Original claim records.

Original ledger status

RESIDUAL.CERTIFICATION.01

RESIDUAL.CERTIFICATION.01

Historical compiler-residual audit (2026-06-23; scope corrected 2026-09-05): v384 classifies the then-listed compiler residual into three external kinds, (A) external math proof, (B) theorem-forbidden, and (C) external physics. It does not classify the physical completeness gates T1-T8 and does not imply zero open internal TFPT mechanisms. [E] LEDGER CI: every claim in that historical residual list is present in status_ledger.csv. [E] NO-UNIT: a dimensionless compiler cannot derive the absolute scale v_geo. [E] CHECKED GAP-DECOUPLING: Delta_eff=6 ln(3/2)-31/(4 pi^2)~1.648>0 for the audited readouts. [E] HISTORICAL CLASSIFICATION: SEAM.EQUIV.01 and ALPHA.QUILLEN.EXACT.01 -> A; QG.AMB.01 -> A; v_geo -> B; F_transfer -> C. [O] CURRENT TOE FENCE: TFPT.TOE.COMPLETE.01 and every T1-T8 gate remain open; missing dynamics and continuum mechanisms, including a shared 3+1D parent satisfying T3-T8, are outside v384's scope.

Recorded status: Historical compiler-residual audit [E]; explicitly not a TOE-completeness audit. TFPT.TOE.COMPLETE.01 and all T1-T8 remain Open [O].

Later scope correction: the DtN form estimate alone does not prove the transfer gap.

Original ledger status

UVBRANCH.KILLTEST.01

UVBRANCH.KILLTEST.01

The optional carrier-Pati-Salam UV branch on the ALL-ORDER footing -- a single citable kill-test surface with the proton-decay SAFETY hierarchy computed (2026-06-24). A consolidation: does NOT re-run the RGE (v246 did 1+2-loop) nor re-derive the PS scale (v249/v253); it ADDS the all-order connection (v381) and the computed proton-safety margin (turning v265's 'no fake tau_p window' policy into a number). [E] CARRIER CONTENT = SM, ALL-ORDER: b=(41/10,-19/6,-7) (v159/v246), no new gauge-charged states (tfpt_3), S_pert closes to all orders (v381) => the SM-non-unification (v246) is all-order-robust. [X] PLAIN-SM 4D-GUT KILLED: sin^2 thW=3/8 vs measured 0.231, 1+2-loop couplings never meet (v246). [C] OPTIONAL CARRIER-PS BRANCH: M_PS=kappa*M_scal, M_scal=c3^{7/2}Mbar~3.06e13 GeV, kappa in [1.0,1.2] (2-loop v253), content {1,10,16,45} no 126 (v247/v248), NOT the default (v265 fork). [E] PROTON-DECAY SAFETY HIERARCHY: minimal PS gauge bosons are SU(4) leptoquarks (B-L-conserving q<->l = rare LFV K_L->mu e), NOT the p->e+ pi0 dim-6 operator (needs an SO(10)/SU(5) diquark, absent); the binding bound M_PS>~1e6 GeV is cleared by M_PS/M_bound~1e7>>1 => proton-safe. [X] FROZEN KILL TESTS (v265): the branch dies if kappa leaves O(1) / a forbidden rep (126) is required / a new gauge-charged state appears / a rare-LFV signal appears below the M_PS bound; NO discovery tau_p window.

Recorded status: UV-branch kill-test surface [E]/[X]/[C] (carrier-PS on the all-order footing; proton-SAFE hierarchy computed; plain-SM GUT killed; no fake tau_p)

Original ledger status

GRAV.AMPLITUDE.01

GRAV.AMPLITUDE.01

The entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary (2026-06-24) -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed spin-2 propagator P(p^2)=e^{-p^2/M^2}/p^2=1/(p^2 a) with a(u)=e^u (u=p^2/M^2), M=M_scal. [E] ONE POLE, GHOST-FREE: a=e^u entire and nowhere zero (v380) => the only pole is p^2=0 with residue lim p^2 P=e^0=1>0 (one healthy massless graviton). [E] UV-SOFTENED: the dressed/GR ratio e^{-u} at u=1,5,10,20 = 0.37,6.7e-3,4.5e-5,2.1e-9 -- suppressed faster than any power (infinite-derivative improvement), monotone->0. [E] LOW-ENERGY = GR + CALCULABLE CORRECTION: e^{-u}=1-u+u^2/2-...; the leading deviation -u=-p^2/M^2 (M=M_scal=c3^{7/2}Mbar~3.06e13 GeV, v253). [C] TREE UNITARITY: a single positive-residue pole, no extra poles / negative-norm states (entire zero-free form factor) => Im A>=0, consistent with v370 (spin-2) + v380 (entire). [C] AMPLITUDE STRUCTURE: A=(kappa^2/2)(T.P2.T')e^{-p^2/M^2}/p^2, GR at low energy, softened in the UV (P2 = Barnes-Rivers spin-2 projector, v370); perturbative-only (QG.AMB.01 stays a [C] redundancy, v369).

Recorded status: Perturbative graviton amplitude [E]/[C] (entire-form-factor exchange: finite, ghost-free, UV-softened, tree-unitary; perturbative-only)

Original ledger status

CORRECTIONS.GAP.01

CORRECTIONS.GAP.01

The practical harvest of v383 (2026-06-24): the same spectral gap that makes each sector parameter-free ALSO sets the SIZE of its first correction -- for a gapped operator the deviation from the attractor decays at the ratio lambda_2/lambda_1 per step, so that ratio IS the leading-correction size. [E] FLAVOR: lambda_1=1, lambda_2=(2/3)^6=64/729 => first Koide correction ~0.0878 (v56/v82). [E] RECOVERY: the seam QECC Petz rate is the same (2/3)^6 (v221). [E] QG DECOUPLING: the ambient correction is bounded by chi=1/(1-(2/3)^6)=729/665 (finite, v337). [E] DISCRETE COMPILER: the main-branch update T_net=(A+2I)/4 fixes the Kac marks (lambda_1=1) and has subleading lambda_2=(phi+2)/4~0.9045 -- the compiler transient decays at the golden rate (carrier-5 facet, v303/v312). [E] UNIFIED: correction_n~(lambda_2/lambda_1)^n everywhere; the rates split into the (2/3)^6 family (flavor/recovery/QG, family-3 dynamic, in Q) and the golden family (the compiler, carrier-5 static, in Q(sqrt5)) -- the two number-field facets of v314/v383. [C] the correction calculus: the gap does double duty -- it is both WHY there is no free parameter and HOW BIG the first correction is, so the magnitude of sub-leading effects across TFPT is organised, not free.

Recorded status: Correction calculus [E]/[C] (each sector's gap sets its first-correction size; (2/3)^6 family vs golden family; the harvest of v383)

Later scope correction: the DtN form estimate alone does not prove the transfer gap.

Original ledger status

CORRECTIONS.BUDGET.01

CORRECTIONS.BUDGET.01

The gap correction (v387) is a TYPED budget, NOT a uniform band on every prediction (2026-06-24): the (lambda_2/lambda_1)^n size is a property of the distance from a gapped operator's leading eigenvector, so it is only defined where a subleading lambda_2 exists. The prediction surface splits into FOUR correction classes (the verdict already implied by v303: of the four F_transfer instances only F_pole carries the seam rate). [E] SEAM-GAPPED class: Koide (F_pole, v303), horizon recovery (v221) and the QG-decoupling bound (capped by chi=1/(1-(2/3)^6)=729/665, v337) carry lambda_2=(2/3)^6=64/729; the discrete compiler decays at the golden (phi+2)/4 (carrier-5 facet, v312) -- the two number-field facets (v314/v383/v387). [E] KOIDE FIRST CORRECTION (door #2): F_pole is the ONE seam-gapped prediction, per-step Moebius rate (2/3)^6~0.0878 (v371), while the source quotient Q_src=0.66446 sits 0.33% below Q*=2/3 -- the rate is the suppression SCALE of the sub-leading texture, NOT the residual itself (an honest distinction). [E] EXACT-IDENTITY class: det R=8, N_Phi=1, theta_eff=0 are exact, sin^2 theta13=phi0 e^{-5/6} a closed form -- NO lambda_2 => correction 0 STRUCTURALLY (a (2/3)^6 band would contradict the [E]-identity status). [E] EXTERNAL-RATE class: eta_B (thermal washout), axion (cosmological freeze), m_p/m_e (RG) share only the gapped SHAPE with external rates, firewalled (v187). [E] FIXED-POINT class: the sub-leading texture is already explicit in the closed form (sin^2 theta12: eps=(3/4)phi0=c3+36 c3^4 EXACTLY). [C] THE BUDGET: a single uniform band on every prediction is WRONG; the size is keyed to the MECHANISM class. A typing of v387 (as v384 is of v383), no new number.

Recorded status: Typed correction budget [E]/[C] (the gap correction is keyed to the mechanism class, not a uniform band; seam-gapped=(2/3)^6/golden, exact-identity=0, external-rate=external, fixed-point=explicit texture)

Later scope correction: the DtN form estimate alone does not prove the transfer gap.

Original ledger status

GRAV.LOOP.FINITE.01

GRAV.LOOP.FINITE.01

The entire-form-factor graviton is UV-finite at the LOOP level by power counting (2026-06-24) -- the honest next step past v386 (which established the tree amplitude), extending v304/v370/v380/v386 from the propagator to the superficial degree of divergence of loop graphs. HONEST SCOPE: this is the standard infinite-derivative/nonlocal-gravity finiteness statement (Tomboulis; Biswas-Mazumdar-Siegel; Modesto); it is NOT a full proof of perturbative quantum gravity. [E] SUPER-POLYNOMIAL FALLOFF: for every polynomial degree k, p^k e^{-p^2/M^2}->0 as p->inf (k=2..20), so the dressed propagator cannot leave a power-counting divergence. [E] ONE DRESSED LINE KILLS A QUADRATIC DIVERGENCE: int_{p0}^Lambda p^3(e^{-p^2/M^2}/p^2)dp -> (M^2/2)e^{-p0^2/M^2} (converged at 10M/20M), while the GR int p^3/p^2 dp grows quadratically. [E] SUPERFICIAL DEGREE -> -infinity: GR has a fixed degree D=4L+2V-2I per L-loop graph; the entire form factor multiplies the integrand by e^{-(#internal)p^2/M^2}, so the effective degree is -infinity at every loop order L (dressed cutoff-ratio ->1 vs GR ->4). [E] the regulator is the SEAM scale M=M_scal=c3^{7/2}Mbar~3.06e13 GeV (v253) with the seam KMS form factor e^{-u} (v259), a derived scale, not a Pauli-Villars dial. [C]/[O] LOOP UNITARITY is the subtle OPEN point: tree unitarity holds (single positive-residue pole, v386), but unitarity of a nonlocal form factor at loop level (Lorentzian continuation/macro-causality, Pius-Sen/Briscese-Modesto) is genuinely subtle and still debated -- NOT claimed solved.

Recorded status: Perturbative graviton loop UV-finiteness [E] (power counting; super-polynomial falloff, degree -> -infinity at every loop order, seam-regulated) + loop unitarity [C]/[O] (the honest open point, not claimed solved)

Original ledger status

COXETER.PRIME2.01

COXETER.PRIME2.01

The prime-2 facet of the order-30 Coxeter clock, completing v383 (2026-06-24). The clock 30=2*3*5=h(E8) had two named number-field facets (the golden phi in Q(sqrt5), prime-5/carrier; (2/3)^6 in Q, prime-3/family); this names the prime-2 facet and identifies it with structure ALREADY in the theory: the Gaussian field Q(i), i.e. the CM point tau=i and the order-4 mu4=Z/4 square seam deck (v282/v288/v333). [E] THE CLOCK FACTORS INTO THREE PRIMES: h(E8)=30=2*3*5 (exactly three prime factors). [E] ONE QUADRATIC FACET FIELD PER PRIME, EACH RAMIFIED AT ITS PRIME: disc Q(i)=-4 (2 ramifies), disc Q(sqrt-3)=-3 (3 ramifies), disc Q(sqrt5)=5 (5 ramifies); ramified primes {2,3,5}, product 2*3*5=30=h(E8). [E] THE PRIME-2 (GAUSSIAN) FACET = the Z/4 seam deck: min poly of i is x^2+1, tau=i has j(i)=1728=12^3 and is fixed by the modular S of order 4=2^2 (S^2=-I); |mu4|=4=2^2 (v288) -- the static, even, seam-orientation facet (previously unnamed). [E] THE PRIME-5 (GOLDEN) FACET (v383): phi=(1+sqrt5)/2, min poly x^2-x-1, 2cos(pi/5)=phi (pentagon), carrier-5. [E] THE PRIME-3 (FAMILY) FACET (v383/v220): the dynamic rational (2/3)^6 in Q (family-3) with the Eisenstein zeta_3 (j=0, delta_CKM=pi/3, hexagonal CP) the prime-3 CM point. [C] COMPLETION: the three primes of the Coxeter clock now each carry a number-field facet -- Gaussian(2)/Eisenstein(3)/golden(5)=square/hexagon/pentagon=seam/CP/carrier; the prime-2 facet was the previously-unnamed one, and the prime set {2,3,5} is forced by h(E8)=30, not chosen.

Recorded status: Prime-2 facet of the Coxeter clock [E]/[C] (h(E8)=30=2*3*5; one quadratic facet field per prime, ramified at it; the prime-2/Gaussian/Z4-seam facet completes v383's golden and family facets)

Original ledger status

FORM.SPECTRALGAP.01

FORM.SPECTRALGAP.01

LEAN 4 FORMALISATION of the SCALAR CORE of the universal spectral-gap principle (door #4, 2026-06-24) -- new module TfptCarrier/SpectralGapAttractor.lean, lake build OK (target TfptCarrier.SpectralGapAttractor; aggregator TfptCarrier rebuilt, 3364 jobs), no sorry, only the three standard kernel axioms. It formalises the meta-theorem of v303/v383/v387 at the one-dimensional reduction: the affine gap contraction iter(r,x*,x0) with multiplier r=lambda_2/lambda_1. [F] iter_sub: the deviation has the closed form iter_n - x* = r^n (x0 - x*) (general n, induction). [F] iter_tendsto: 0<=r<1 (the spectral gap) => iter_n -> x* (the unique attractor), via Mathlib tendsto_pow_atTop_nhds_zero_of_lt_one. [F] starts_agree: two starts a,b differ by r^n (a-b) -> 0, so the attractor is INDEPENDENT of the initial state (parameter-freeness). [F] no_gap_no_forget: r=1 (no gap) => iter_n - x* = x0 - x* is CONSTANT (the start is a free parameter) -- the gap r<1 is exactly what removes it. [F] seam_rate_lt_one: (2/3)^6 in [0,1) (prime-3/family facet); golden_rate_lt_one: (5+sqrt5)/8=(phi+2)/4 in [0,1) (prime-5/carrier facet). FINITE-DIM EXTENSION (the multi-dimensional case, reduced to the scalar core): component_tendsto (a non-dominant eigencomponent |r|<1 decays r^n c -> 0); deviation_tendsto (with the dominant eigenvalue normalised to 1, the deviation vector -- all non-dominant components -- tends to 0, so the iterate converges to the dominant eigendirection = the unique attractor, for any start); deviation_unique (two starts give deviation vectors both -> 0 => the selected eigendirection is independent of the start = parameter-freeness); flavor_deviation_tendsto (concrete instance on the cusp-transfer spectrum {1,(2/3)^6,(1/3)^6}, v56/v82/v383). HONEST SCOPE: the scalar reduction PLUS the finite-dimensional diagonalisable case; the general non-diagonalisable / infinite-dimensional Perron-Frobenius statement stays the cited theorem.

Recorded status: Formal [F] (Lean kernel; no extra axioms) -- the scalar core + the finite-dimensional diagonalisable case of the spectral-gap meta-theorem (v383): gap => unique attractor + geometric decay => parameter-free

Original ledger status

ALPHA.QUILLEN.PROGRESS.01

ALPHA.QUILLEN.PROGRESS.01

An HONEST attempt at the external target ALPHA.QUILLEN.EXACT.01 (door #5, 2026-06-24): it REDUCES the open step to a sharper named sub-target via a solvable model, but does NOT close it -- the status of ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384). [E] SOLVABLE MODEL: det_zeta(-d^2/dtau^2 + m^2) on a circle of circumference beta = (2 sinh(beta m/2))^2 (textbook); its m-variation is the closed form beta*coth(beta m/2) = 2/m + (beta^2/6)m - (beta^4/360)m^3 + ... an exact heat-kernel/Laurent series (the m^3 coefficient -beta^4/360 = -1/360 verified). [E] ZETA-DET VARIATION = HEAT-KERNEL DATA: the variation is governed entirely by closed heat-kernel coefficients, so a zeta-determinant's coupling-variation is STRUCTURED anomaly data, not a free constant -- hence v382's counterterm 8 b1 c3^6 (a Gauss-Bonnet heat-kernel power, c3=1/(8 pi)) is the RIGHT KIND of object. [E] THE v382 SPLIT re-verified at alpha^-1=137.0359992 (8 b1=(4/5)*41 a U(1) index, c3^3/c3^6 heat-kernel powers). [E] THE REDUCTION: the open step now reduces to the named sub-target 'the seam U(1) operator's Seeley-DeWitt coefficient = 8 b1 c3^6 (with a_0,a_1 vanishing on the mu_4 seam moduli)' -- a heat-kernel computation, sharper than 'prove the functional identity'. [O] NOT CLOSED: computing the actual seam-operator zeta-determinant (not the toy) and showing its variation = the cubic is the from-first-principles AQFT/zeta proof (stays [O]); SEAM.EQUIV.01 continuum existence (MMST, v336) likewise stays the other external [O]; the value alpha^-1 stays [E].

Recorded status: Honest attempt / reduction [E]/[O] (a solvable-model zeta-det mechanism + the reduction of ALPHA.QUILLEN.EXACT.01 to the named sub-target 'seam a_2 = 8 b1 c3^6'; the headline target stays OPEN, not closed)

Original ledger status

ALPHA.QUILLEN.PROGRESS.02

ALPHA.QUILLEN.PROGRESS.02

A SECOND HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-27, v433): it GROUNDS and CONNECTS, it does NOT close it -- ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384), alpha^-1 stays [E]. [E] SOLVABLE 4D MODEL REACHES a_4: the flat Delta=-d^2+m^2 on T^4 (vol V) has Tr e^{-tD}=V/(4 pi)^2 t^-2 e^{-t m^2}, Gilkey coeffs a_0=V/(4 pi)^2, a_2=-V m^2/(4 pi)^2, a_4=V m^4/(2(4 pi)^2); the t^0/a_4 conformal-anomaly order is NON-ZERO -- the order v391's 1D circle toy (a_0,a_1 only) could not reach. [E] IT IS THE ORDER v342 USES: v342 grounds the quadratic term in the Gilkey a_4 gauge-curvature coefficient 30/360=1/12 (Omega^2/12, Gilkey Thm 4.8.16); v433 exhibits that a_4 is the operative, computable order -- unifying v391 (a zeta-det variation IS heat-kernel data) with v342 (the seam term IS the Gilkey a_4). [E] MEASURE IS c3-BUILT: (4 pi)^-2=1/(16 pi^2)=(2 c3)^2=4 c3^2 in the seam 2D-boundary normalisation c3=(1/2)(4 pi)^-1. [E] the v382 split re-verified at alpha^-1=137.0359992. [O] NOT CLOSED: the actual seam U(1) zeta-det a_4 coefficient (=8 b1 c3^6) on the mu_4 seam moduli and the origin of the cubic a^3 Maxwell/Chern moment stay open (external math, type A, v384); the exact seam F-normalisation fixing the coefficient VALUE stays [C] (v342); SEAM.EQUIV.01 continuum existence (MMST, v336) stays the other external [O]; alpha^-1 stays [E].

Recorded status: Second honest step / grounding [E]/[O] (a solvable 4D model exhibiting the nonzero a_4 conformal-anomaly order + the v391<->v342 connection; the headline target stays OPEN, not closed)

Original ledger status

ALPHA.QUILLEN.PROGRESS.03

ALPHA.QUILLEN.PROGRESS.03

A THIRD HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-28, v434): it settles the status of the three residuals named after v433 and shows they are NOT three independent open problems -- the target stays [O], alpha^-1 stays [E]. [E] b1 IS THE U(1) a_4 HEAT-KERNEL COEFFICIENT (the beta-function = a_4 theorem, Vassilevich): computed from the carrier hypercharge content with the standard spin weights (2/3 per Weyl fermion, 1/3 per complex scalar), sum (2/3)Y_f^2 + (1/3)Y_s^2 = 41/6 (SM normalisation) and (3/5)*that = 41/10 = b1 (GUT) -- so the b1 in the counterterm 8 b1 c3^6 is the a_4 heat-kernel coefficient of the carrier U(1)_Y content (same number as the beta, v159/v246), the SAME KIND of object as the alpha^2 Calderon a_4 (v342), NOT a fitted multiplicity. [E] the geometry factors off: 8 b1 c3^6 = b1*(rank E8)*c3^6 (rank E8=8 the chi=2 seam boundary, v216; c3^6 the six boundary insertions, v342). [C] RESIDUAL (1) 'exact a_4 = 8 b1 c3^6 on the mu_4 seam moduli' == RESIDUAL (3) 'the seam F-normalisation': with b1 and the c3-powers heat-kernel-forced, the only freedom left in the exact a_4 value is how the gauge curvature couples to the boundary measure -- ONE [C] obligation, not two. [E] RESIDUAL (2) located (not closed): a^3 - 2 c3^3 a^2 = a^2 (a - 2 c3^3), with a^2 the Gilkey gauge-curvature (Quillen/Chern) density (v342), so the leading a^3 = a*a^2 is the first MOMENT of the Chern density -- a topological level at boundary order c3^0, not a Seeley-DeWitt curvature integral; its from-first-principles (Chern-Simons-type) origin stays [O]. [E] NET REDUCTION: the EM-Ward residual is ONE [C] (residuals 1&3) + ONE [O] (residual 2), not three independent problems. [O] NOT CLOSED: the alpha^3 Chern level + the from-first-principles proof are external math (type A, v384); the seam F-normalisation stays [C]; SEAM.EQUIV.01 continuum existence (MMST, v336) stays the other external [O]; alpha^-1 stays [E].

Recorded status: Third honest step / grounding+reduction [E]/[C]/[O] (b1 = the U(1) a_4 heat-kernel coefficient via beta=a_4; residuals 1&3 collapse to one seam F-normalisation [C]; residual 2 the alpha^3 Chern level located but [O]; the headline target stays OPEN)

Original ledger status

ALPHA.QUILLEN.PROGRESS.04

ALPHA.QUILLEN.PROGRESS.04

A FOURTH HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-29, v435): it attacks the SINGLE remaining [O] left after v434 -- residual (2), the cubic alpha^3 Chern/Maxwell moment -- and SHARPENS it with a verifiable test plus a conditional typing, it does NOT close it; the target stays [O], alpha^-1 stays [E]. [E] pi-POWER / METRIC-INDEPENDENCE TEST: the three EM-closure coefficients carry pi-powers exactly {0,3,6} = their c3-orders -- Maxwell k0=1 -> pi^0/c3^0, Calderon -2 c3^3 = -1/(256 pi^3) -> pi^3, transport -8 b1 c3^6 = -41/(327680 pi^6) -> pi^6 -- so the Maxwell a^3 is the UNIQUE pi^0/c3^0 (metric-INDEPENDENT) term. A heat-kernel boundary coefficient ALWAYS carries the (4 pi)^{-d/2} measure (c3=1/(8 pi)); a metric-independent term carries none -- the defining signature of a TOPOLOGICAL term (a Chern-Simons/eta level does not see the metric, a curvature integral does). So the test PARTITIONS the closure into ONE topological level (a^3) + TWO heat-kernel boundary terms, confirming v342/v434's 'a^3 is a level, not a Seeley-DeWitt curvature integral' typing from a TEST rather than a claim. [E] DUAL LADDER: coupling power (3-n) at c3-order 3n for n=0,1,2 (the n=2 transport carries log(1/phi) in place of a^1); a^3 is the n=0 rung -- maximal coupling power, ZERO boundary insertions, the only bulk/topological rung. [C] CONDITIONAL LEVEL QUANTISATION: IF a^3 is the seam U(1) Chern-Simons/eta boundary level (the EM1 reading, v48 -- a [P] input, NOT proven here), large-gauge invariance (Dirac quantisation of the U(1) level on the closed seam 3-boundary) forces the level into Z, and k0=1 is the UNIT (minimal nonzero) level -- a topological integer, NOT a tunable real; this converts 'the coefficient happens to be 1' into 'the coefficient is an integer level and 1 is the unit'. [O] NOT CLOSED: the EM1 lemma itself (the from-first-principles proof that d_tau log Z_Maxwell = a^3 IS the seam U(1) CS/eta level -- the genuine Chern-Simons-boundary computation) stays external math (type A, v384); the seam F-normalisation stays the one [C] (residuals 1&3, v434); SEAM.EQUIV.01 continuum existence (MMST, v336) stays the other external [O]; alpha^-1 = 137.0359992 stays [E].

Recorded status: Fourth honest step / metric-independence test + conditional level typing [E]/[C]/[O] (the pi-power test isolates a^3 as the unique pi^0/c3^0 metric-independent topological rung; conditional on the CS/eta reading the a^3 coefficient is an integer level, =1 the unit; the EM1 CS-boundary proof and the headline target stay OPEN)

Original ledger status

SEAM.S3.SCALINGLIMIT.01

SEAM.S3.SCALINGLIMIT.01

An HONEST attack on the one open lemma of SEAM.EQUIV.01 -- the continuum scaling-limit existence (2026-06-24). It does NOT close v336 (the abstract existence is the cited MMST theorem); it STRENGTHENS the case with the existence-relevant observable v376 did not test: that the finite-size data CONVERGE (a divergent/drifting sequence would have no continuum limit). [E] MULTI-SIZE CONVERGENCE: the Calabrese-Cardy correlation-matrix EE slope c1(L) at L=66,130,258,386,514 is a monotone sequence approaching 1, with |c1(L)-1| strictly decreasing from 4.6e-4 to 7.1e-6. [E] RICHARDSON EXTRAPOLATION: a 1/L fit gives c1(inf)~0.9999, so the 16-Majorana (=8 complex mode) collar has c=8*c1(inf)~7.9993~8=g_car+N_fam -- the (E8)_1/SO(16)_1 continuum value reached IN the limit. [E] CAUCHY SIGNATURE: the successive differences |c1(L_{k+1})-c1(L_k)| are themselves strictly decreasing and tiny -- a numerical Cauchy sequence (necessary, not sufficient, for existence). [O] convergent finite-size DATA are strong evidence but NOT a proof that the continuum limit exists (the cited MMST theorem, v336), and do not pin (E8)_1 over the same-c SO(16)_1 (the holomorphy det K=1 discriminator, v377/v378). Strengthens the residual, does NOT close it -- SEAM.EQUIV.01 stays closed modulo the cited theorem.

Recorded status: Scaling-limit convergence evidence [E] (the finite-size central charge converges to c=8 and Richardson-extrapolates there -- the existence-relevant observable) + the abstract existence stays [O] (cited MMST v336); an honest attack that strengthens, does not close

Original ledger status

CORRECTIONS.NUMERIC.01

CORRECTIONS.NUMERIC.01

The typed correction budget (v388) turned into ACTUAL first-correction magnitudes -- a computed theoretical-uncertainty surface (2026-06-24), the short-term testable harvest of v388: instead of merely TYPING each prediction's correction, this gives the NUMBER, so a parameter-free central value can be quoted as 'value +- computed first correction'. [E] FIXED-POINT band: the phi0-derived fixed points (theta12, theta13, lambda_C, beta_rad) carry the EXPLICIT phi0 puncture term as their first correction, dtop/phibase = 36 c3^4/c3 = 9/(128 pi^3) ~ 0.227% (exact, no fit); the SAME number is theta12's epsilon first-correction (eps=(3/4)phi0=c3+36 c3^4). [E] SEAM-GAPPED band: the seam-gapped class (Koide F_pole, recovery) has rate (2/3)^6=64/729 ~ 8.78%; the QG-decoupling bound is CAPPED by the susceptibility excess chi-1 = (2/3)^6/(1-(2/3)^6) = 64/665 ~ 9.62% (finite, v337). [E] EXACT-IDENTITY band = 0 STRUCTURALLY (det R=8, N_Phi=1, theta_eff=0 are exact -- a band would contradict [E]). [E] EXTERNAL-RATE band = external physics, quoted from the modules (m_p/m_e +-7.5% v374; n_s/r N* in [50,60]; eta_B ~1.07x v212; axion scenario), fenced by v187 -- NOT a seam band. [C] the assembled per-class numeric budget gives each prediction a 'central value +- computed first correction'.

Recorded status: Numeric correction budget [E]/[C] (the typed budget v388 as actual first-correction magnitudes: fixed-point 0.227%, seam-gapped 8.78%/QG-capped 9.62%, exact-identity 0, external quoted -- a computed theoretical-uncertainty surface)

Later scope correction: the DtN form estimate alone does not prove the transfer gap.

Original ledger status

COXETER.ATOMS.01

COXETER.ATOMS.01

The clockwork coherence (2026-06-24, bird's-eye): the three Coxeter primes ARE the three anchor atoms ARE the three number-field facets, and the prime-2 seam is the common dynamical factor. A re-reading tying v390 (facets) to the anchor a=(1,1,2) and v319 (5x6 clock). [E] ANCHOR ATOMS = COXETER PRIMES: a=(1,1,2) has e3=2=|Z2|, p0=3=N_fam, e2=5=g_car, product 2*3*5=30=h(E8) -- the clock's three primes ARE the anchor's three atoms. [E] ATOMS = FACET FIELDS (v390): 2->Q(i) (disc -4), 3->Q(sqrt-3) (disc -3), 5->Q(sqrt5) (disc 5), each ramified at its prime; {atoms}={primes}={fields}. [E] QG SUSCEPTIBILITY PURE {2,3}: chi=1/(1-(2/3)^6)=729/665=3^6/(3^6-2^6), (2/3)^6=2^6/3^6, exponent 6=2*N_fam. [E] PRIME-2 COMMON DYNAMIC FACTOR: 2/3=|Z2|/N_fam (prime-2/prime-3) and (phi+2)/4=(phi+2)/|mu4| with |mu4|=4=2^2, so both dynamic rates carry prime-2 (the seam involution). [E] 30=5x6=g_car*(2 N_fam) (v319). [C] the prime-2 seam is the universal dynamical engine; prime-3 (family) and prime-5 (carrier golden) the two attractors.

Recorded status: Clockwork coherence [E]/[C] (Coxeter primes = anchor atoms = facet fields; chi=3^6/(3^6-2^6); both dynamic rates carry prime-2; 30=5x6) -- a bird's-eye re-reading, no new number

Original ledger status

HYP.COUPLED.01

HYP.COUPLED.01

HYP.COUPLED.01: finite local carrier/family recursion F(m)=T_net m M^T, checked on all 27 basis inputs; full v486/v487 M has spectrum {1,2/3,1/3}. The joint Perron line is marks tensor e0. One hand is one network step and six family substeps, T_net tensor M^6, not T_micro^6. Exact even/odd conjugacy O^T M^6 O=diag(1,64/729,1/729) supplies the complete v324 readout. v299 growth is unchanged. P2 and phi0 remain inputs. No physical OS-transfer or local charged-field identification is claimed. Correction 2026-10-27: the former routine discarded its network update and its test did not call that routine; the former v327 matrix also erased the odd mode.

Recorded status: Coupled hypergraph rewrite [E]/[O] (one local rule unifies carrier x family; joint attractor marks x e0; recovery (2/3)^6 after one hand; v324 fiber emerges as cusp readout; v299 growth unchanged) -- mechanism unified, phi0 + seed remain

Original ledger status

HYP.PHI0.01

HYP.PHI0.01

THE phi0 LEADING TERM FROM ICOSAHEDRAL COMBINATORICS (2026-06-24, sharpening v312/v395): the tree-level retained seed phibase = 1/(6 pi) has a forced combinatorial reading on the icosahedral hypergraph; the puncture 48 c3^4 stays analytic. [E] ICO COUNTS ANCHOR-FORCED: V=12, E=30=h(E8), F=20=g_car(g_car-1), |Aut|=120=4h=|2I| (all from {g_car,N_fam}={5,3}). [E] LEADING TERM EXACT: phibase = 1/(6 pi) = (4/3) c3 = F/(4 h pi) = F/(|Aut| pi) = (F/(g_car N_fam)) c3. [E] F/h = |Z2|/N_fam (hyperedge/Coxeter = v327 survival); phibase = (F/h)/(4 pi) = c3 (g_car-1)/N_fam. [E] GAUSS-BONNET: icosahedron vertex-deficit sum = 4 pi; c3 = 1/(|Z2| 4 pi) same boundary datum (v216/v342). [E] HONEST NEGATIVE: puncture dtop = 48 c3^4 not a rational hypergraph fraction; full phi0 still has analytic piece. [C] phibase is tree-level seed = (hyperedges)/(g_car N_fam) x c3, not an independent rewrite injection; puncture stays [O].

Recorded status: phi0 leading term [E]/[C]/[O] (phibase = F/(g_car N_fam) c3 = 1/(6 pi); F/h = |Z2|/N_fam; Gauss-Bonnet consistent; puncture 48 c3^4 still analytic) -- combinatorial reinterpretation, not full phi0 closure

Original ledger status

HYP.PHI0.PUNCTURE.01

HYP.PHI0.PUNCTURE.01

NAMES THE phi0 PUNCTURE TERM AS A TRACKED [O] HEAT-KERNEL TARGET (2026-06-24, v408): dtop = Omega_adm c3^4 = 48 c3^4 = 3/(256 pi^4) IS the order-4 (|mu4|) local boundary Seeley-DeWitt contact term of the mu4 puncture divisor, summed over Omega_adm = N_fam dim S+ = 48 admissible fermion states -- the analytic complement of the icosahedral tree term phibase (v396, HYP.PHI0.01). Elevates v396's flagged puncture residual to its own citable target WITHOUT a new number (a FACE of the seam boundary analysis, not a new gate). [E] THE SPLIT IS EXACT: phi0 = phibase + dtop = 1/(6 pi) + 48 c3^4 (v396/ARCH.QUAD.01). [E] PUNCTURE COUNT = Omega_adm = N_fam dim S+ = 48, order = |mu4| = 4. [E] CLOSED FORM dtop = 3/(256 pi^4); c3 = 1/(|Z2| 4 pi) Gauss-Bonnet (v216/v342) so c3^4 is a fourth-order boundary heat-kernel power (the right KIND of object, cf. v391). [E] HONEST NEGATIVE: dtop not a rational hypergraph fraction (dtop/phibase < 1%). [O] THE TARGET: the from-first-principles heat-kernel proof that Omega_adm c3^4 IS the order-4 boundary contact term. [C] two engines, two terms: the hypergraph gives phibase, the boundary heat-kernel gives dtop -- a FACE of the seam boundary analysis (the c3 datum), not a second independent gate. No new number (reuses v396/ARCH.QUAD.01, Wolfram-mirrored under ARCH.QUAD.01/v37). UPDATE 2026-07-14 (v483/HYP.PHI0.GEOM.01): the geometric/equivariant side is EXACT (all twisted pillowcase traces t-independent rationals), so the target narrows to the ONE rule 'per-mark insertion weight = c3'; stays [O]. UPDATE 2026-07-14 (v484/SEAM.CONTACT.UNIT.01): the per-mark weight rule MERGES with ALPHA.QUILLEN.EXACT.01 into one analytic step -- the contact unit is the KMS seam unit (v239), derived for the finite cycle sector; the remaining [O] is the diagonal zeta-renormalisation + multiplicity matching (48 = Omega_adm). UPDATE 2026-07-14 (v485): the computable side is COMPLETE (the flat 48-count is the same state set as alpha's Y^2-weighted 41; diagonal zero at the KMS scale); the remaining [O] is the SEAM.EQUIV.01 face alone.

Recorded status: Named target [E]/[O] (the phi0 puncture 48 c3^4 as the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture, summed over Omega_adm=N_fam dim S+=48; a face of the seam boundary analysis, elevates v396's puncture residual to a citable target; no new gate)

Original ledger status

RES.COXETER.SYMMETRY.01

RES.COXETER.SYMMETRY.01

CLOSED AS A STRUCTURAL LEMMA (2026-06-24, v409): prime-2 (the seam sheet involution) is NECESSARY but NOT autonomous, so no prime-2-only attractor exists -- resolving the v394 open question's falsifiable corollary. The facets are prime-2 (Q(i)/tau=i/Z4 seam deck, static) + prime-3 (Eisenstein zeta3 CP, static; (2/3)^6, dynamic) + prime-5 (golden, static; (phi+2)/4, dynamic). The prime-2 seam appears as the common FACTOR in BOTH dynamic rates (2/3=|Z2|/N_fam; (phi+2)/4=(phi+2)/|mu4|, |mu4|=2^2), NOT as a separate attractor. THE LEMMA (v409): the sheet involution sigma=diag(1,-1,-1) has spectrum {+1,-1} and projector (I+sigma)/2 spectrum {0,1} -- none in the open interval (0,1), so prime-2 supplies parity/projection, never a nonzero contraction rate; the genuine rates 2/3 and (1/3)^6 lie in (0,1) and carry prime-2 only as a FACTOR (2/3=|Z2|/N_fam needs prime-3; (phi+2)/4, |mu4|=2^2, needs the golden phi/prime-5; 30=5x6=g_car*(2 N_fam), carrier static, 2*3 dynamic). [E] So no prime-2-only attractor exists; [C] prime-2 is the universal dynamical parity factor, necessary in every sheet-paired transport, not autonomous -- dynamics begins only after coupling to family-3 or carrier-5 (mu4=2^2 the Galois bridge). This closes the falsifiable corollary and sharpens v383's 'every sector is the same gapped operator' towards 'the same SEAM-driven operator'; the full 'appears in every gap' universality stays the v383 reading.

Recorded status: Structural lemma [E]/[C] (prime-2 necessary, not autonomous: the sheet involution has spectrum {+-1} and projector {0,1}, none in (0,1), so no prime-2-only attractor; reuses established atoms, no new number) -- closes the v394 open-question corollary

Original ledger status

FORM.COXETER.PRIME2.01

FORM.COXETER.PRIME2.01

LEAN 4 FORMALISATION of the RES.COXETER.SYMMETRY.01 falsifiable corollary (2026-06-24): new module TfptCarrier/CoxeterPrime2.lean machine-proves 'no prime-2-only attractor exists', upgrading the v409 Python check to a Lean theorem. [E] involution_eigenvalue: r*r=1 -> r in {1,-1}; idempotent_eigenvalue: r*r=r -> r in {0,1}; involution_not_contraction / idempotent_not_contraction: neither set meets the open interval (0,1); seam_rate_is_contraction: 2/3 in (0,1); no_prime2_only_attractor: the conjunction (parity + projection carry no contraction rate, while 2/3 does). [E] dynamical reading via the SpectralGapAttractor core: parity_eigenvalue_remembers_start (r=1 keeps the start = no attractor) vs seam_rate_has_attractor (r=2/3 converges to the attractor). Built clean (lake build, 3286 jobs); the new theorems are axiom-pure (#print axioms = propext, Classical.choice, Quot.sound only), and #check (AuditCheck) + signature-lock (AuditContract) pass. Strengthens v409/RES.COXETER.SYMMETRY.01 to the machine-proof tier.

Recorded status: Lean formalisation [E] (no prime-2-only attractor: involution eigenvalues +-1, projector {0,1}, none in (0,1), while 2/3 is a contraction rate; axiom-pure) -- machine-proves the v409 corollary