Original ledger status
QGEO.ENERGY.02
THE ENERGY-COMMUTATOR CONTRACT (external-review proposal 2026-06-14; the NON-CIRCULAR sharpening of QGEO.ENERGY.01): the proposed premise is the operator identity [rho, Lambda_Sigma]=0 on the rank-8 Calderon polarisation -- rho the carrier clock, Lambda_Sigma the Dirichlet-to-Neumann (Calderon) energy form of the RAW RP seam double. Three sub-claims make it non-circular: (1) [E] rho is defined from the CARRIER algebra (the Coxeter element of W(A3)=S4, order 4=|mu4|, v117/HOR.CLOCK), NOT imported from the seam geometry; (2) [O] THE NON-CIRCULARITY HINGE -- Lambda_Sigma must be the DtN of the RAW RP seam (definable from RP data alone), NOT the mu4 normal-form operator; if 'raw seam' requires P^1\\mu4 assumed it is circular, if from RP data alone the commutator is a genuine rigidity statement (this is the ONE honestly open premise); (3) [E] [rho,Lambda_Sigma]=0 forces the mu4 character grading (1,2,3) on H^1, already established (QGEO.COHOM.01, eigenforms z^{k-1}dz/(z^4-1), v177). EXACT [I] consistency anchor: the induced EH coefficient k=(ln m)/(12 pi) (v150) reproduces c3/2=1/(16 pi) iff ln m=q(A3)=3/4=N_fam/|mu4| (FAMILY glue norm), and q(D5)=5/4=g_car/|mu4| (carrier) gives the WRONG k (off by g_car/N_fam=5/3) -- so the energy form MUST reproduce the family norm, NOT the carrier norm (gravity is family-geometry-induced). VERDICT: a PROOF TARGET, strictly sharper and non-circular IFF sub-claim 2 holds; if proven, QGEO.SYM.01 turns from definitional bedrock into an ENERGY-RIGIDITY THEOREM. Not a proof -- the bedrock stays [O]. Python-only (the q(A3) rigidity is exact and Wolfram-mirrored)
Recorded status: Geometric premise [O] (energy-commutator proof target; sharper, non-circular IFF sub-claim 2)
Dependencies, status detail and source
Canonical status: Geometric [O]: QGEO.ENERGY.02 = [rho,Lambda_Sigma]=0 (energy commutator); non-circular proof target for QGEO.SYM.01 IFF the raw-seam DtN (sub-claim 2) is RP-definable; exact rider: the EH coefficient selects q(A3)=3/4 (family), not q(D5)=5/4 (carrier)
Dependencies: QGEO.ENERGY.01; QGEO.SYM.01; QGEO.COHOM.01; HOR.CLOCK.01; v150_replica_eh_model.py; v192_qgeo_energy_clock.py
Scripts: v193_qgeo_energy_commutator.py
Location: tfpt_research_contracts
Original CSV, line 267Original ledger status
FORM.QGEO.01
LEAN 4 FORMALISATION of the QGEO.SYM.01 CONDITIONAL THEOREM (2026-06-15; the algebraic core of v201/v210, machine-proved) -- AUDIT: PASS, no sorry/admit, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound only; the two block-diagonality theorems even use only propext+Quot.sound). New module TfptCarrier/SeamDeckClosure.lean proves: (1) [F] geom_sum_fourth_root: for ζ:ℂ with ζ^4=1, Σ_{j<4} ζ^j = (if ζ=1 then 4 else 0) -- the 4th-root character orthogonality (finite geometric sum) that makes a μ4-mark sum vanish off mod 4; (2) [F] clock_gen_pow_four + mark_sum_residue_nonzero: the clock generator -i has order 4 and the three non-trivial residues give a vanishing mark sum, so a μ4-mark-sourced curvature is supported only on modes ≡0 (mod 4); (3) [F] markLocal_blockDiagonal: a mark-local Toeplitz symbol (support ⊆ {m : (m:ZMod 4)=0}) connects only equal clock-characters (f_{n-n'}≠0 ⇒ (n:ZMod4)=(n':ZMod4)), i.e. [ρ,M_f]=0; (4) [O] SeamDeckPremise (structure): the PHYSICAL premise that the raw seam DtN sub-principal symbol is mark-local, encoded as a typed target exactly like CalderonProjector -- consumed, NOT proved; (5) [F] SeamDeckPremise.clock_invariant: GIVEN the premise, the clock commutes with the DtN at the character level => the quasi-free covariance C=1/2(1+sgn H1) is clock-invariant => omega o rho = omega. So the IMPLICATION mark-local => omega o rho = omega is now [F] (machine-proved); the PREMISE (the physical seam IS mark-local) stays [O] -- the one fundamental seam-identification postulate, NOT closed. Complements FORM.GLUE.01/FORM.LADDER.01; mirrors v201/v210.
Recorded status: Formal [F] (conditional theorem) + [O] (the seam-deck premise)
Dependencies, status detail and source
Canonical status: Formal [F]/[O]: the QGEO.SYM.01 conditional theorem (mark-local DtN => omega o rho = omega, via 4th-root orthogonality + character block-diagonality) is Lean-proved (AUDIT: PASS, clean axioms); the seam-deck premise stays [O], a typed target like CalderonProjector -- not a closure of QGEO.SYM.01
Dependencies: QGEO.MARKLOCAL.01; QGEO.SUBPRIN.01; QGEO.MARKS.01; FORM.GLUE.01
Scripts: lean4-carrier-rigidity
Location: tfpt_research_contracts
Original CSV, line 296Original ledger status
CMNORM.DUAL.01
CM-NORM DUALITY (2026-06-16): the two exceptional CM moduli give two central TFPT integers as ideal NORMS. SQUARE seam (Gaussian Z[i], j=1728): N(g_car+i|mu4|)=5^2+4^2=41=10 b1 -- the EM index IS the Gaussian norm of the carrier-glue vector; N(3+2i)=13=Delta_Q. HEX partner (Eisenstein Z[omega], j=0): N(3+2 omega)=3^2-3*2+2^2=7=scalaron exponent. The (3,2)=(colour,weak) split generates (5,6,7,13)=(g_car,|R^+(A3)|,scalaron,Delta_Q) by sum/product/Eisenstein-norm/Gauss-norm; rings rigid (Eisenstein of (5,4)=21!=41, Gauss of (3,2)=13!=7).
Recorded status: Identity (exact ring arithmetic)
Dependencies, status detail and source
Canonical status: [E] 41=N_Zi(5,4)=10 b1, 13=N_Zi(3,2)=Delta_Q, 7=N_Zomega(3,2)=scalaron; (3,2)->(5,6,7,13); the square<->EM, hex<->scalaron architecture bridge [C]
Dependencies: ANCHOR.GEN.01; EM.B1.01; SEAM.KHALF.01
Scripts: v222_cm_norm_duality.py
Location: origin_theory
Original CSV, line 307Original ledger status
E8.CHAN.01
DEGREE/EXPONENT CHANNEL SPLIT (2026-06-16): 248=120+128 as a magnitude/phase channel typing (replaces the over-strong 'S^- is dark matter'). E8 exponents {1,7,11,13,17,19,23,29} sum=120=|R^+(E8)| (MAGNITUDE channel: positive roots/root transitions); E8 degrees {2,8,12,14,18,20,24,30} sum=128=2^(rank-1)=rank*dim S^+ (PHASE/GLUE channel); 248=120+128=adj(D8)+spinor(D8); sum(deg)-sum(exp)=rank=8. The (ratios,product) magnitude bijection (Target D) lives in the 120 channel, the un-covered CP phases in the 128 phase/glue channel; whether 128 hosts a dark sector is Frontier (NOT asserted). STRENGTHENED on the fiber (2026-07-29, T177/v561): the channel typing has an EXACT hexagonal realisation -- sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly) and sum_k rho^{m_k} = 4 (arg = 0 exactly) on the CM unit rho = e^{i pi/3} -- with a parity typing forced by integer parity: all degrees are EVEN (phase channel SHEET-EVEN under rho -> rho^4), all exponents ODD (magnitude channel SHEET-ODD). CONSEQUENCE: the phase-channel angle is sheet-blind -- it carries pi/3 but cannot distinguish quark from lepton (not the CP.MU6.01 sheet split). Honest caveat: reality of the exponent sum alone is not hexagon-specific; only the degree half (= 4 rho) is. The channel typing stays [C].
Recorded status: Identity (exact)
Dependencies, status detail and source
Canonical status: [E] 248=120+128, exponents sum 120=|R^+(E8)|, degrees sum 128=rank*dim S^+; magnitude channel 120 / phase channel 128 [C]; dark-sector reading [O]; exact hexagonal realisation sum rho^{d_k}=4rho (arg pi/3, sheet-even) vs sum rho^{m_k}=4 (arg 0, sheet-odd) [E] -- the phase-channel angle is sheet-blind (T177/v561)
Dependencies: E8.CAS.01; FLAV.CP.01
Scripts: v227_degree_exponent_channel_split.py, v561_cp_channel_identities.py
Location: tfpt_5_redteam
Original CSV, line 309Original ledger status
GATE.HOLO.02
SEAM CHERN-SIMONS REALISATION (2026-06-17): the closing step of GATE.HOLO.01 realised in standard abelian Chern-Simons / quantum-Hall language, where 'holomorphic <=> det K = 1' is a THEOREM -- a genuine reduction of the analytic step into anyon condensation, NOT a closure. A free gapped BOSONIC 2+1d bulk = an even integer K-matrix; #anyons (torus degeneracy) = |det K|, edge chiral central charge c = signature(K), and the edge chiral net is holomorphic (single sector) <=> |det K| = 1. So the v234 condition 'no nontrivial abelian sector' = exactly |det K| = 1. The TFPT extension tower (v92/GATE.METRIC.07) IS the anyon-condensation tower read by determinant: carrier D5(+)A3 (even, det 16, c=8, 16 anyons, mu=16) -> SO(16)_1=D8 (det 4, 4 anyons, mu=4) -> (E8)_1 (det 1, 1 anyon, mu=1, HOLOMORPHIC); all rank 8 with c = signature = 8 = g_car+N_fam. Holomorphic <=> det 1 <=> E8 = the unique even unimodular rank-8 K-matrix = the Kitaev E8 quantum-Hall state (edge (E8)_1). CONDENSATION: a Lagrangian (maximal isotropic) glue of order sqrt(16)=|mu4|=4 takes det 16->16/4^2=1 (carrier->E8); an order-2 isotropic only ->16/2^2=4 (D8). So 'holomorphic' = 'condense the order-|mu4| Lagrangian glue', not a partial. NEG: D8 (det 4) is free+bosonic yet has 4 anyons (not holomorphic, the SO(16)_1 rival); an odd-diagonal K is fermionic (spin-CS) -- 'free+bosonic' does NOT imply holomorphic, det=1 is the extra physical condition. RESIDUAL [O]: the closing step = 'the free RP gapped seam condenses the order-|mu4| Lagrangian glue (det->1), not a partial isotropic (det->4)' -- the same sheet/mu4 selection as GATE.QGEO, now with holomorphy<=>det1 a theorem and the residual a single integer condition.
Recorded status: Lattice/CS realisation (exact) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] free gapped bosonic bulk = K-matrix; #anyons=|det K|, c=signature, holomorphic<=>det 1; the v92 tower D5(+)A3(16)->D8(4)->E8(1) is the condensation tower; holomorphic=E8=Kitaev E8 state; residual = 'condense the |mu4| Lagrangian glue' = the sheet/QGEO selection [O]
Dependencies: GATE.HOLO.01; GATE.METRIC.07; TOPO.E8.01; QGEO.SYM.01
Scripts: v235_seam_chern_simons.py
Location: tfpt_research_contracts
Original CSV, line 321Original ledger status
GATE.HOLO.03
SEAM SRE CLOSURE (2026-06-17): the closing step of GATE.HOLO.01/02 recast as a PHYSICAL, falsifiable condition -- no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens the residual from definitional ('condense the Lagrangian glue', v235) to a yes/no statement about topological order. (1) the abelian K-matrix ground-state degeneracy on a genus-g surface is |det K|^g: carrier D5(+)A3->16, SO(16)_1=D8->4, (E8)_1->1 on the torus; so 'no topological degeneracy on ANY closed surface' <=> |det K|=1. (2) SRE <=> det 1 <=> E8: among rank-8 even positive-definite K (c=signature=8=g_car+N_fam) only E8 has det 1 -- THE unique nontrivial bosonic SRE 2+1d phase (Kitaev E8), edge (E8)_1 holomorphic; D8 and the carrier are long-range-entangled (topologically ordered). (3) PLANE vs TORUS: a unique ground state on the PLANE (RP+gap+cluster+OS, the established admissible-sector facts) is NECESSARY but not sufficient -- the plane has no non-contractible cycles and cannot see |det K|, the torus does; so the residual is exactly 'the seam unique-vacuum property extends to the torus' = SRE. (4) NEG: a topologically-ordered (LRE) bulk has |det K|>1 (D8: 4-fold torus degeneracy + a non-holomorphic boundary 1,v,s,c = SO(16)_1 rival). (5) SHARPENED RESIDUAL: the one open analytic step is now the physical statement 'the free RP gapped seam bulk is short-range-entangled (no topological ground-state degeneracy)' = det K=1 = the Kitaev E8 phase -- sharper than 'condense the Lagrangian glue' (v235) and than 'the seam is P^1 minus mu4' (QGEO.SYM.01). [E] the degeneracy=|det K|^g dictionary + SRE<=>det1<=>E8 selection; [O] the physical SRE premise. NOT a closure.
Recorded status: Lattice/topological-order (exact) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] genus-g GSD=|det K|^g, no topological degeneracy <=> det K=1 <=> SRE; only E8 (det 1) is the bosonic SRE c=8 phase (Kitaev E8); plane unique-vacuum is necessary not sufficient (torus sees det K); residual = 'the seam is SRE' [O], a physical yes/no statement
Dependencies: GATE.HOLO.02; GATE.HOLO.01; QGEO.SYM.01
Scripts: v237_seam_sre_closure.py
Location: tfpt_research_contracts
Original CSV, line 323Original ledger status
DHR.SECTORS.01
PARTICLES = DHR SUPERSELECTION SECTORS (2026-06-17): the discriminant/anyon content of the carrier and the condensation tower (v235/v237) made explicit as an abelian modular tensor category (MTC) -- the particle-spectrum layer of the emergent QFT. The carrier discriminant form is the Lean-verified glue form (FORM.GLUE.01): on Z4 x Z4, q(x,y)=(5x^2+3y^2)/8 mod 1, bilinear B((x,y),(x',y'))=(5xx'+3yy')/4 mod 1, topological spin theta(a)=e^{2 pi i q(a)}. (1) [E] 16 sectors = Z4 x Z4 (= det K_carrier = dim S^+ = 16, v235); fusion = abelian group law (closed, associative, vacuum (0,0), inverses). (2) [E] spin/condensability: bosonic <=> theta=1 <=> q in Z <=> 5x^2+3y^2=0 mod 8 -- exactly the six isotropic elements {(0,0),(1,1),(1,3),(2,2),(3,1),(3,3)}. (3) [E] condensation tower = v235/v237: condensing the Lagrangian H1=<(1,1)> (order 4, self-dual H1^perp=H1) leaves |H^perp/H|=1 sector = (E8)_1 (det 1, holomorphic); the order-2 isotropic <(2,2)> leaves 4 sectors = SO(16)_1 = D8 (det 4); so carrier 16 -> D8 4 -> E8 1. (4) [E] NEG: a non-isotropic anyon (1,0), q=5/8, theta != 1, is confined; <(1,0)> contains non-isotropic elements so cannot be a condensation algebra -- the tower is forced by isotropy. (5) [C] identifying sectors / deconfined anyons with SM particle multiplets is the interpretation; the MTC data (fusion + spins + tower) is exact
Recorded status: Numerical (finite MTC) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] 16-sector abelian MTC from the glue form, fusion = group law, condensation tower 16->4->1 = v235/v237 (Lagrangian -> E8, order-2 -> D8); [C] sector<->SM-multiplet identification -- particles = stable defect sectors of the seam code, made precise
Dependencies: GATE.HOLO.02; GATE.HOLO.03; FORM.GLUE.01
Scripts: v241_dhr_sectors.py
Location: tfpt_research_contracts
Original CSV, line 327Original ledger status
DHR.MODULAR.01
SPIN-STATISTICS + MODULAR (S,T) DATA (2026-06-17): the exchange statistics, modular S/T matrices, Verlinde fusion and Gauss-Milgram central charge of the carrier MTC -- the statistics+kinematics layer on top of v241. Same abelian MTC: Z4 x Z4, q(x,y)=(5x^2+3y^2)/8 mod 1 (the Lean glue form FORM.GLUE.01), B(a,b)=q(a+b)-q(a)-q(b), theta(a)=e^{2 pi i q(a)}. (1) [E] spin-statistics: T=diag(theta_a) splits the 16 anyons into 6 BOSONS (theta=1, the condensable/isotropic set), 2 FERMIONS (theta=-1) = {(0,2),(2,0)}, and 8 genuine anyons. (2) [E] modular S_ab=(1/sqrt 16) e^{-2 pi i B(a,b)} is unitary, symmetric, S^2=C (charge conjugation, C_ab=delta(b,-a)), S^4=I. (3) [E] Verlinde N_ab^c = sum_x S_ax S_bx conj(S_cx)/S_0x = delta(c,a+b) -- the fusion ring is RECOVERED from the modular data, not posited. (4) [E] Gauss-Milgram (1/sqrt 16) sum_a theta_a = e^{2 pi i c/8} with c=8=g_car+N_fam -- the anyon data already encodes the chiral central charge of the (E8)_1 net (v156/v175); statistics and c=8 are one fact. (5) [C] the boson/fermion split is the kinematic skeleton of the matter content; mapping sectors to physical fermion multiplets is the interpretation
Recorded status: Numerical (finite MTC) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] T=diag(theta) spin-statistics (6 bosons, 2 fermions, 8 anyons); modular S unitary/symmetric, S^2=C, S^4=I; Verlinde reproduces the group-law fusion; Gauss-Milgram gives c=8=g_car+N_fam. [C] the boson/fermion-to-field map is the interpretation
Dependencies: DHR.SECTORS.01; GATE.HOLO.02
Scripts: v242_spin_statistics_modular.py
Location: tfpt_research_contracts
Original CSV, line 328Original ledger status
ARCH.K3.01
KUMMER/K3 UNIFICATION OF SEAM + CARRIER-16 + E8 (2026-06-17): one smooth Kummer/K3 surface carries the seam (pillowcase = the elliptic-involution quotient of the square torus tau=i, j=1728, v214), the carrier-16 (the 16 Kummer nodes = dim S+, v197) and the E8 lattice (the H^2(K3) intersection form U^3(+)E8(-1)^2), so the v1 glue D5(+)A3 + mu4 => E8 is the lattice shadow of a single geometric object (the K3/Kummer proposal). A unification, not a closure.
Recorded status: Lattice (K3/Kummer) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] E8 Cartan even/det1/pos-def + K3 lattice rank22/det-1/even/signature(3,19) with E8(-1)^2 a summand + seam=T^2/(z->-z) 4 fixed points (pillowcase, orbifold Euler char 0) + carrier-16=Kummer nodes |A[2]|=2^4=16=dim S+=4x4 + honesty (the rank-16 Kummer lattice is NOT literally E8(-1)^2, distinct sublattices of H^2(K3)); [C] two faces of E8 in K3 (local du Val C^2/2I v232/v236; global H^2 summand) + the carrier<->node geometric unification.
Dependencies: E8.GLU.01; QGEO.PILLOW.01; ARCH.RRCAR.02
Scripts: v260_k3_kummer_unification.py
Location: tfpt_research_contracts
Original CSV, line 346Original ledger status
QFT.MSC.01
MODULAR SPECTRAL CLOSURE (2026-06-17): the assembly/reduction certificate turning the whole QFT layer (v238-v260) into ONE relative object TFPT_QFT=(A_Sigma,omega_Sigma,Delta_Sigma,rho,A_F,H_F,D_F,J,gamma,S_rel) reduced to ONE open premise. Cross-validates the invariants that must agree across the round (index=marks=fixed points=glue order=4; carrier-16 across spinor/lattice/triple; one gap 6log(3/2) static+dynamic), re-derives the three closures (v258 Kasparov, v259 KMS cutoff, v260 K3), and certifies the relative-object manifest. The Modular Spectral Universality master statement: the unique RP holomorphic index-4 KMS seam state induces via Kasparov the 96-dim KO-6 triple whose inner fluctuations give the gauged Pati-Salam spectral action -- so Dirac, cutoff, gauging, glue and orientability are facets of one seam state, complete modulo QGEO.SYM.01.
Recorded status: Numerical (assembly certificate) [E]/[C]/[O]
Dependencies, status detail and source
Canonical status: [E] one index=marks=fixed points=glue order=4 + one carrier-16 (spinor/lattice/triple) + one gap 6log(3/2) (OS/recovery/Lindblad) + the three closures re-derived (Kasparov/KMS cutoff/K3) + the 10-component relative-object manifest; [O] the whole QFT layer reduces to one premise QGEO.SYM.01 (seam realisation), ambient QG QG.AMB.01 separate; [C] the Modular Spectral Universality master statement holds modulo QGEO.SYM.01.
Dependencies: PS.DIRAC.03; PS.SPECACT.02; ARCH.K3.01; PS.DIRAC.02; GATE.METRIC.06; GATE.METRIC.07; QGEO.MARKS.03; DYN.KMS.01; DYN.GNS.01
Scripts: v261_modular_spectral_closure.py
Location: tfpt_research_contracts
Original CSV, line 347Original ledger status
QGAMB.ROUTEII.01
ROUTE (ii) (SEAM-NET CONDENSATION) LEMMA DECOMPOSITION + ROUTE-COINCIDENCE (2026-06-18): a 4-lemma chain with 3 discharged and the open lemma shown to COINCIDE with Route (i)'s (the v282 unification at the lemma level; does NOT prove the open premise). M1 [E] no nontrivial abelian sector <=> |det K|=1 <=> holomorphic (mu-index 1) (v234 GATE.HOLO.01: #(1-dim irreps)=|Gamma^ab|=|H1|=1 <=> E8; v235 GATE.HOLO.02 Chern-Simons det K=1). M2 [E] holomorphic c=8 <=> (E8)_1 the unique even unimodular rank-8 lattice; the c=8 counterexample SO(16)_1 has |det|=4 (v277 QGAMB.TIERB.01 + v281 QGAMB.MODULAR.01 #anyons=|det Gram|). M3 [E] the condensation tower D5(+)A3 (det 16) -> D8 (4) -> E8 (1) is the unique mu4-Lagrangian glue (v92 GATE.METRIC.07 + v281 + v235). THE DISCRIMINATOR [E]: det 1 (E8, holomorphic) vs det 4 (SO(16)) at the same c=8. ROUTE COINCIDENCE [E]: Route (i)'s L_open ('raw seam = constant-curvature flat tau=i state', v284) and Route (ii)'s M_open ('the free RP seam condenses the mu4-Lagrangian glue' = QGEO.SYM.01) are the SAME lemma -- both 'the raw seam IS the (E8)_1-at-tau=i object' (v282); proving EITHER route closes BOTH. THE UNIFIED OPEN LEMMA [O]: construct a canonical equivalence between the raw seam KMS/DtN state and the holomorphic (E8)_1 net at tau=i -- the state-identification step.
Recorded status: Lemma decomposition [E] (3/4 discharged + route coincidence) + [O] (unified lemma)
Dependencies, status detail and source
Canonical status: [E] 3/4 Route-(ii) lemmas discharged + the discriminator + the route-(i)/(ii) coincidence; [O] the unified open lemma (canonical seam<->(E8)_1 equivalence). Decomposes Route (ii), isolates its single open lemma, and shows it coincides with Route (i)'s -- confirming v282 at the lemma level. Does NOT close it.
Dependencies: QGEO.SYM.01; GATE.HOLO.01; GATE.HOLO.02; QGAMB.TIERB.01; QGAMB.MODULAR.01; QGAMB.UNIFY.01; QGEO.ROUTEI.01
Scripts: v285_route_ii_seam_condensation.py
Location: tfpt_research_contracts
Original CSV, line 380Original ledger status
WITNESS.ECON.01
WITNESS-INDEPENDENCE / GENERATOR-ECONOMY AUDIT (2026-06-21): the STRUCTURAL anti-numerology firewall complementing the v100 phenomenological null test. [E] GENERATOR ECONOMY: 13 headline integers (|mu4|=4, g_car=5, |Z2|=2, N_fam=3, dim S+=16, rank E8=8, |R(E8)|=240, dim E8=248, |2I|=120, h(E8)=30, |W(D5)|=1920, Omega_adm=48, gap exponent 6) are all documented images of the single anchor a=(1,1,2) (e=(4,5,2), p_n=2+2^n; v23/v228), with pi the only transcendental primitive (ARCH.CORE.01) => 13 atoms / 2 free primitives = 6.5x compression made EXPLICIT; the recurring 2/3=|Z2|/N_fam and (2/3)^6 are ONE ratio, not many. [E] WITNESS INDEPENDENCE: E8, g_car and the anchor are overdetermined (>=3 structurally distinct derivations sharing only leaf inputs: v1/v15/v77+v92; v2/RR/reverse-glue), while the 5 pure-seed readouts (theta12/theta13/beta/Omega_b/lambda_C) are single-witness (multiplicity 1) = correlated, NOT 5 independent confirmations. [E] CORRELATION HONESTY: the 9 phi0-sharing scorecard observables must be scored JOINTLY (v100 fixes phi0 in MC-A), never as p^9. [E] NEG/POWER: alpha^-1's '137' is foreign to the anchor family (prime; no e_k/p_n/product) = an INDEPENDENT witness (F_U1 cubic, v3), and foreign integers stay un-generated (the map discriminates). Structural bookkeeping that quantifies the compression and correlation so neither masquerades as independent evidence; NOT a new physical claim and NOT a proof the anchor is forced (P2/v23/v228).
Recorded status: Identity/Numerical [I]/[N] (structural firewall)
Dependencies, status detail and source
Canonical status: [I]/[N] the generator-economy images + the 6.5x compression ratio + the witness-multiplicity bookkeeping + the shared-seed correlation map + the foreign-integer negative control. Makes the compression and correlation explicit; does NOT add physics and does NOT upgrade any status.
Dependencies: ANCHOR.GEN.01; REG.FREEZE.01; DATA.SCORECARD.01
Scripts: v305_witness_independence.py
Location: tfpt_5_redteam
Original CSV, line 401Original ledger status
GOLD.ATOMS.01
THE GOLDEN RATIO IS THE g_car=5 SIGNATURE -- THE (2,3,5) ATOMS ARE THE NETWORK SPECTRAL ANGLES (2026-06-21, v312 follow-up made exact). [E] EXACT: the affine-E8 adjacency charpoly factors x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1); the golden minimal polynomial x^2-x-1 divides it, so phi=2cos(pi/5)=(1+sqrt5)/2 is an EXACT algebraic eigenvalue (not a numerical near-value). [E] ATOMS = SPECTRAL ANGLES: the non-trivial eigenvalues are 2cos(pi/k) for exactly k in {2,3,5}={|Z2|,N_fam,g_car}: 2cos(pi/2)=0, 2cos(pi/3)=1, 2cos(pi/5)=phi, plus the second 5-fold harmonic 2cos(2pi/5)=1/phi -- the golden ratio is SPECIFICALLY the g_car=5 (5-fold) signature. [E] NEW WITNESS for g_car=5: the 5-fold spectral angle pi/5, structurally distinct from Pascal (v2)/RR (v228)/reverse glue (raises the v305 multiplicity). [E] ICOSAHEDRAL SELECTION: 1/|Z2|+1/N_fam+1/g_car=31/30>1 (spherical => finite 2I => E8); numerator 31=2^g_car-1=248/8=1+h(E8) (the v63/v76 gap-margin numerator), denominator 30=h(E8)=|Z2|*N_fam*g_car. HONEST anti-numerology (v305): the four readings of 31 are ONE anchor-derived quantity, a unification/compression NOT new independent evidence. [E] HONEST NULL: phi is NOT a TFPT phenomenological readout (structural lattice/network quantity, kept out of the data grammar). [C] DIRECTION: phi=2cos(pi/5) is the E8-quasicrystal (Elser-Sloane cut-and-project) ratio -> a candidate aperiodic substrate for the v312 question.
Recorded status: Identity/Lattice [E] (spectral) + [C] (quasicrystal direction)
Dependencies, status detail and source
Canonical status: [E] the exact golden-min-poly factorisation + the (2,3,5)=2cos(pi/k) spectral-angle identification + the new g_car spectral witness + the 31/30 icosahedral-selection identity (with the honest anti-numerology framing) + the phi-not-a-readout null; [C] the E8-quasicrystal substrate direction. A new structural reading; does NOT add a physical readout and does NOT close the substrate question.
Dependencies: MCKAY.E8.01; HYP.INJECT.01; v219; v312; v63
Scripts: v313_golden_atoms_spectral.py
Location: origin_theory
Original CSV, line 411Original ledger status
SEAM.EQUIV.CONTINUUM.01
THE ONE OPEN LEMMA OF SEAM.EQUIV.01, stated precisely and mapped to the recent rigorous literature (2026-06-22): the continuum-limit and OS-reconstruction legs are now CITABLE, the genuinely-open residual narrows to 'the raw collar is a gapped quasi-free state whose massless scaling limit is the c=8 (E8)_1 net'. [C] CONTINUUM LEG: Osborne-Stottmeister (CFT from Lattice Fermions, doi:10.1007/s00220-022-04521-8, CMP 398 (2023) 219) give, building on the MMST operator-algebraic (wavelet/Wilson-Kadanoff) renormalization framework (Morinelli-Morsella-Stottmeister-Tanimoto, CMP 387 (2021) 299; PRL 127 (2021) 230601), the chiral-CFT scaling limit of free lattice fermions (Koo-Saleur -> Virasoro, correct c); WZW range rank <= c <= D (D Majorana copies). (E8)_1: c=8, rank 8, D=16 Majoranas (SO(16)_1 -> (E8)_1), 8<=8<=16 IN range; the collar is gapped quasi-free (CAR). [C] OS LEG: Adamo-Moriwaki-Tanimoto (arXiv:2407.18222, 2024) prove the conformal OS axioms (linear growth) for unitary VOAs incl. WZW/lattice VOAs; (E8)_1 is the even self-dual rank-8 lattice VOA. [E] TARGET PINNED: c=g_car+N_fam=8, det Cartan E8=1, the D=16 Majorana SO(16)_1 IS the carrier-16, the mu4 extension IS the seam glue. [O] OPEN RESIDUAL: c=8 alone does NOT pin the net (SO(16)_1 also c=8, det Cartan D8=4), so the open lemma = the holomorphy discriminator det K=1 (v277/v281/v335). A literature-mapping/reduction; does NOT close SEAM.EQUIV.01.
Recorded status: Reduction [C]/[O] (continuum lemma narrowed + literature-anchored)
Dependencies, status detail and source
Canonical status: [C] the two legs are citable as general theorems (not yet specialised to the raw collar in print); [E] the arithmetic target pins; [O] the narrowed residual. Does NOT close SEAM.EQUIV.01.
Dependencies: SEAM.EQUIV.CHAIN.01; SEAM.EQUIV.UNIFY.01; v308; v277; v335
Scripts: v336_continuum_limit.py
Location: origin_theory
Original CSV, line 438Original ledger status
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])
Dependencies, status detail and source
Canonical status: [E] the Quillen split at the root + named-atom coefficients + the value alpha^-1=137.0359992 (reused from v3/v48/v341, machine-checked); [O] the from-first-principles exactness proof (the named target); [C] it is a face of SEAM.EQUIV.01, not a second independent gate. A typing/registration of the pre-existing EM.WARD.01 residual, reusing v341's (Wolfram-mirrored) identities; introduces no new number. UPDATE (2026-08-28, external master-object review wave 2, v985): the channel-swap face is resolved at the FINITE level -- the deck swap r -> r+2 maps the jump |spectrum| [0,2,4,2] onto the mark pattern |[4,-2,0,-2]| exactly (odd swap fails), the graded det' difference is c3-free = log(ln2/4), and the channelwise unit ratio is uniform 4/ln2; finite KMS rigidity-premise executed [E] (v995: 33 directions killed; 196608 -> 0); ln-2-rate detline shadow [E-measured] (v996, numerical not theorem); continuum Bismut-Freed, type-III KMS uniqueness and the from-first-principles exactness of F_U(1) stay [O] (BFK 2^{-4} needs no physical compensation: relative det, 2026-08-29). | 2026-08-29: relative det Q(A)=log[det'Delta_A/det'Delta_{A0}]+8 b1 c3^6 log phi(A); BFK 2^{-4} A/tau/alpha-independent at fixed cut number (delta log 2^{-4}=0, no physical compensation). Stays [O]. WAVE-5 (2026-08-29): rigidity premise of SEAM.MMST.TYPEIII.CHARGED.01; no marker move. | LATE EVENING (2026-08-30 v1014): finite restriction isomorphism verified; orientation fixes the conjugate branch; the residual constant phase is fixed by the A0 reference normalization -- recorded. Stays [O].
Dependencies: EM.WARD.01; SEAM.EQUIV.01; v341; v342; v3; v48; v216; v336
Scripts: v382_alpha_quillen_exact.py, v985_quillen_channel_swap.py, v995_kms_subnet_rigidity.py, v996_gauge_grammar_kill.py, v1014_bridge_refinements.py
Location: tfpt_1_architecture_e8
Original CSV, line 445Original ledger status
SEAM.GALOIS.NET.01
The Galois<->Net bridge (2026-06-25): the seam mu4 = Gal(Q(zeta5)) is the SAME cyclic Z/4 as the (E8)_1 simple-current glue -- NOT a mere order-4 coincidence -- connecting the Galois gearbox of v419 to G_net/SEAM.EQUIV.01. [E] CARRIER GLUE CYCLIC Z/4: disc(A3)=coker(Cartan A3)=Z/4 and disc(D5)=Z/4 (one Smith invariant factor 4 = CYCLIC, not Klein), det=4 each; the D_n discriminant is Z/4 for n ODD and Z2xZ2 for n EVEN, so the carrier D5 (rank 5=g_car, odd) is cyclic while the control D8 (rank 8, even) is Klein -- the cyclicity of the carrier glue is rooted in g_car=5 being odd. [E] CARRIER-GALOIS SAME Z/4: Gal(Q(zeta5))=(Z/5)^x=<2> is cyclic of order 4 (max multiplicative order 4, not Klein); among the atoms only the carrier prime 5 gives order 4 (|(Z/2)^x|=1, |(Z/3)^x|=2, |(Z/5)^x|=4). [E] E8 GLUE CYCLIC Z/4: in disc(D5(+)A3)=Z4xZ4 (order 16=dim S+) the simple current (1,1) has order 4 (cyclic <(1,1)>); the Lagrangian quotient is 16/|glue|^2=16/4^2=1, so the extension is unimodular = (E8)_1 (one primary, holomorphic, v89/v154). [E] CYCLIC vs KLEIN LOAD-BEARING (negative control, v100): the order-4 Klein group Z2xZ2 has max element order 2 (NOT cyclic); the even-rank D8 carries it, and the order-2 halfway glue <(2,2)> gives 16/2^2=4=|disc(D8)|=SO(16) (det Cartan 4, four primaries), NOT E8 (det 1). So cyclic Z/4 -> E8, Klein/order-2 -> D8 -- the carrier-Galois being cyclic Z/4 (5 prime) matches the E8 glue, never the D8 Klein. [C] THE BRIDGE = THE FOUR-FOLD mu4 IDENTITY: ONE cyclic Z/4 threads the four mu4 readings -- the seam deck/divisor mu4 (z->iz, v419), the carrier-Galois Gal(Q(zeta5)) (v419), the discriminant disc(D5)=disc(A3)=Z/4 and the (E8)_1 simple-current glue <(1,1)> (v1/v89/v154) -- so the Galois gearbox (Z/30)^x of v419 IS the simple-current glue of the holomorphic net, a direct bridge from the Galois side to G_net (SEAM.EQUIV.01). All four computably cyclic-Z/4 [E]; the canonical identification (one functorial Z/4) is the [C] bridge, cyclicity forced (5 odd/prime), Klein excluded. Per v428 this four-fold identity is a COMPRESSION (one object read four ways, a unification that makes the carrier less axiomatic), NOT four independent witnesses that multiply. Exact lattice/Galois; no new number.
Recorded status: Galois<->Net bridge / four-fold mu4 identity [E]/[C]: the seam mu4=Gal(Q(zeta5))=(Z/5)^x is the SAME cyclic Z/4 as the (E8)_1 glue <(1,1)> AND the discriminant disc(A3)=disc(D5)=Z/4 (D5 cyclic because rank 5 odd; D8 even=Klein control); only the carrier prime 5 gives (Z/p)^x=Z/4; glue order 4 => 16/4^2=1=E8 (vs Klein/order-2 => D8 det 4); cyclic Z/4 selects E8, Klein excluded -- the v419 Galois gearbox IS the holomorphic net's glue, a direct Galois->G_net bridge. Deck/divisor=Galois=discriminant=simple-current is a compression per v428 (one object read four ways), not four witnesses [C]
Dependencies, status detail and source
Canonical status: Lattice
Dependencies: SEAM.GALOIS.01; SEAM.EQUIV.01; E8.GLU.01; GATE.METRIC.06; ARITH.HULL.01; v419; v1; v89; v154; v92; v281; v403; v428
Scripts: v422_galois_net_bridge.py
Location: origin_theory
Original CSV, line 489Original ledger status
FORM.SEAM.RESIDUAL.01
LEAN 4 FORMALISATION reducing the SEAM.EQUIV.01 residual to a SINGLE named realization axiom (2026-06-30, G4 of the post-F next steps) -- new module TfptCarrier/SeamResidualAxiom.lean, lake build OK. It kernel-checks the arithmetic backbone of the whole G-block over Nat/Int: [F] c3_eight_one_sided (the one-sided count |Z2|*(intK/pi)=2*4=8, v456), [F] two_sided_nonchiral (a reflection sends C->-C so a two-sided boundary forces C=0), [F] cMinus_eq_eight (c_-=8=g_car+N_fam=rank E8), [F] mmst_range (rank<=c<=D, 8<=8<=16), [F] decoupled_additivity (16*1/2=8), [F] currents_fermionic (120 so(16) bilinears) + currents_lattice (248=8+240), [F] roots_split (240=112+128, 248=120+128), [F] holomorphic_discriminator (det K_E8=1 vs det K_SO16=4) -- ALL by kernel decide. UPDATE (2026-06-30, v461/v462 round): the two cited existence theorems are MERGED into ONE combined external axiom seam_realisation_theorem (dropping the intermediate ChiralCFT_c8), so #print axioms seamResidualClosed now lists exactly FOUR axioms (CollarRealizedAsLatticePhase, SeamIsE8, collar_realizes, seam_realisation_theorem), down from six; and two more kernel facts are added -- [F] strict_locality_forbidden (v461: the Wannier winding=|C|=1!=0 and c_-=8!=0, so a strict finite-range commuting projector is topologically forbidden) and [F] fock_sectors (v462: C(16,2)=120 currents, 2^8=256 Ramond states, spinor 128, 120+128=248). residual_arithmetic (now incl. v461/v462) depends only on [propext]. So the residual is reduced to ONE TFPT-internal realization axiom + ONE combined cited theorem. UPDATE (2026-06-30, v463/v464 round): two more kernel facts -- [F] c8_three_candidates (A8/D8/E8 each dim=8*(1+h^v), so c=8 is not unique at level 1) and [F] holomorphy_selects_e8 (the forced dim V_1=248=dim E8 != 80(A8) != 120(D8), so holomorphy promotes 'c=8' to 'E8' uniquely, v463); v464 (the one-particle realization rigidity) is NUMERICAL (symbol idempotency + Cauchy convergence + entanglement c-fit), so it sharpens the meaning of collar_realizes ('the unique quasi-free realization, modulo Araki/Shale-Stinespring') but is not a kernel fact. seamResidualClosed stays exactly FOUR axioms; residual_arithmetic (now incl. v463) depends only on [propext]. UPDATE (2026-07-02, v469 round): a PARALLEL peer-reviewed derivation seamResidualClosed' is added -- the invariant-level axiom collar_invariants (R1': quasi-free [C] + gap [E] + class D + c_-=8 [E from P1], replacing the model-level fiat) plus ONE combined 1995-2001 package crossedproduct_route_theorem (Kitaev/Kapustin-Spodyneiko phase classification o MMST+Boeckenhauer scaling limit o Longo-Rehren/BE local Z2 crossed product + KLM o Dong-Mason uniqueness); its joints are NEW kernel facts with NO axioms -- [F] lr_locality_integer (h_s = 16/16 in Z), [F] glue_locality_integers (mu4 h(J^k) = {1,1,1} in Z), [F] klm_holomorphic (4/2^2 = 1 and 16/4^2 = 1), [F] sixteenfold_pin (nu = 16 = 0 mod 16, c_- = nu/2 = 8), bundled as crossedproduct_arithmetic [propext only]. #print axioms seamResidualClosed' = exactly FOUR (CollarHasInvariants, SeamIsE8, collar_invariants, crossedproduct_route_theorem); the original seamResidualClosed (AGT/AMT witness) is kept unchanged as the independent second route. lake build OK (3285 jobs).
Recorded status: Formal [F] (Lean kernel): the G-block arithmetic (one-sided 8=|Z2|*intK/pi, reflection C->-C, c_-=8, MMST range 8<=8<=16, decoupled additivity, 248=8+240=120+128, 240=112+128, det K 1 vs 4, + v461 winding=|C|=1!=0 obstruction + v462 Fock counts 120/128/256 + v463 holomorphy selector forced dimV1=248=E8) all kernel-proved by decide; the two cited theorems MERGED into ONE combined axiom seam_realisation_theorem so seamResidualClosed depends on FOUR axioms (down from six); v464 one-particle rigidity is numerical; residual reduced to ONE realization axiom + ONE combined cited theorem; PLUS the v469 parallel peer-reviewed route seamResidualClosed' (invariant-level collar_invariants + crossedproduct_route_theorem; new kernel facts lr_locality_integer, glue_locality_integers, klm_holomorphic, sixteenfold_pin, all [propext only]); SEAM.EQUIV.01 stays [O]
Dependencies, status detail and source
Canonical status: Formal
Dependencies: SEAM.EQUIV.01; SEAM.S3.FROM-P1.01; SEAM.S3.LOCALITY.01; SEAM.EQUIV.KILLTEST.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.SPINOR.01; SEAM.EQUIV.UNIQ.01; SEAM.EQUIV.ONEPARTICLE.01; SEAM.EQUIV.CROSSEDPRODUCT.01; v456; v457; v458; v459; v461; v462; v463; v464; v469
Scripts: lean4-carrier-rigidity/TfptCarrier/SeamResidualAxiom.lean
Location: tfpt_research_contracts
Original CSV, line 523Original ledger status
SEAM.EQUIV.CROSSEDPRODUCT.01
The NET-LEVEL CROSSED-PRODUCT certification of the 128-spinor extension + the R1 -> R1' invariant-level reduction (2026-07-02, closure-route round) -- re-founds BOTH halves of the SEAM.EQUIV.01 residual on harder-to-reject ground; does NOT close it. [E] LR LOCALITY INTEGER (index-2): the SO(16)_1 spinor has h_s = N/16 = 16/16 = 1 in Z => statistics phase e^{2 pi i h_s} = +1 -- EXACTLY the Longo-Rehren locality criterion, so the Z2 simple-current crossed product SO(16)_1 x| {1,s} is a LOCAL index-2 extension (Longo-Rehren RMP 7 (1995); the level-1 so(N) net WITH its DHR sectors from even-CAR: Boeckenhauer RMP 8 (1996); simple-current extensions of nets: Boeckenhauer-Evans CMP 197 (1998)); KLM gives mu(B) = mu(SO16)/[B:A]^2 = 4/4 = 1 => B HOLOMORPHIC => B = (E8)_1 by the v463 classification pin (E4/eta^8 q^1 = 248 re-verified). THE 2024/2025-PREPRINT LEG (AGT arXiv:2506.01008 + AMT arXiv:2407.18222, v459) IS DEMOTED TO AN INDEPENDENT SECOND WITNESS -- the extension certification now rests on 1995-2001 peer-reviewed journals. [E] INDEX-4 PARALLEL: the mu4 glue J = (s, Lambda1) of (D5)_1 x (A3)_1 has h(J^k) = {1,1,1} for k=1,2,3 -- ALL integer (5/8+3/8=1; 1/2+1/2=1), the v125 isotropy q(k(1,1))=k^2 restated at net level; mu = 16/4^2 = 1, the SAME holomorphic endpoint. [E] R1' INVARIANTS COMPUTED: per-copy FHS Chern C(M=1)=1 vs C(M=3)=0 (control), nu = 16 x |C| = 16, c_- = nu/2 = 8 = g_car + N_fam = rank E8; nu mod 16 = 0 is EXACTLY the class-D phase whose edge admits a purely bosonic description = the (E8)_1 level-1 state (Kitaev Ann. Phys. 321 (2006), sixteen-fold way) -- the identification endpoint pinned from published condensed-matter theory. [E] THE CHAIN COMPOSES (v297 typing): T1 invariants -> nu=16 phase (Kitaev 2006/2009; c_- a PHASE invariant: Kapustin-Spodyneiko PRB 101 (2020), Kim et al. PRL 129 (2022)) -> T2 SO(16)_1 net (MMST CMP 397 (2023) + Boeckenhauer 1996) -> T3 local holomorphic extension (LR/BE + KLM CMP 219 (2001)) -> T4 (E8)_1 (Dong-Mason + v463). [C] R1 -> R1': the Lean axiom collar_realizes (model-level fiat 'the seam IS this lattice model') is replaceable by collar_invariants (invariant-level: quasi-free [C v155/v160] + gap [E v302] + class D + c_- = 8 [E v456, from P1]) -- any realisation with these invariants is phase-equivalent to the v367 stack, hence has the SAME edge scaling limit; quasi-freeness stays the ONE [C] hypothesis. [O] NOT CLOSED: the cited theorems stay cited (certification, not re-proof); the abstract continuum existence remains; SEAM.EQUIV.01 stays [O].
Recorded status: Net-level crossed-product certification + R1 invariant reduction [E]/[C]/[O]: h_s = 16/16 = 1 in Z => the LR locality criterion holds, the Z2 crossed product SO(16)_1 -> (E8)_1 is a LOCAL index-2 extension by 1995-2001 PEER-REVIEWED subfactor theory (LR/Boeckenhauer/BE/KLM), AGT/AMT demoted to second witness; mu4 glue h(J^k)={1,1,1} parallel; R1 reduced to computed invariants (FHS |C|=1, nu=16, c_-=8, the Kitaev-E8 16-fold-way class); SEAM.EQUIV.01 stays [O]
Dependencies, status detail and source
Canonical status: -
Dependencies: SEAM.EQUIV.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.UNIQ.01; SEAM.EQUIV.ONEPARTICLE.01; v125; v154; v297; v336; v367; v456; v458; v459; v463; v464
Scripts: v469_seam_crossedproduct_route.py
Location: tfpt_research_contracts
Original CSV, line 530Original ledger status
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)
Dependencies, status detail and source
Canonical status: Computable side complete: diagonal = 0 at KMS scale, resummation closed-form, 48/41 = one state set under two weights; remaining [O] = the SEAM.EQUIV.01 face (v382 typing substantiated)
Dependencies: SEAM.CONTACT.UNIT.01; ALPHA.QUILLEN.EXACT.01; HYP.PHI0.PUNCTURE.01; HYP.PHI0.GEOM.01; EM.WARD.02; DYN.KMS.01; v3; v151; v239; v245; v434; v470; v483; v484
Scripts: v485_contact_diagonal_closed.py
Location: tfpt_1;origin_theory
Original CSV, line 546Original ledger status
CELEST.WP1.01
WP1 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-20; CELEST.SEAM.01 work package 1, verdict B): the E8 mu4-glue grading (v128) IS the flat Z4 monodromy of the glue-equivariant celestial chiral algebra on the A3 ALE space C^2/Z4 -- the Bittleston-Homans-Sharma CCA construction (arXiv:2305.09451, JHEP 09 (2023) 008; the Z2/Eguchi-Hanson case) refined to Z4 with a Kronheimer-Nakajima flat connection at infinity. Sympy exact throughout. [E] INNER GRADING / FLAT MONODROMY: h = (2,2,2,2,2;0^4) gives <alpha,h> = glue class mod 4 for ALL 240 roots => glue = Ad(exp(2 pi i h/4)), an order-4 torus element = a flat Z4 monodromy; the A3-side detector h' = (0^5;1,1,1,-3) reads the SAME class -- the glue charge is the diagonal (1,1) of the discriminant group Z4 x Z4 (the v92/v125 Lagrangian glue); Z2 halfway: 120 = SO(16), 128 = spinor (v125 sub-Q {0,2}). [E] SPATIAL SIDE: C^2/Z4 under (z1,z2) -> (i z1, i^-1 z2) IS the A3 singularity XY = Z^4 (invariant ring exact; Hilbert series (1+t^4)/((1-t^2)(1-t^4)); Molien table verified; conjugation symmetry N[d][1] = N[d][3]). [E] EQUIVARIANT SECTOR CLOSES: the glue-equivariant SDYM(E8) modes (j + m = 0 mod 4) form a Lie subalgebra with D[d] = 60(d+1) even / 64(d+1) odd -- uniform per parity ONLY because dim g_j = (60,64,60,64) (the v128 dims are the consistency condition); zero modes (d=0) = g0 = carrier D5+A3+Cartan = 60; asymptotic density 62/248 = 1/4 = 1/|Z4|; EH/Z2 halfway towers 120/128. [E] CHARACTER: Theta_E8 = sum of the 4 glue-coset thetas (shell 1 = (52,64,60,64) from the LATTICE, independent of the root construction); the 4 sector characters Theta_Cj/eta^8 sum EXACTLY to chi_(E8)_1 = 1+248q+4124q^2+34752q^3 (v377 series); sector weights h_D5 = (0,5/8,1/2,5/8), h_A3 = (0,3/8,1/2,3/8) = the v92/v125 discriminant form (5x^2+3y^2)/8 mod 1; glue diagonal h = (0,1,1,1) INTEGER = v125 isotropy = the extension to (E8)_1 is local. [E] CRITICAL CORRECTION (why verdict B): the A3 deck diag(i,i^-1) induces z -> -z on the celestial sphere (projective order 2, the sheet flip) -- NOT the order-4 clock z -> iz; any SU(2) lift of the clock has order 8 (spin group Z8, would quotient to A7); exact bridge (spin clock)^2 = deck, |Z8| = 8 = 2|mu4| (the c3 = 1/(8 pi) winding integer); the order-4 clock IS realised as the U(2) phase diag(i,1) (order 4, fixed {0,inf}, free mu4 orbit -- all v180 properties; normalises the deck, det = i rotates the holomorphic symplectic form by the mu4 generator -- Kaehler, not triholomorphic). [E] GRAVITY SIDE: clock-invariance selects from the versal A3 family XY = Z^4 + a2 Z^2 + a1 Z + a0 EXACTLY the 1-parameter family XY = Z^4 + a0; its 4 branch points are ONE mu4 orbit with cross-ratio 2 -- the seam marks (v179 clock orbit; v168/v214 pillowcase j = 1728). [E] NEGATIVE CONTROLS: false spatial action diag(i,i) killed 3 ways (det = -1 not in SL(2,C); Poisson closure fails 14/14; grades unsymmetric); false glue (60/64 swap) breaks additivity on 3112/6720 root pairs; rigidity: exactly {id, j -> -j} = Aut(Z4) of 24 relabelings are additive. [C] the clock-deck identification is a NAMED extra identification (clock^2 = deck on the sphere, sheet-Z2 spin bookkeeping) -- verdict B, not A. [O] structural arithmetic ONLY: no celestial duality is constructed; CELEST.SEAM.01 (WP2-WP5) stays a research contract; SEAM.EQUIV.01 stays [O], untouched. No gate closes, no marker moves.
Recorded status: Formal/Identity [E] (exact Z4-orbifold/character/spin arithmetic, sympy, negative controls) + [C] (the named clock^2 = deck identification, verdict B) + [O] (celestial programme; SEAM.EQUIV.01 unchanged)
Dependencies, status detail and source
Canonical status: WP1 [E]/[C]/[O]: E8 mu4-glue = inner order-4 torus element = flat Z4 monodromy on the A3 ALE; equivariant SDYM(E8) sector closes (60/64 towers, zero modes = carrier, density 1/4); (E8)_1 character = sum of the 4 glue sectors, weights = discriminant form; clock = U(2) diag(i,1), clock^2 = deck (Z8, 8 = 2|mu4|); clock-invariant deformation XY = Z^4 + a0, branch points = one mu4 orbit, cross-ratio 2; negative controls + Aut(Z4) rigidity; verdict B; SEAM.EQUIV.01 stays [O]
Dependencies: CELEST.SEAM.01; SEAM.EQUIV.01; E8.GLU.01; v92; v125; v128; v168; v179; v180; v214; v377
Scripts: v492_celestial_z4_orbifold.py
Location: tfpt_research_contracts
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