_carrier_probe.py 31/31, verdict FIBER-PINNED; one module, 22 checks, ~2 s, sympy-exact generic-frame algebra + one 3x3 unitary matrix at 40 dps). T177/v561 left R1 (can a frame-coupled, scale-free, character-covariant pi/3-carrier exist at all) and R2 (which of the two degenerate Tier-2 characters is physical) open; both are decided here, and NOTHING about CP violation is derived. (1) EULER FACTORISATION: the fiber acts on the frame by a scalar on the n-row, so P(rho n) = rho^m P(n) for every homogeneous block (fully generic degree 1..4 polynomials, symbolic coefficients): every scale-free functional decomposes as sum_k A_k Im(rho^k) with A_k real degree-0 frame ratios -- the fiber content is QUANTISED. (2) THE NATURAL CLASS IS FIBER-ONLY (R1, natural half, NEGATIVE BY THEOREM): metric-free invariants of vector tuples are generated by volume-form brackets (Weyl 1946 FFT, the one cited class boundary [C]); the exact enumeration on {1, d, n} gives ONE generator (the six permutations = +-Delta; the other 21 brackets vanish identically in a GENERIC n), so every scale-free ratio is constant: no frame-coupled scale-free pi/3-carrier exists without a metric -- T177's obstruction sentence ('one determinant only') is now a theorem. (3) THE METRIC DOOR IS NON-CANONICAL (R1, metric half): declared metrics admit frame-coupled Tier-2 carriers, non-unique at BOTH levels -- characters: Delta/<d,n> and Delta/<1,n> carry (kappa, sigma, deck-Ref) = (-1,-1,+1) (the odd Delta-power absorbs the reflection) while Delta^2/<n,n> carries (-1,-1,-1); values: the admissible normalisers contain the continuum q_t = t n1^2 + n2^2 + n3^2 (deck-invariant for EVERY t) with carrier values 441 sin(pi/3)/(25t+117), strictly monotone in t -- NO canonical frame factor exists; anti-numerology wired as a check (21/8, 21/2, 441/142 pairwise distinct, none claimed -- normaliser-relative frame data). (4) THE SINGLE-SINE LEMMA (the pattern): {|Im(rho_n^k)|} has exactly ONE nonzero element iff n is crystallographic (n in {1,2,3,4,6} = {n : phi(n) <= 2}; Barlow 1894), by the exact identity sin(4pi/n) - sin(2pi/n) = 2 sin(pi/n) cos(3pi/n) with its only zero at n = 6 on n >= 5, enumerated exactly to n = 24; the compiler's two clocks mu4 (seam deck, j = 1728) and mu6 (CP fiber, j = 0) are the two MAXIMAL single-sine fibers (the two CM points with extra automorphisms): value-based pinning of functionals is impossible BY THEOREM on both -- T177's DEGENERATE verdict was FORCED, not found (mutation: on mu5 values DO separate carriers). (5) THE ANCHOR SELECTION (R2, SELECTED): the Jarlskog invariant on the TFPT CKM rebuild (v88, frozen delta per REG.FREEZE.01) has full character tuple (-1,-1,-1) under (kappa = conjugation, sigma = delta -> delta+pi, deck reflection V -> V Ref), each certified at 40 dps below 1e-25: it matches the sheet-ODD orientation class V5 = (-1,-1,-1) and NOT the sheet-even channel class P2 = (-1,+1,-1) -- of T177's two degenerate classes exactly ONE matches; the (-1,-1,+1) metric carriers are ANCHOR-REJECTED and the matching (-1,-1,-1) family carries the continuum, so the UNIQUE anchor-matching CANONICAL carrier is the fiber-pure V5 = Im(rho) = sin(pi/3); consistency: Im(rho^4) = -Im(rho) flips exactly as sin(delta+pi) = -sin(delta) (the CP.MU6.01 wiring). NAMED LIMITS AS CONTENT: the selection is CONDITIONAL ON THE ANCHOR (Jarlskog 1985 is imported physics -- SELECTED, not derived; the word 'derived' appears nowhere); the deck-reflection column is the T177 DECLARED MODEL (kappa/sigma model-free); the CP residual is NOT closed, it is RELOCATED with a proof: the invariant CP core is the fiber datum Im(rho) = sin(pi/3) and provably cannot be made frame data without a non-canonical metric import; REG.FREEZE.01 and the 3-vs-2 lambda_C^2 question untouched; NO marker of any pre-existing contract moves; NO RH statement (finite exact statements about roots of unity, 3x3 determinants, one 3x3 unitary matrix and one trigonometric identity).
Recorded status: Identity [E] (exact theorems and certified character accounts with mutation controls -- Euler factorisation on fully generic homogeneous blocks, the one-generator bracket enumeration, the character split and the q_t continuum, the single-sine lemma with the crystallographic equivalence, the anchor tuple at 40 dps) + [C] (the Weyl 1946 FFT class boundary; the selection conditional on the Jarlskog anchor; the deck column a declared model); R1 decided, R2 selected, no marker moves
Dependencies, status detail and source
Canonical status: [E] natural class fiber-only (6 brackets = +-Delta, 21 vanish identically; generic degree 1..4 Euler factorisation exact); metric door non-canonical (character split (-1,-1,+1) vs (-1,-1,-1); continuum 441 sin(pi/3)/(25t+117)); single-sine <=> n in {1,2,3,4,6} = phi(n) <= 2 (identity + enumeration to 24); anchor tuple (-1,-1,-1) selects sheet-odd, J = 3.327021e-5 = v88; unique canonical anchor-matching carrier = fiber-pure sin(pi/3); 22/22 checks
Dependencies: CP.CHANNEL.IDENT.01; REDTEAM.D.01; E8.CHAN.01; CP.MOD.01; DUAL.FRAME.01; CP.MU6.01; REG.FREEZE.01; v88; v225; v561; T177; T178
Scripts: v564_cp_fiber_pin.py
Location: tfpt_5_redteam
Original CSV, line 603Original ledger status
WOIT.BETA3.DUALITY.01
THE WOIT-BETA3 MILESTONE EXECUTED (2026-07-30; one module, 22 checks, ~2 s; probe woit_os_beta3_pt_dual_probe.py 25/25, verdict SUCCESS per the frozen preregistration): 'the PT <-> PT* duality typed against sigma_std' -- contract wording: success = Woit's Minkowski conjugation identified with the family-D conjugation on the quotient; kill = the duality forces a clock-centralising (family A) structure. (1) THE COMPATIBLE CLASS (block theorem): a duality is a nondegenerate Hermitian form Phi on C^4 (sigma(Z) = Z^dagger Phi); clock compatibility (rho4 = diag(i,1,i,1), the v519 W-S4 blockwise lift) has entrywise residual (conj(lam_j) lam_k - 1) Phi_jk and forces the four cross-eigenspace entries to ZERO: two 2x2 Hermitian blocks on {e1,e3} (+) {e2,e4}, 16 -> 8 real parameters; deck compatibility adds nothing; the wrong clock lift diag(i,i,1,1) forces a different split (the compiler clock is load-bearing). (2) THE DICHOTOMY + THE FORCED (2,2): the rho_tw pairing M_tw^dagger Phi M_tw = eps conj(Phi) (rho_tw = Woit's Euclidean structure, v519 W-S4.1) splits the class exactly in two -- EUCLIDEAN (eps = +1; sigma_std = Phi = 1 lives here): seam-line norm a(|z|^2 + 1), NO null point, no OS cut ever; MINKOWSKI (eps = -1): seam-line norm a(|z|^2 - 1) -- the null locus meets the seam line EXACTLY in the seam circle |z| = 1 for EVERY member (the OS cut is FORCED, not imposed) -- and Phi_1 = -conj(Phi_i) exactly (charpoly_1(x) = charpoly_i(-x)): the TOTAL SIGNATURE IS (2,2) for every nondegenerate member -- Woit's Minkowski signature is a THEOREM of clock + rho_tw pairing, not an input. (3) THE KILL IS EMPTY BY ALGEBRA: s_Phi = Phi^T o conj inverts clock AND deck identically in the block parameters (family D, both branches); family A would need rho4^-1 = lambda rho4, i.e. rho4^2 = scalar, but rho4^2 = diag(-1,1,-1,1): NO solution -- decided, not scanned; s_Phi^2 = diag(a^2,a^2,c^2,c^2) > 0: the Kramers-free class. (4) THE INDUCED MEMBER IS UNIQUE AND PERPENDICULAR TO sigma_std: seam preservation <=> b = 0; every seam-preserving Minkowski member induces the SAME projective conjugation z -> -conj(z) (mu = -1, fixed points +-i), perpendicular to sigma_std's z -> +conj(z) (mu = +1, fixed points +-1); the clock conjugation exchanges exactly these two (mu -> -mu) -- the projective shadow of theta_cut o theta_perp = alpha_{N/2}. (5) THE QUOTIENT IDENTIFICATION: exact placement arithmetic (cut axis k = 7 fixes bond midpoints {7pi/8, 15pi/8}, perp axis k = 3 fixes {3pi/8, 11pi/8}; offsets exactly -+pi/2 -- under the v519 precision-(ii) RP-side placement the perp axis carries the +-i mark pair) + coordinate transport (axis angle 11pi/8 = 3pi/8 mod pi): THE INDUCED MINKOWSKI MEMBER IS theta_perp, the mirror whose descent v524 certified (Theta_phys) -- sigma_std's member transports to the CUT axis (the OS metric itself): role separation complete; v524 regressions re-verified at N = 8 (Gram PD (16,0,0) min 3.3471e-3 at 40 digits, theta_perp anti-unitary wrt the Gram exactly with eta_perp = +i, Theta_phys^2 = +1 on BOTH parity sectors, time reversal exact, torsor closure exact at support level). (6) CONTROLS: family A has no quotient ((4,4,0) one-particle, v524 C4.2 verbatim); the Euclidean branch cannot cut; a non-mu4 reflection (e^{2 pi i/5}) is not mark-anchored. NAMED LIMITS AS LOAD-BEARING CONTENT: free/quotient level ONLY -- nothing constructs the interacting algebra A_hol, all seven contract kill tests stay formally live there, WOIT.OS.TWISTOR.01 stays [O], gamma (the chirality theorem + the mark incidence) is the next milestone; the declared [C] conventions (seam line span(e1,e2) with the v519 blockwise lift; 'the duality respects the seam' read as seam-line preservation; the RP-side bond-midpoint placement, v519 precision (ii); the clock relabeling of the torsor) are cited from v492/v519/v524, not invented; 'identified' means inside these declared compatibility classes, NOT a derivation of Minkowski space; the word 'derived' appears nowhere for any physics statement.
Recorded status: Identity [E] (exact sympy algebra on generic block parameters -- block theorem, branch dichotomy, signature-mirror theorem, kill emptiness, unique induced member, exact rational-pi placement arithmetic, exact lattice regressions) + two 40-digit inertia certificates + [C] (the declared conventions: seam line, seam preservation, RP-side placement, torsor relabeling; contract-level identification, not a derivation); verdict SUCCESS, kill branch empty by algebra, no marker moves
Dependencies, status detail and source
Canonical status: [E] block theorem (4 cross entries forced zero; 16 -> 8 params); dichotomy eps = +-1 with the OS cut forced on the Minkowski branch (seam norm a(|z|^2 - 1)) and signature (2,2) by the mirror theorem; kill empty (rho4^2 = diag(-1,1,-1,1) not scalar); induced member unique z -> -conj(z) = theta_perp = the v524 Theta_phys carrier (placement offsets exactly -+pi/2; axis 11pi/8 = 3pi/8 mod pi); N = 8 regressions: Gram PD (16,0,0) min 3.3471e-3, eta_perp = +i, Theta^2 = +1 both sectors, time reversal + torsor closure exact; family A (4,4,0); 22/22 checks
Dependencies: WOIT.OS.TWISTOR.01; WOIT.THETA.FREE.01; WOIT.BETA1.GSO.01; WOIT.BETA2.OS.01; SEAM.BIT.RPBLIND.01; v492; v519; v522; v524
Scripts: v565_woit_beta3_pt_duality.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 604Original ledger status
DIAMOND.PARA.SELFCODE.01
THE PARABOLIC ANCHOR SELF-CODE (2026-07-31; external structural review audited by discovery probe parabolic_selfcode_audit_probe.py 23/23, verdict SELFCODE-VERIFIED, and promoted; one module, 14 checks, ~1 s, exact integer/symbolic sympy, no floats). The v218 sheet-diamond direction operators U = Q diag(1,0,0) (rank-1 winding) and V = Q diag(0,1,1) (rank-2 sheet, Spec V = {0,1,2}) carry a previously unstated exact operator structure. (1) PARABOLIC THEOREM: A = Q<I,U,V> is the FULL line-stabiliser (maximal parabolic) algebra of block type 2|1 -- seven words independent (coordinate det -81), multiplicatively closed (49/49), all seven matrix units contained, dim 7 = 9-2; mutation of Q's third column breaks it. (2) DOUBLE SELF-CODE: Pi2 = V(V-I)/2 idempotent trace-1; H = I + Pi2 has spectrum EXACTLY {1,1,2} = a (ANCHOR.GEN.01/v23); chi_H = x^3 - 4x^2 + 5x - 2 with (e1,e2,e3) = (4,5,2) = (|mu4|, g_car, |Z2|) AND = (dim_R(GL3/P), dim(A/J), dim J) -- the anchor reproduced spectrally (dominant projector of V) and categorically (flag/Levi/radical of A) from ONE structure. (3) UNIQUENESS THEOREM: x^3 - 2m x^2 + (m^2+1) x - m = (x-m)(x^2-mx+1) identically; positive-integer spectra force m^2 - 4 = k^2, (m-k)(m+k) = 4, m = 2 UNIQUELY -- a = (1,1,2) is the only anchor this parabolic family can code. (4) THE 81 AS LATTICE INDEX: the SATURATED integral order (closure stable at word length 4) has elementary divisors (1,1,1,3,3,3,3): [P_Z : Z<U,V>] = 3^4 = 81, cokernel (Z/3)^4 -- equal to the v218 determinant-staircase sum 3+4+8+14+20+32 = N_fam^4 (cross-link typed; the mark-local mechanism, one Z/3 per mu4 mark, stays [O]: if no canonical local decomposition exists the 81 stays a fingerprint). (5) A2 BIT CARRIER: the basic algebra e A e is the A2 path algebra (dim Ext^1 = 1): dim-vector-(1,1) modules fall into EXACTLY two iso classes (split / one nonsplit) -- the alignment bit gains a canonical algebra carrier; uniqueness [E], SELECTION stays with RP/geometry (v528/v534) [C]. (6) TRACE CODE (re-encoding): p_n(a) = 2 + 2^n = 1 + tr(V^n); recurrence, Hankel 2^{n+1}; (1+trV)(1+trV^2)(1+trV^3) = 240 = |R(E8)|; tr(V^4-V^3) = 8 = rank E8 -- AnchorLadder read through V, one object fewer, NO new content. (7) CR TEST DESIGN (CONTRACT.F.01): CR(alpha_{-2},alpha_{-1};alpha_0,alpha_1) = 4/3 exactly on the v533 line; honesty wired (universal arithmetic-progression cross-ratio -- content = preregistered solver-state export); negative control 28/25; y_F forced fit-free. (8) LORENTZ FORM (reformulation): det X = t^2 - x^2 - y^2 under Phi; D(P,Q) = 2<Phi,Phi>_{1,2}; delta = sech^2(atanh r); pencil identities det(B-S) = det B det(I-Z), D(B,S) = det B tr Z, det S = det B det Z -- eigenvalue locking as the named prime-front instrument (no measurement, no RH statement). NAMED LIMITS AS CONTENT: NO P2 REDUCTION -- 'g_car = dim(A/J) derived' is conditional on the OPEN 'No Carrier Reconstruction' audit (rebuild Q/V from mu4, D4, Q_+ = A3 exponent grading, H^1, Q_- = sheet monodromy, WITHOUT g_car, a, rank E8 or carrier-aware budgets; Q's historical provenance runs through such budgets); AX.P2.01 and ANCHOR.GEN.01 markers UNTOUCHED; the 2..9 dimension table is COMPRESSION of one operator system, not nine independent hits (no-free-pattern rule); the bit selection, the mark-local 81 mechanism and the CR-test execution stay open and typed open; the word 'derived' appears nowhere for any physics statement. UPDATE (2026-07-31, v567): the review's Priority-1 audit is EXECUTED at Stage A -- verdict RECONSTRUCTS-TO-FAMILY: the anchor self-code is carrier-free; Q reconstructs up to one binary sheet-coupling choice; see QGEO.QRECON.01. FURTHER UPDATE (2026-07-31, v568): Priority 3 executed -- the A2 Ext arrow is NONZERO on the whole reconstruction class (the split member collapses to dim 5 and is excluded); Priority 2 sharpened -- the mu4-grading candidate fails, the F3[V]-action on the cokernel exists (see DIAMOND.BIT.SELECT.01). [2026-07-31: the S8 pencil identities are now executed on the REAL Paper-II surface by v569 (machine-tight at 2e-14 on 70 windows, verdict ONE-MODE); see PRIME.PENCIL.ONEMODE.01.] [2026-08-01 X: the per-mark Z/3 mechanism appears geometrically -- v597: the cusp-class group of the mu3-cover is (Z/3)^4 of order 81 with four free local classes; see QGEO.COVER.01.] [2026-08-01 XVI: the self-code algebra has a geometric realization -- v600: (U, V) as Gamma-even degree-2 cusp-Gram operators on the mu3-cover, GL3-conjugate to the compiler pair, with the SAME saturated Z-order structure (index 81 = 3^4, divisors (1,1,1,3,3,3,3)); existence [E], canonicity open; see QGEO.EMBED.01.]
Recorded status: Identity [E] (exact integer/symbolic algebra with mutation controls -- parabolic closure, double self-code, uniqueness enumeration + divisor argument, saturated Smith form, A2 quiver, trace code, cross-ratio identities, Lorentz/pencil identities) + [C] (the TFPT readings of the invariants; the bit-carrier and CR-test interpretations) + [O] (the No-Carrier-Reconstruction audit, the mark-local 81 mechanism, the CR-test execution); NO marker moves
Dependencies, status detail and source
Canonical status: [E] A = full 2|1 parabolic, dim 7, word det -81, closed 49/49, mutation-fragile; a = Spec(I + V(V-I)/2) = (1,1,2) with chi_H = x^3 - flag x^2 + Levi x - radical (4,5,2 double-coded); m = 2 unique (enumeration to 2000 + divisor argument); saturated Smith (1,1,1,3,3,3,3), index 81 = 3^4 = staircase sum; A2 Ext^1 = 1 (two module classes); p_n = 1 + tr V^n (240, rank 8 as traces); CR = 4/3 design with 28/25 control; Lorentz/pencil identities exact; 14/14 checks
Dependencies: DIAMOND.AXIS.01; ANCHOR.GEN.01; AX.P2.01; FLAV.QGEO.01; CONTRACT.F.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v23; v218; v224; v528; v533; v534
Scripts: v566_parabolic_anchor_selfcode.py
Location: tfpt_1;tfpt_2;tfpt_research_contracts
Original CSV, line 605Original ledger status
QGEO.QRECON.01
THE NO-CARRIER-RECONSTRUCTION AUDIT, STAGE A (2026-07-31; Priority 1 of the self-code review; one module, 9 checks, ~1 s, exact enumeration with integer prefilters + sympy verification; discovery probe carrier_free_q_reconstruction_probe.py 10/10, verdict RECONSTRUCTS-TO-FAMILY). THE QUESTION: can Q -- hence V and the v566 parabolic anchor self-code -- be reconstructed WITHOUT carrier/anchor inputs? THE CIRCULARITY LOCATED: v11's uniqueness certificate for Q enumerates over row sums (4,5,6), column sums (9,5,1) and chi_Q = (t-1)(t^2-5t+3) -- the 5 = g_car sits in the budgets and in chi_Q; all of it FORBIDDEN here. ALLOWED (each carrier-free, with corpus source): (S) Sigma = diag(1,-1,-1) [v10 sheet]; (W) Q(I+Sigma) = 2 N_fam W [v10 winding]; (E) Spec(Q_+) = {1,2,3} [FLAV.QGEO.01, A3 exponents]; (M) Q_- != 0, Q_-^2 = N_fam P, P^2 = P [FLAV.QGEO.01]; (Z) nonneg integers, bound 6 (robust at 9); (L) the seam-line demand [geometric, [C]]; (X) the saturation index N_fam^4 = 81 [v566 S4]. RESULTS [E]: (1) exactly 52 admissible matrices under (S)(W)(E)(M)(Z), corpus Q among them, first column forced to N_fam(1,1,1) by (W); (2) the seam-line demand cuts 52 -> 28 (real teeth); (3) THE ANCHOR IS CARRIER-FREE: all 28 parabolic members code the SAME anchor -- H' = I + Pi_dom(V') with char poly x^3 - 4x^2 + 5x - 2, spectrum (1,1,2) = a, ONE code class, no exceptions: the anchor self-code sits UPSTREAM of the carrier budgets, conditional on the declared geometric inputs; (4) THE RESIDUAL BIT: the 81-pin selects EXACTLY TWO members -- the corpus Q (q32 = 2 = |Z2|) and Q_alt (q32 = 0), difference matrix 2 E32 (the sheet-block coupling); every classical carrier-free certificate coincides on the pair (anticommutator spectrum {6,-4,-2} = (|R+(A3)|, -|mu4|, -|Z2|); commutator charpoly t(t^2+12); det = 3; saturation 81), while the ONE separating certificate is the carrier column budget (9,5,1) vs (9,3,1) -- exactly the forbidden input: the residual freedom is ONE binary coupled-vs-uncoupled sheet-block choice; (5) ablations: dropping (W) widens the bound-3 set 28 -> 1376 over 36 first columns (the winding input carries real load); bound robustness 6 -> 9 adds zero new (L)+(X) members; the forbidden inputs were evaluated nowhere. NAMED LIMITS AS LOAD-BEARING CONTENT: STAGE A ONLY -- whether (S)(W)(E)(M)(L) themselves derive from mu4/D4/H^1 parabolic geometry without family/sheet inputs is EXACTLY the open gate GATE.QGEO.01: the audit is RELOCATED there, not closed (N_fam = 3 is used throughout; family data was never forbidden -- the forbidden list is the CARRIER list); the carrier-free selector of the residual bit is OPEN, and its structural resonance with the split/nonsplit alignment-bit dichotomy (v528/v534, v566 S5) is a TYPED OBSERVATION, not a claim; NO P2 reduction -- AX.P2.01 and ANCHOR.GEN.01 markers untouched; the word 'derived' appears nowhere for any physics statement. UPDATE (2026-07-31, v568, DIAMOND.BIT.SELECT.01): the residual bit is located and given a canonical witness -- the twins generate different integral orders, and the ladder self-consistency (dominant mode = its own eigenvalue ladder (1,2,4)) selects the compiler Q uniquely on all 28 members; the split geometry (q32 = 1) is excluded by the demands already imposed; the physical selection stays open. Markers unchanged. [2026-07-31: Stage B narrowed by v574 -- the involution type is forced by a rank theorem and N_fam = 3 by the double self-consistency (ladder + sat = N^4); (E)(M)(L) stay the remaining gate; see QGEO.WINDING.SELF.01.]
Recorded status: Identity/enumeration [E] (exact admissible-set census 52/28/2 with integer prefilters verified by sympy on survivors; one anchor code class on all 28; separator dissection exact; ablations quantified) + [C] (the seam-line demand as declared geometric input; the bit-resonance observation) + [O] (Stage B = GATE.QGEO.01 relocation; the binary selector); verdict RECONSTRUCTS-TO-FAMILY; no marker moves
Dependencies, status detail and source
Canonical status: [E] 52 admissible under (S)(W)(E)(M)(Z) at B = 6; 28 under the seam-line demand; ONE anchor code x^3-4x^2+5x-2 = spectrum (1,1,2) on all 28 (carrier-free anchor); 81-pin -> exactly 2 (corpus Q vs q32 = 0 twin; all carrier-free certificates equal, separator = the forbidden column budget (9,5,1)); winding ablation 28 -> 1376 at bound 3; bound-stable at 9; 9/9 checks; verdict RECONSTRUCTS-TO-FAMILY
Dependencies: DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; GATE.QGEO.01; FLAV.KQ.01; AX.P2.01; ANCHOR.GEN.01; v10; v11; v218; v566
Scripts: v567_carrier_free_q_reconstruction.py
Location: tfpt_1;tfpt_2
Original CSV, line 606