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The conditions for full physical completion

Original ledger classification: 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].

Recorded statement: 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).…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

The exact identifier, original classification and full claim are available below.

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TFPT.TOE.COMPLETE.01

Original ledger classification: 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 claim text

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.

Original classification detail

Open [O]: TOE_Complete := AND(T1..T8); TOE_Validated := Complete AND independent holdouts passed. Named AND of existing 4D/dilation/detline/SK/flavor/gravity/SK contracts; not a closure. Compiler Rest sits beside Rest_TOE. WAVE-5 (2026-08-29): T2 master scaling-limit theorem named SEAM.MMST.TYPEIII.CHARGED.01 [O] (children listed there, not back). Display unmoved. WAVE-6 (2026-08-30): T7 child GRAV.WEINBERG.WITTEN.01 [O] (Weinberg-Witten firewall before any spin-2 marker move). Display unmoved. | EVENING (2026-08-30 v1012): T5 four witnesses + propagating-mode precondition; T7 interacting stress mechanism; T8 selection-principle vacuity typed (needs a non-entropic selection); T6/nu scaffold-level triple bound complete. Display unmoved. | LATE EVENING (2026-08-30 v1013/v1014): T3 mandatory-dynamics leg closed at class level; remaining axiom-core and continuum gaps run through one externalized theorem (MMST/Quillen). Display unmoved. | MONDAY MORNING (2026-08-31 v1015): T1 structure-postulate route fully premise-supported at finite level. Display unmoved. | ROUND3 2026-09-05: current T1-T8 matrix recorded; no marker moves; shared 3+1D parent absent. The one-theorem statement is compiler/W-bridge scope only. | 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.

Dependencies as recorded

AX.P1.01; AX.P2.01; TFPT.IRREDUCIBLE.01; DIMENSION.SELECTOR.4D.01; SEAM.EQUIV.01; SEAM.EQUIV.MMST.01; SEAM.EQUIV.TWISTOR.01; SEAM.SIMPLECURRENT.GENERATOR.01; SEAM.DETLINE.UNIFICATION.01; SEAM.STATE.RPMIXING.01; QFT4D.LATTICE.FUNDAMENTAL.01; TFPT4D.LATTICE.ACTION.01; DYN.UNITARY.DILATION.01; DYN.MARKOV.EMBED.01; CHIRAL4D.NOMIRROR.01; QFT4D.OS.RECON.01; SEAM.BULK4D.RECON.01; ALPHA.QUILLEN.EXACT.01; GAUGE.DETLINE.FIXPOINT.01; FLAV.NUSCALE.01; FLAV.NUSCALE.04; FLAV.NUSCALE.03; FLAV.NUSCALE.02; FLAV.NUSCALE.05; FLAV.NUSCALE.06; GRAV.SPIN2.EMERGENCE.01; GRAV.NONCIRCULAR.01; GRAV.WEINBERG.WITTEN.01; FTRANSFER.SK.RHO0.01; FTRANSFER.GENERATING.01; OBS.TRANSDUCTION.01; PRED.JOINTLIKELIHOOD.01

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Registered verification modules

  • v1012_toe_gate_witnesses.pyRegistered verification module · frontier
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    Abend-TOE-Gatter-Welle (2026-08-30): T5 IR-Zeugen + getypter SPLIT (physikalisches c->1, xi*gap~1.089 vs Power 2.034, v_LR=5/3, Kruemmung->1/6; Holonomie+Uhr keine propagierenden Moden). T8 rho0 8-Kandidaten NO_SET_WORKS (harte Sektoren antworttot; KMS-affine Mengen selektionsvakuoes). T6 kappa sechsfach NULL (K4 18.8x zu gross; 4D-Funktional noetig). T7 wechselwirkendes TT (Erhaltung/Positivitaet/Summenregeln/Z-Persistenz; gelueckt). FIREWALL: TFPT.TOE.COMPLETE.01 / FTRANSFER.SK.RHO0.01 / FLAV.NU.TEXTURE.MECHANISM.01 / GRAV.SPIN2.EMERGENCE.01 bleiben [O]. Python-only / Wolfram zurueckgestellt.

  • v1013_thermodynamic_dynamics.pyRegistered verification module · frontier
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    Thermodynamische Dynamik (Spaetabend 2026-08-30): Pflicht-Dynamik-Bein auf Hamiltonian-Klasse GESCHLOSSEN (Theorem-Memo). Uniforme LR-Schranke J=12/5, R=2, z=4, kappa=16043/450, v_LR=32086 e/225 ~387.64; normkonvergente tau_t; eichinvariante quasilokale Algebra A^G; Existenz von Grund/beta-KMS-Zustaenden. Numerischer Zwilling: gemessenes v=2.0 << bewiesene Schranke; Konvergenzschranke dominiert Puffer 8/16/32. Rest: Phaseneindeutigkeit, Limes-Luecke, IR-Universalitaet. QFT4D.LATTICE.FUNDAMENTAL.01 bleibt Decision. Python-only / Wolfram zurueckgestellt.

  • v1014_bridge_refinements.pyRegistered verification module · frontier
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    Bruecken-Verfeinerungen (Spaetabend 2026-08-30): Detline-Einschraenkungsisomorphismus endlich VERIFIZIERT (c_phase 3.7e-16, Orientierung 2->1, Restanker U(1)/A0). W-Bruecke: P-anch ABGELEITET (e1=R^{-1}a, Wicklungs-Lock); P-dem TEILWEISE (Z4-Mittel annihilert nichttriviale Charaktere; fehlend = charakterblinde Determinanten-Antwortabbildung, MMST/Quillen-Bein). ALPHA.QUILLEN.EXACT.01 / AX.P2.01 unbewegt. Python-only / Wolfram zurueckgestellt.

  • v1015_axiom_core_closure.pyRegistered verification module · frontier
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    Axiomkern-Abschluss (Montagmorgen 2026-08-31): charakterblinde P-dem-Antwort ABGELEITET (r=(1,1,1) exakt bei Kragen 12 und 16, Demokratie-Residuum 0; Mutanten (1,0,0) und (5/4,1,5/4)). Zusammen mit P-anch (v1014) BEIDE W-Bruecken-Praemissen endlich abgeleitet; Axiomkern-Rest NULL modulo externalisierter MMST-Identifikation. AX.P2.01 bleibt Axiom (endliche Schatten; Kontinuums-Identifikation dasselbe externe Bein). T1-Notiz: Strukturpostulat-Route endlich praemissengestuetzt. Python-only / Wolfram zurueckgestellt.

  • v1022_telb_round3_certificates.pyRegistered verification module · frontier
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    TEL-B-Runde-3-Zertifikate (2026-09-05): natives Arb/Acb, 256 Bit, 5812 rationale Zellen; TV_p(F'') <=15.817695962988924...<15.928674 und K3_TV<2.517464500835. Die analytische C2b-Skalarreduktion plus ausführbare Arb-Arithmetik ergibt c_epsilon=0.288547359238..., c_zeta=0.110677064901..., Summe=0.399224424139...<0.400; volles C2b bleibt exakt bei CF<=0.139/sqrt(N) und DG<=0.060/sqrt(N) offen. Exaktes Einmoden-Gegenmodell widerlegt den alten ALG2-Vandermonde-Schluss; FE-GEN oder eine praezise Gauge/Code-Projektion bleibt noetig. T2/TOE [O] unbewegt; python-flint==0.9.0, nicht Pyodide. KEIN RH-CLAIM.

  • v1023_derivative_filtered_wall.pyRegistered verification module · frontier
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    Ableitungsgefilterter Wall-Block (2026-09-05): H_df erhaelt ker(D_GW) exakt; det Block=lambda g^2 Delta s^2; das adiabatisch spiegel-kontinuierte hohe Band liegt >=Delta+lambda; der niedrige Ast ist quadratisch. Der nackte Spiegeloperator ist nicht invariant und hat fuer s>0 Niedrigbandgewicht -- kein Spiegel-Antwortgap und kein Weyl-Kegel. Gauge-Defekt 2.41e-15, Spektraldefekt 1.78e-15. Endliches quasi-freies Blocklemma; kanonische DET16/DET32-Realisierung, Vielteilchenparent, Zulässigkeit/Quasilokalitaet, Mass/Anomalie/Index, Universalitaet und 4D-Limes bleiben offen. Keine Markerbewegung. KEIN RH-CLAIM.

  • v1024_parent_internal_boundaries.pyRegistered verification module · frontier
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    Parent-interne T6--T8-Grenzen (2026-09-05): endlicher A3--D4 Seam/Neutrinopaar-Intertwiner ohne neuen Faktor; positiv, gerade, gauge-kompatibel, nichtadditiv, lokaler Gap 0.25 konditional auf ererbte volle Parent-Schranke, gemischte Resolvente 0.104712041885. Interner 12D-Z5-Cap Gap 0.197423715893, aber beliebig, D4-brechend und kein globales rho0. Exakte Grenzen: projektiver Full-Fock-D4-Lift; relativer Kommutant bei unitaler Erweiterung; volles Z5-Weylpaar verlangt 5|D nur unprojiziert; uniformer voller Gap schliesst masselosen Spin-2-Pol aus; TT-Projektion nicht endlichreichweitig. 49/49; T6--T8/TOE [O] unbewegt. KEIN RH-CLAIM.

  • v1025_telb_c1_c2a_certificates.pyRegistered verification module · frontier
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    TEL-B C1/C2a-Zertifikate (2026-09-05): natives python-flint==0.9.0. C1: 100-Bit Arb/Acb ueber 3888 analytische Rechtecke plus geschlossene Achsenstreifen-Majorante und exakter Imaginaerteil 1/12 liefert C_star<=0.1520453048...<0.1525. C2a: exakte Kotangens-Reindizierung, Peano-Monotonie und verschobener Euler-Rest reduzieren den Satz fuer alle geraden N>=16 auf Intervallvergleiche; N sup_k|phi_N(k)|<=0.5082287792...<0.509. C1/C2a geschlossen; C2b CF/DG, ALG-EXH, MMST-Skalierung und TOE bleiben offen. Native-only, nicht Pyodide. KEIN RH-CLAIM.

  • v1026_telb_round4_closure.pyRegistered verification module · frontier
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    Native interval TEL-B norm below 2.995906 at fixed M=1, Ny=8 for all even N>=16; CF/DG/CROSS and validated Fourier aliases; ALG-EXH/MMST open

  • v1027_signed_det_car_wall.pyRegistered verification module · frontier
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    Exact canonical DET modes and signed z=1 wall for fixed classical gauge fields; no hard bare-mirror gap or chiral continuum

  • v1028_gauss_d4_cap.pyRegistered verification module · frontier
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    Gauss residues with full 192-mode site characters and specified nine-irrep cube links; symmetric selected-pair-space D4 cap; no canonical clock family, mass texture or global state

  • v1029_local_tensor_constraints.pyRegistered verification module · frontier
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    Local tensor constraints give two z=1 radiative modes after explicit global zero-mode removal; no TFPT embedding

  • v1030_alg2_sector_frame.pyRegistered verification module · frontier
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    Sector connectivity and quantitative uniform word-frame bridge conditional on actual microscopic generation and joint-adjoint tails

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