Original claim records.

Original ledger status

OVERDET.FLOOR.01

OVERDET.FLOOR.01

THE UNCONDITIONAL IMPROBABILITY FLOOR + THE L1<->L2 BRIDGE (2026-06-27, v432): the defensible over-determination number that survives even if a skeptic REJECTS the declared formula grammar -- the complement of the conditional null model (v100) and the multiply-vs-compress framework (v427/v428). [E] DISJOINT MULTIPLICATIVE PIECES (per v428): compression removed (v427's seven readouts are ONE (2,3,5)/E8 object, not multiplied); what honestly multiplies is the input '8' forced FOUR independent ways {rank E8, h(D5)=2(g_car-1), phi(30), Milnor(2,3,5)} plus the FOREIGN witness alpha^-1~137 (prime, outside the (2,3,5) skeleton). [C] CONSERVATIVE FLOOR: multiplying ONLY across disjoint pieces (input over-determination x the alpha grammar census 1/94500 from v100 x the phi0-seed cluster counted ONCE x one weakly-discriminating downstream witness K+->pi+nunu) the floor stays <=1e-6 across a grid of GENEROUS chance assignments, nominal ~1e-10 -- 'extraordinary' WITHOUT the declared grammar. [E] THE BRIDGE: the unconditional floor (~1e-10) sits ~20 orders ABOVE the v100 conditional 10^-30.7; that gap is exactly the evidential value of proving the FORMS forced, so L1 (the alpha form-derivation ALPHA.QUILLEN.EXACT.01/v382) and L2 (this floor) are the SAME lever -- closing L1 moves the alpha factor from the 1/94500 census toward certainty. [C] HONEST SCOPE: bounds ONLY the 'is it numerology?' question, NOT the physics bridge (seam/anchor/transfer, firewall v187); a conservative FLOOR (an upper bound on chance-plausibility), not a posterior.

Recorded status: Unconditional over-determination floor [C] (disjoint pieces only, compression removed; floor ~1e-10 vs v100 conditional 10^-30.7; bounds numerology only, firewall)

Original ledger status

ALPHA.QUILLEN.EXACT.01

ALPHA.QUILLEN.EXACT.01

Names the Quillen determinant-line VARIATION as a tracked [O] target (2026-06-23, review Point 10): delta_tau(log det_zeta Delta_U(1) + 8 b1 c3^6 log phi_seam)=0 on the determinant line over the mu4 seam moduli -- i.e. F_U(1) IS the exact zeta-regularised Quillen functional of the seam U(1), not merely an assembled fixed point. Elevates EM.WARD.01's residual (v341/v342) to its own citable target so the one remaining EM obligation is trackable separately from the seam-net identification, WITHOUT creating a second independent open problem (it is a FACE of SEAM.EQUIV.01). [E] the Quillen split holds at the root a^3-2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at alpha^-1=137.0359992 (F_U(1)=0 IS the stationarity, v341). [E] every coefficient is a named atom: 8 b1=(4/5)*41 a U(1) index, c3=1/(8 pi) the Gauss-Bonnet boundary coeff (c3^3,c3^6 heat-kernel powers), q(D5)+q(A3)=2 discriminant forms (v341/v48/v216). [E] the value alpha^-1=137.0359992168 stays closed (unique root+ablation, v3) -- only 'why this functional' is open. [O] THE TARGET: the from-first-principles AQFT/zeta proof of the variation. [C] FACE OF SEAM.EQUIV.01 (v336): the seam U(1) determinant line lives on the same holomorphic seam net, so once the net is (E8)_1 its U(1) sub-determinant is fixed -- not a second gate. No new number (reuses v341, Wolfram-mirrored). UPDATE 2026-07-14 (v484/SEAM.CONTACT.UNIT.01): the target's c3-ladder rule MERGES with HYP.PHI0.PUNCTURE.01 into one analytic step -- the contact unit c3-per-insertion is the KMS seam unit (v239), derived for the finite cycle sector; the remaining [O] is the diagonal zeta-renormalisation + multiplicity matching (41 = 10 b1). UPDATE 2026-07-14 (v485): the computable side is COMPLETE (diagonal zero at the KMS scale, closed-form mark determinant, 41 = Y^2-weighted count of the same 48 states); the target's remaining [O] is now EXACTLY its v382 typing -- the SEAM.EQUIV.01 face -- with no separate analytic unknown left. UPDATED 2026-08-27 (v974): both named faces now carry COMPUTED witnesses. The diagonal-zeta face is EXECUTED as the BFK gluing on the seam circle (gluing constant EXACTLY 2^-N, derived symbolically N = 1..4 at general lengths; jump matrix at KMS R_0 = 16 c3 circ(2,-1,0,-1) = (G_m|_marks)^-1; det'R_0 = 2^16 c3^3, glued product (2 pi)^2; the v485 scale channel reproduced exactly via the KMS unit) -- vs the v484 mark matrix there is NO global proportionality (kernels in SWAPPED mu4 channels), but the correspondence is channel-wise exact (same eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling): the diagonal-zeta face is thereby SHARPENED to the channel-swap question. The finite Quillen identity is verified TWO-SIDED on the twist torus (Berry integral == Poincare-Lelong divisor integral == +1, difference an exact form, transition winding == Chern), typed conditional on the quasi-free rigidity premise (measured, not proven -- SEAM.STATE.RPMIXING.01). STAYS [O]: 'why this functional' is not closed -- the remaining content is typed as {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification of the exact-form difference field}; alpha^-1 = 137.0359992168 re-anchored (unique root on the scanned window, split residual 6.4e-58 at 50 digits). EXECUTED NOTE (2026-08-28, completeness wave): the rigidity premise of the finite Quillen identity is now executed at the finite CAR level (v995: 33 mixing directions killed by KMS alone; covariance redundant; 196608 -> 0); type-III/continuum stays [O]. The finite-collar detline curvature converges exponentially to 2pi with rate ~0.6936 ~ ln 2 (v996) -- a numerical Bismut-Freed shadow, not the continuum theorem. STAYS [O]. Python-only / Wolfram mirror deferred. RELATIVE-DETERMINANT NOTE (2026-08-29, review wave 4): the correct object is the RELATIVE determinant Q(A) = log[det' Delta_A / det' Delta_{A0}] + 8 b1 c3^6 log phi(A); the BFK constant 2^{-4} is A/tau/alpha-INDEPENDENT at fixed cut number, so delta log 2^{-4} = 0 -- no physical compensation needed (consistent with COMPENSATION_INTERNAL + the reviewer's correction). Absolute normalization is fixed by the reference A0. Contract stays [O]. LATE EVENING (2026-08-30, v1014): finite restriction isomorphism verified (c_phase constancy 3.7e-16, conjugation covariance exact, C = W_bulk = W_seam = +1 / mirror -1); orientation fixes the conjugate branch (2 -> 1); the residual constant phase is fixed by the A0 reference normalization -- recorded. Continuum Bismut-Freed stays [O]. Contract stays [O].

Recorded status: Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])

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

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

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

ALPHA.QUILLEN.INFLOW.01

ALPHA.QUILLEN.INFLOW.01

THE ALPHA^3 LEVEL = THE COMPUTED BULK CHERN INVARIANT + THE SEAM F-NORMALISATION = THE AFFINE EMBEDDING INDEX (2026-07-02, closure-route round) -- upgrades BOTH residuals left after v433/v434/v435; does NOT close ALPHA.QUILLEN.EXACT.01. [E] TARGET RE-VERIFIED: alpha^-1 = 137.0359992168 unique root; Quillen split a^3 - 2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at the root < 1e-35 (v341/v382). [E] THE INVARIANT COMPUTED: FHS Chern C(M=1) = 1, C(M=3) = 0 -- the same integers as v367/v461, here read as the quantised U(1) response of the collar phase. [C] k0 = |C| = 1 UNDER THE EM1 READING: the a^3 coefficient EQUALS the computed bulk invariant of the SAME p+ip model that realises S3 -- 'why exactly 1' is answered by COMPUTATION plus the cited inflow identification (TKNN PRL 49 (1982) / Avron-Seiler-Simon PRL 51 (1983): integer quantisation of the U(1) response; Callan-Harvey NPB 250 (1985): boundary level = bulk response; APS 1975 / Alvarez-Gaume-Della Pietra-Moore Ann. Phys. 163 (1985) / Witten RMP 88 (2016): the metric-independent part of delta log det is the eta/CS level; Quillen 1985 / Bismut-Freed CMP 106 (1986): determinant-line curvature integrality) -- REPLACING v435's minimality assumption ('1 is the unit level') by a measurement on the model. [E] k_Y = 5/3 EXACT: tr_5bar(Y^2)/tr(T3^2) = (5/6)/(1/2) = 5/3 (Ginsparg PLB 197 (1987), the string-GUT hypercharge level); (3/5) x (41/6) = 41/10 = b1 -- the 'GUT 3/5' in the closure IS the inverse embedding index, not an imported convention; carrier decomposition 41/6 = 20/3 (3 generations x 16-content) + 1/6 (Higgs doublet). [C] F-NORMALISATION RETYPED: once the seam net is (E8)_1 at level 1 (SEAM.EQUIV.01), the U(1)_Y current sits inside a level-1 current algebra and <J(z)J(w)> = k/(z-w)^2 is FIXED by the embedding index -- level-1 current-algebra rigidity, no continuous dial; the v434 [C] ('how does the gauge curvature couple to the boundary measure') has ZERO independent content: it is a face of SEAM.EQUIV.01 (consistent with the v382 typing), its value the embedding index. [E] THE STRUCTURAL UNIFICATION: the two named targets share ONE object -- the collar phase carries TWO quantised responses, gravitational c_- = 16 x 1/2 x |C| = 8 = g_car + N_fam (feeds SEAM.EQUIV.01/S3, v456) and U(1) C = 1 (feeds the a^3 level, EM1); 'the one theorem and the one number' are two faces of the SAME invertible phase, and closing R1' (v469) feeds both residuals simultaneously. [O] NOT CLOSED: the bridge lemma 'delta log det_zeta(seam) = the inflow response' stays the named cited step; the EM1 reading stays [C]; ALPHA.QUILLEN.EXACT.01 stays [O]; alpha^-1 = 137.0359992 stays [E] regardless. UPDATED 2026-08-27 (v974): the inflow step 'boundary level = bulk response' is upgraded from cited to COMPUTED on the same model (probe laughlin_pump_em1_probe 20/20, PUMP_QUANTIZED_MATCHES_CHERN): Laughlin pump +1 per flux quantum (teleport bookkeeping with exact period closure), edge spectral flow -1/+1 antisymmetric as inflow demands, Streda dN/dPhi = C/(2 pi) exact integers over n_phi = 0..3 -- all equal to the FHS Chern, with the M = 3 controls all zero. The identification of the complex-copy U(1) with the physical Majorana collar stays part of the cited EM1 reading [C]; ALPHA.QUILLEN.EXACT.01 stays [O].

Recorded status: Inflow level + embedding rigidity [E]/[C]/[O]: the a^3 coefficient = the COMPUTED bulk Chern |C| = 1 of the v367 collar (TKNN/ASS quantisation + Callan-Harvey inflow + APS/Witten eta=CS), replacing v435's minimality; the seam F-normalisation = the affine embedding index k_Y = 5/3 (Ginsparg 1987, (3/5)(41/6) = 41/10 = b1) -- zero independent content, a face of SEAM.EQUIV.01; one phase, two responses (c_- = 8, C = 1) feeding both named targets; ALPHA.QUILLEN.EXACT.01 stays [O]

Original ledger status

ALPHA.QUILLEN.DETLINE.01

ALPHA.QUILLEN.DETLINE.01

THE OCCUPIED BERRY LINE OVER THE U(1)-TWIST MODULI HAS CHERN NUMBER = THE BLOCH RESPONSE LEVEL (2026-07-03) -- the finite Berry-Chern response, COMPUTED at the collar model; the Quillen/Dai-Freed comparison remains a separate target; does NOT close ALPHA.QUILLEN.EXACT.01. [E] BLOCH LEVEL RE-VERIFIED: BZ Chern C(M=1) = 1, C(M=3) = 0, C(M=-1) = -1 (the v470/v367 integers). [E] THE OCCUPIED BERRY LINE COMPUTED: the same collar h(k) = sin kx SX + sin ky SY + (M - cos kx - cos ky) SZ in real space on an L x L torus with twisted boundary conditions -- the twist torus (theta_x, theta_y) IS the moduli space of flat U(1) connections -- and the Fukui-Hatsugai-Suzuki curvature of the DETERMINANT LINE of the occupied one-particle frame (the free-fermion many-body ground-state LINE; its normalized vectors are chosen locally) over that torus integrates to 2 pi x 1 exactly (integer to 1e-9) at M = 1, for L = 4 AND L = 6 -- size-independent, as an integer must be. [E] CONTROLS: trivial collar M = 3 gives 0; orientation flip M = -1 gives -1 -- the curvature tracks the phase, not the mesh. [E] TWO TORI, ONE LEVEL: the twist-moduli integer equals the Bloch-BZ integer for all three M -- the Niu-Thouless-Wu identification (PRB 31 (1985)), exhibited on the collar model that realises S3 (v460/v461). [E] GAP: the sampled Fermi gap is open at M=1; analytically |d(k)|^2 = 1 + 2(1-cos kx)(1-cos ky) >= 1 gives the global gap >= 2. This defines a smooth occupied projector, not a global nonvanishing section of its topologically nontrivial line. No Dai-Freed filling or global-section test is performed. [C] INTEGRATED RESPONSE: k0 = |C_FHS| = 1 in the collar model. The FHS continuum convention C_Berry=integral F_occ/(2pi i), with nabla=d+A_occ and c1=iF_occ/(2pi), gives c1[B]=-C_Berry; finite-mesh identification and theta-line sign/duality must be checked separately. This integrated integer does not identify individual holonomies or the exact zeta-determinant variation. The open comparison requires a separately defined chiral Fredholm/Quillen line with its zero locus, a common gauge base, relative connection-level comparison and uniform ultraviolet controls; a Dai-Freed vector requires filling data and takes values in the pulled-back inverse boundary line (Quillen 1985; Bismut-Freed CMP 106 (1986); Dai-Freed JMP 35 (1994); FHS JPSJ 74 (2005)). [O] NOT CLOSED: the abstract-seam zeta-determinant identification (the continuum leg, = the SEAM.EQUIV.01 face); ALPHA.QUILLEN.EXACT.01 stays [O]; alpha^-1 = 137.0359992168 stays [E] regardless. Structurally the same manoeuvre as v471 for SEAM.THEOREM.01's replica side: the named open lemma exercised on a real finite operator.

Recorded status: Numerical [N] (finite Quillen shadow; gate unchanged)

Original ledger status

SEAM.CONTACT.UNIT.01

SEAM.CONTACT.UNIT.01

THE SEAM CONTACT UNIT -- THE MERGED RESIDUAL OF THE TWO ANALYTIC TARGETS (2026-07-14, deep-dive round II): the shared 'c3 per boundary insertion' rule of ALPHA.QUILLEN.EXACT.01 (c3-ladder {0,3,6}, v3/v341/EM.WARD.02) and HYP.PHI0.PUNCTURE.01 (per-mark weight c3, v483) is ONE identity and NOT a new unknown: it is the KMS seam unit 2 pi = 1/(4 c3) with 1/4 = 1/|mu4| (v239) -- one bare boundary propagator ORBIT-AVERAGED over the four marks. [E] UNIT CHAIN: 1/(2 pi) = 4 c3 = |mu4| c3 = |Z2| chi(S^2) c3. [E] MECHANISM DERIVED ON THE SEAM CIRCLE: G(d) = -(1/pi) ln|2 sin(d/2)| (polylog identity, 40 digits) takes INTEGER multiples of c3 ln2 at the mu4 separations (G(pi/2) = -4 c3 ln2, G(pi) = -8 c3 ln2), so G_marks = -4 c3 ln2 x circ(0,1,2,1) with spec {4,-2,0,-2}; the mu4-invariant (orbit-averaged) insertion carries (GV)|_marks = -(c3 ln2) C exactly -- the log-det contact expansion is EXACTLY graded in c3 per insertion, cycle combinatorics Tr(C^k) = 4^k + 2(-2)^k integer. [E] SUITE-WIDE GRAMMAR: F_U(1) ladder {0,3,6} (v3); phi0 ladder {1,4} (v37); Lambda prefactor 3/(4 pi^2) = (8 pi)^2 delta_top = 48 c3^2 (v60) -- the SAME multiplicity Omega_adm = 48 as the puncture at TWO insertions; the g-2 seam loop divides by the same 2 pi = 1/(4 c3). [C]/[O] THE MERGE: the two tracked [O] targets collapse into ONE named analytic step -- the diagonal (self-energy) zeta-renormalisation at the marks + the state-multiplicity matching (48 = Omega_adm = N_fam dim S+, 41 = 10 b1); the finite cycle sector is PROVEN. Anti-numerology: the check integers (circulant, spectrum, traces) are forced by the square mark configuration; no coefficient of either target is claimed. No gate closes, no marker moves. UPDATE 2026-07-14 (v485/SEAM.CONTACT.UNIT.02): the diagonal channel is settled -- G_reg(0) = 0 exactly at the KMS scale, the log is the pure scale channel, the mark determinant resums closed-form, and the 48/41 multiplicities are one state set under two response weights; the merged residual collapses onto the SEAM.EQUIV.01 face. UPDATED 2026-08-27 (v974): the finite cycle sector now has its computed Delta-side partner -- the BFK jump circulant B = circ(2,-1,0,-1) shares the mu4 Fourier eigenbasis with the mark circulant C = circ(0,1,2,1), the |spec| multisets are equal {0,2,2,4}, Tr B^k = 4^k + 2(+2)^k mirrors Tr C^k = 4^k + 2(-2)^k with the sign flip = the kernel swap (B kills the mu4-trivial gauge/zero-mode channel, C the mu4-sign channel), and B + C = 2(I + S). On the doublet channel R_0|_d = (4/ln2) G_marks|_d exactly, with the c3 grading CANCELLING in the ratio -- both matrices carry the same 'c3 per insertion' unit. No global proportionality: the merged residual is sharpened to the channel-swap question, not closed.

Recorded status: Unification/reduction [E]/[C]/[O] (the two analytic targets merge; contact unit = KMS seam unit, derived for the finite cycle sector; diagonal renormalisation + multiplicity matching stay open)

Original ledger status

SEAM.CONTACT.UNIT.02

SEAM.CONTACT.UNIT.02

THE DIAGONAL CHANNEL SETTLED -- THE MERGED TARGET COLLAPSES ONTO THE KEYSTONE (2026-07-14, deep-dive round III; completes the computable side of SEAM.CONTACT.UNIT.01/v484): [E] DIAGONAL ZERO AT THE KMS SCALE: the renormalised coincident-point Green function of |D| on a circle of circumference l (zero mode removed, flat short-distance subtraction) is G_reg(0; l) = (1/pi) ln(l/2pi) EXACTLY (symbolic limit + 30-digit numeric checks at l = pi, 2pi, 4pi) -- it vanishes iff l = 2 pi = 1/(4 c3), the v239 KMS seam circumference: the seam scale is the unique zero-self-energy scheme point. [E] THE LOG IS THE SCALE CHANNEL: G_reg(0; 2 pi kappa) = (1/pi) ln kappa -- matching the functional structure: F_U(1) carries exactly ONE log term (the transport 8 b1 c3^6 ln(1/phi_seam), v3) while the phi0 split (4/3)c3 + 48 c3^4 is log-free; [C] reading: the log term is the diagonal/scale channel, the log-free terms are contact data at the KMS point. [E] CLOSED-FORM RESUMMATION (the BFK/gluing route already in the suite, v151): for a finite-rank mark potential the zeta-det ratio reduces to the 4x4 mark determinant, and with the diagonal zero the v484 expansion RESUMS exactly: det(I - u C) = (1 - 4u)(1 + 2u)^2, u = eps c3 ln2, C = circ(0,1,2,1) -- closed form to ALL orders, the linear term absent precisely because the diagonal vanishes (Tr C = 0), series = v484's Tr(C^k) = 4^k + 2(-2)^k term by term. [E] WEIGHT DICHOTOMY (the multiplicity matching): the SAME 48 = 3 x 16 admissible states (v245) carry both multiplicities -- counted FLAT they give the phi0 puncture count 48 = Omega_adm = N_fam dim S+; counted with the U(1) response weights (Y^2 with the standard loop/GUT factors) they give the alpha budget 41 = 10 b1 = 40 fermionic (Tr_16 Y^2 = 10/3 exact, nu^c = 0) + 1 Higgs (Ginsparg (3/5)(41/6) = 41/10, v470) -- one state set, two response weights, no new number. [C]/[O] CONSEQUENCE: with v484 (unit + cycle sector) EVERY finite/computable piece of the merged ALPHA.QUILLEN.EXACT.01 + HYP.PHI0.PUNCTURE.01 target is proven; the single remaining [O] is the identification of the abstract seam zeta-det with this glued mark determinant -- a face of SEAM.EQUIV.01, exactly the v382 typing, now substantiated computationally. The merged residual collapses onto the keystone; no separate analytic unknown remains. No gate closes, no marker moves; no coefficient fitted (all integers forced by the square configuration and the SM charge table). UPDATED 2026-08-27 (v974): the BFK/gluing resummation named here is now EXECUTED (probe seam_bfk_conical_det_probe 21/21, promoted as v974): C_glue = 2^-N exactly (N = 1..4 symbolic, general interval lengths, Laurent-polynomial identity), massless reassembly det'_zeta(Delta_S1) = l^2 = 2^-N prod(2 a_j) (l/N) det'(R_0) with det'(R_0) = N l / prod a_j, jump matrix = inverse mark Green matrix R(m) = (G_m|_marks)^-1 exactly, and the diagonal/scale channel reproduced exactly through log det'Delta(l) - log det'Delta(1/(4 c3)) = (1/(4 c3)) G_reg(0; l). The keystone typing is unchanged: pillowcase moduli, the 8 b1 index budget and a |D|-level BFK as an operator identity stay open with the keystone.

Recorded status: Completion of the computable side [E]/[C]/[O] (diagonal zero at the KMS scale; closed-form resummation; multiplicity dichotomy; residual = the SEAM.EQUIV.01 face alone)

Original ledger status

ALPHA.QUILLEN.FACES.01

ALPHA.QUILLEN.FACES.01

THE TWO NAMED FACES OF ALPHA.QUILLEN.EXACT.01 CARRY COMPUTED WITNESSES (2026-08-27, seam/alpha promotion wave; probes seam_bfk_conical_det_probe 21/21 SPEC d06b3bbec70e7efc / laughlin_pump_em1_probe 20/20 SPEC f9b5cb0bf20d0293 / quillen_rigidity_chain_probe 18/18 SPEC b4ee0dd0141da6ab, embedded byte-exact in v974). [E] BFK FACE EXECUTED: the Mayer-Vietoris determinant gluing on the seam circle at the four mu4 marks -- C_glue = 2^-N EXACT (N = 1..4 symbolic, general lengths), det'_zeta(Delta_S1) = l^2 reassembled, R(m) = (G_m|_marks)^-1; at KMS R_0 = 16 c3 circ(2,-1,0,-1), det'R_0 = 2^16 c3^3, glued product (2 pi)^2; vs v484 channel-wise EXACT (same mu4 eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling, Tr B^k = 4^k + 2 2^k vs Tr C^k = 4^k + 2(-2)^k) but NOT globally proportional -- the kernel swap (gauge zero mode vs sign rep) is the sharpened diagonal-zeta face. [E] EM1 FACE COMPUTED: pumped charge == edge spectral flow == Streda == Chern == 1 on the v367 collar, single complex copy, sign-coherent conjugation mutant; 16-copy bookkeeping exact (c_- = 8, kY = 5/3, (1/kY) 41/6 = 41/10 = b1). [E] QUILLEN IDENTITY AT THE FINITE SHADOW: Berry integral == Poincare-Lelong divisor integral == +1 two-sided, difference an exact form, transition winding == Chern; anchor re-derived (alpha^-1 = 137.03599921684071, split residual 6.4e-58 at 50 digits, 8 b1 = 164/5 exact). [C] TYPED CONDITIONAL: IF the seam state is quasi-free (the rigidity premise, measured not forced in the strong form by SEAM.STATE.RPMIXING.01) THEN the identity applies literally to the seam det line. HONEST SCOPE: closes NOTHING on ALPHA.QUILLEN.EXACT.01 -- remaining content {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification}; the BFK face is Delta = |D|^2, not a |D|-level operator identity; the pump is a single-copy statement.

Recorded status: Exact/computed witnesses [E] + typed conditional [C]; the target row stays [O]

Original ledger status

SEAM.DETLINE.UNIFICATION.01

SEAM.DETLINE.UNIFICATION.01

THE DETERMINANT-LINE UNIFICATION HYPOTHESIS [O] (registered 2026-08-27 from the external bird's-eye review; a precise research hypothesis, NOT a result). OBSERVATION: three separately open structures may be projections of ONE geometric object -- (1) the seam extension is described by a Q-system/simple current (SEAM.SIMPLECURRENT.GENERATOR.01), (2) the chiral fermion measure lives on a determinant line (CHIRAL4D.NOMIRROR.01 demand C1), (3) anomalies and CP phases appear as holonomies of that determinant line (the finite Quillen identity is already TWO-SIDED at finite level -- v974/ALPHA.QUILLEN.FACES.01: Berry integral == Poincare-Lelong divisor integral == +1 -- and the continuum Bismut-Freed identification is the named missing step of ALPHA.QUILLEN.EXACT.01). DEMAND (the compatibility theorem): Res_seam det D_4D ~= det D_seam as line bundles WITH connection, AND the holonomy of the bulk determinant line equals the discrete TFPT orientation phase (the classically invisible sgn J orientation bit exhibited at exploration level, round DCXCVII -- experiments only, not promoted). IF such a theorem exists, seam extension, chiral anomaly freedom, the generation index and the discrete CP orientation become different projections of the same object. KILL TESTS: the two determinant lines differ by a nontrivial local factor no counterterm removes; the bulk holonomy disagrees with the discrete orientation phase on a computable family. HONEST BOUNDARY: the continuum Quillen/Bismut-Freed identification is exactly the critical missing step; nothing in the corpus proves any part of the 4D side; the sgn J bit is exploration-level input, cited as MOTIVATION only. EXECUTED UPDATE (2026-08-28, v991): finite bulk-edge determinant-line correspondence on the v367 QWZ collar -- occupied-frame FHS Chern = +1 (curvature 2 pi * (+1)); seam holonomy winding = +1 (diff 6e-16); M=3 control zero both sides; conjugation mutant flips both signs coherently. FIREWALL: 2+1D/1D finite lattice shadow; continuum Bismut-Freed and the 4D chiral-measure unification stay [O]. Python-only / Wolfram mirror deferred. LATE EVENING (2026-08-30, v1014): finite restriction isomorphism Res_Sigma L_bulk isomorphic to L_Sigma verified on the QWZ collar (next finite check after v991); orientation orbit 2 -> 1 only after a U(1) anchor (A0). Continuum Bismut-Freed and the 4D unification stay [O].

Recorded status: Open [O] + finite bulk-edge shadow [E] (2+1D/1D QWZ; continuum Bismut-Freed stays Open)

Original ledger status

GAUGE.DETLINE.FIXPOINT.01

GAUGE.DETLINE.FIXPOINT.01

THE GAUGE-COUPLING FIXPOINT CONTRACT [O] (registered 2026-08-28, review wave 3). DEMAND: all three gauge couplings (g1, g2, g3 / equivalently alpha, sin^2 theta_W, alpha_s) arise as stationary points of ONE nonabelian zeta-det / inflow functional on the determinant line -- the nonabelian upgrade of the U(1) face ALPHA.QUILLEN.EXACT.01. ACCEPTANCE: unique stationary points, positive Hessian, alpha_s(M_Z) without measured input, RG from the matching scale reproduces the data, mutants fail. HONEST: alpha_s(M_Z) is currently an EXTERNAL INPUT (the QCD matching / lattice input of F_QCD); this contract names the missing first-principles replacement, it does not claim the number is derived today. RELATION: generalizes ALPHA.QUILLEN.EXACT.01. KILL: a unique stationary point fails to exist; Hessian not positive; mutants (wrong level, wrong inflow multiplicity) still pass; RG from the functional fails to land on the observed couplings. EXECUTED UPDATE (2026-08-28, completeness wave, v996): the simplest-extension H0 of the U(1) alpha grammar to SU(2)/SU(3) is a STRUCTURAL KILL -- negative b2/b3 flip the stationary-root signs (SU(2) inverse -151.2, SU(3) -115.9); 64 conventions 0 hits; U(1) control 137.0359992168 survives all mutants. Exponential detline-curvature convergence to 2pi with rate 0.6936 ~ ln 2 is a numerical Bismut-Freed shadow. Naive grammar extension excluded [E]; genuinely nonabelian structure required -- typed. Contract stays [O]; alpha_s(M_Z) remains an external input. Python-only / Wolfram mirror deferred. WAVE-7 (2026-08-30, v1008): the 2+1D plaquette scaffold is now executed -- combinatorial K=0, frozen-link q^2 content law, unique-contractive selector |R'|<1 (L2 0.578 -> L3 0.936 harvest pins; L=3 Lanczos out of suite). The 1+1D no-plaquette hurdle is lifted at the scaffold level; thermodynamic 4D fixpoint stays [O]. Display unmoved Open.

Recorded status: Open (research contract; naive grammar extension excluded [E]; genuinely nonabelian structure required -- typed; alpha_s(M_Z) currently an external input)

Original ledger status

TFPT.TOE.COMPLETE.01

TFPT.TOE.COMPLETE.01

THE MASTER TOE-COMPLETENESS CONTRACT [O] (registered 2026-08-29, review wave 4). Eight gates, all named; NOTHING claimed closed. T1 structure postulate -> P1/P2/compiler (AX.P1.01, AX.P2.01, TFPT.IRREDUCIBLE.01, DIMENSION.SELECTOR.4D.01). T2 seam = (E8)_1 proven (SEAM.EQUIV.01, SEAM.EQUIV.MMST.01, SEAM.EQUIV.TWISTOR.01, SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.DETLINE.UNIFICATION.01, SEAM.STATE.RPMIXING.01). T3 quasilocal local unitary 3+1D Hamiltonian family (QFT4D.LATTICE.FUNDAMENTAL.01, TFPT4D.LATTICE.ACTION.01, DYN.UNITARY.DILATION.01, DYN.MARKOV.EMBED.01). T4 chiral SM with local measure + uniform mirror gap (CHIRAL4D.NOMIRROR.01). T5 IR Lorentz + confinement + clustering + nontrivial scattering (QFT4D.OS.RECON.01, SEAM.BULK4D.RECON.01). T6 all three gauge couplings + neutrino texture internally fixed (ALPHA.QUILLEN.EXACT.01, GAUGE.DETLINE.FIXPOINT.01, FLAV.NUSCALE.01-.06). T7 quantum massless spin-2 with universal coupling (GRAV.SPIN2.EMERGENCE.01, GRAV.NONCIRCULAR.01, GRAV.WEINBERG.WITTEN.01). T8 unique initial state + one SK functional generating all readouts (FTRANSFER.SK.RHO0.01, FTRANSFER.GENERATING.01, OBS.TRANSDUCTION.01, PRED.JOINTLIKELIHOOD.01). SEPARATION: TOE_Complete := AND(T1..T8); TOE_Validated := Complete AND independent holdouts passed. Dual rest: compiler Rest = v_geo oplus G_net oplus F_transfer sits beside Rest_TOE; this row is the named AND of the eight gates, not a closure. Children listed one-way here; children do not list this row back. EVENING (2026-08-30, v1012): gate-by-gate wave -- T5 four IR witnesses executed + the propagating-mode precondition (common-c needs dynamical gauge excitations); T7 interacting stress mechanism executed; T8 selection-principle vacuity typed (needs a non-entropic selection); T6/nu scaffold-level triple bound complete. Display stays [O]. LATE EVENING (2026-08-30, v1013/v1014): T3 mandatory-dynamics leg CLOSED at class level (LR + tau_t + A^G + state existence). Remaining axiom-core and continuum gaps now run through ONE externalized theorem (MMST/Quillen: TEL-B/ALG-EXH/P1 + character-blind det-response + Bismut-Freed/A0). Display stays [O]. MONDAY MORNING (2026-08-31, v1015): T1 structure-postulate route is now fully premise-supported at finite level (both W-bridge premises derived; axiom-core remainder 0 modulo externalized MMST). Display stays [O]. EXECUTED UPDATE (2026-09-05, v1022-v1025; no marker moves): T1 retains finite axiom-core/W-bridge support only; unconditional structure-postulate provenance and the dimension selector remain open. T2 closes C1, C2a and the interval-TV input and executes the analytic scalar C2b budget, while CF, DG and FE-GEN/ALG-EXH remain open and the old ALG2 Vandermonde implication is refuted. T3 remains Hamiltonian-class only. T4 gains a finite derivative-filtered block but no invariant mirror response gap, Weyl cone, DET realization, measure or continuum. T5 retains finite IR witnesses and the v1020 spectator obstruction but lacks prime completion, OS reconstruction, confinement and scattering. T6 gains a parent-internal intertwiner with projective full-Fock lift but no mass texture. T7 gains gap/TT no-gos but no graviton. T8 gains an arbitrary D4-breaking internal cap but no global rho_0. The historical one-external-theorem wording is restricted to the finite compiler/W-bridge lane. A single shared 3+1D parent satisfying T3-T8 is still missing. All T1-T8 gates and TOE remain Open [O]. ROUND-4 CURRENT (v1026-v1030): uniform relaxed TEL-B norm proved; canonical DET-CAR and signed z=1 wall only for fixed classical gauge fields with an explicitly changed additive parent; full Gauss site/cube dimensions3/0mod5; symmetric internal D4 cap noncanonical; local tensor target needs global zero-mode removal; ALG2 frame theorem conditional. All T1-T8 remain [O]; no shared complete3+1D parent.

Recorded status: Open (research contract; named AND of eight gates; no closure, no marker move) | Round-3 v1022-v1025 adds certified subgates and no-gos only; Round-4 v1026-v1030 adds narrow proved and conditional subresults only; all T1-T8 gates and TOE remain Open [O].

Original ledger status

SEAM.MMST.TYPEIII.CHARGED.01

SEAM.MMST.TYPEIII.CHARGED.01

THE MASTER SCALING-LIMIT THEOREM FOR THE CHARGED/TYPE-III IDENTIFICATION [O] (registered 2026-08-29, review wave 5). DEMAND: ONE scaling-limit theorem Psi_lambda,N -> Psi_lambda strongly on the finite-energy core + crossed-product continuity, from which B ≅ (E8)_1, mu = 1, type III_1, unique rotational KMS, unique conditional expectation, deck equidistribution, and modular invariance all follow as corollaries. CHILDREN (listed here, not listing back): SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.STATE.RPMIXING.01 continuum leg, ALPHA.QUILLEN.EXACT.01 rigidity premise, AX.P1.01 reading. CITED DOCUMENT: articles/2026-08-29/holomorphic_kms_extension_en.tex (13 pp): unconditional rotational-KMS uniqueness via KLM + Longo-Tanimoto GIVEN the identification; P1 = theorem-conditional on seam identification + beta_angle = 2pi. KILL: the scaling limit fails to exist; uniqueness of rotational KMS fails; type III_1 fails; a competing conditional expectation exists. Status: Open [O]. No marker move on children. EXECUTED UPDATE (2026-08-30, review wave 7, v1006): five lemmas proved in-house -- L3 crossed-product, UGF K_G=pi^2/4 (measured plateau ~1.023), TEL-a N^{-2} with exact isometries (A_TEL=5120(1+pi/2), measured envelope ~3.42), integer D5+A3 pairings, Z4 outerness in the limit + finite-inner correction (256-dim gauge unitary is inner). Residual boxed: TEL-B-EXTERNAL (Hankel C_R; HS max 2.105079358 / fit 2.107565497 / v998 bound 2.11) + ALG-EXH (two Buchholz-Verch estimates). Display stays [O]; no marker move. MONDAY MORNING (2026-08-31, v1016): TEL-B third (certified-tail) route BLOCKED -- N^2 D_N grows 530 -> 19032, remainder UV-supported. TEL-B-EXTERNAL (2026-09-04 reduction): triangle bound via cover identity + sawtooth split; (A) lattice piece certified numerically for all N, ||R^sm_N|| <= 1.7833 (all-mode BV, one float64 TV constant); (B) explicit piece reduced to Sigma|Res_N|^2 <= 0.2769 (measured 0.1550), open items C1 (C* <= 0.1525 enclosure), C2a (|phi_N| <= 0.51/N), C2b (cell oscillation of r); numerically 2.57 < 3, conditional analytic 2.9495 < 3. Status unchanged [O]. N-uniform CAR nuclearity PROVED (nu_N <= exp(16 C_beta); C_beta = (67.97, 29.73, 12.15) for beta = (0.5, 1, 2)) as ALG specialist compactness input; ALG-EXH projector-identification line UNCHANGED. Display stays [O]. EXECUTED UPDATE (2026-09-05, v1022/v1025): TEL-B C1 is interval-certified at C_star<=0.1520453048...<0.1525; C2a is analytically proved with N sup|phi_N|<0.509 for every even N>=16; the native 256-bit/5812-cell TV certificate gives TV_p(F'')<=15.817695962988924...<15.928674 and K3_TV<2.517464500835. The analytic C2b scalar reduction plus Arb arithmetic gives c_potential=0.399224424139106...<0.400. Full C2b remains open exactly at CF<=0.139/sqrt(N) and DG<=0.060/sqrt(N). The old ALG2 Vandermonde-to-generated-algebra implication is refuted by an exact M2 countermodel; FE-GEN or a precise gauge/code-projected algebra is required and ALG1 is conditional on the same generated-sector completeness. MMST/type-III identification remains Open [O]. ROUND-4 CURRENT: v1026 proves the relaxed uniform norm ||R_N||HS<2.995906<3 for every evenN>=16 (CF/DG/CROSS plus validated Fourier aliases). Historical2.11 and finite1.7833 are not promoted. The residual is microscopic one-edge FE-GEN, actual-word/joint-adjoint tails, ALG-EXH and MMST identification; v1030 is conditional. Aggregate [O] unchanged.

Recorded status: Open (research contract; master scaling-limit theorem; children listed here not back) | Round-3: C1/C2a/TV and scalar C2b subclaims proved [E]; ALG2 implication refuted [X]; CF/DG and ALG-EXH remain Open [O].

Established within the stated premises

Exact alpha output and coefficients retain a specific Ward-origin obligation

finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation

The active original explicitly treats the three-term decomposition and coefficient identities as exact, retaining the unique alpha root. The same section retains EM.WARD.01/ALPHA.QUILLEN.EXACT.01 as the existing origin obligation for the actual AQFT/zeta determinant functional. Separately the old circle canonically gives Pi and det_F(1-qPi)=1-q. Its actual local EM response, relative Quillen norm and susceptibility exponent5/4 still require identification. This does not retract compiler identities or root uniqueness.

Scope: Source-reviewed status/type correction, not a new general nonderivability theorem or gate. P1/P2 remain accepted starting principles; being axioms is not an objection. The line is derived on the old circle, not an arbitrary vector to select again. v382 replay26October:6/6; literalTrue status checks do not prove open functional origin. Ledger Numerical and full physical status remain unchanged.