A registered result in its source context
Original ledger classification: Open (research contract; naive grammar extension excluded [E]; genuinely nonabelian structure required -- typed; alpha_s(M_Z) currently an external input)
Recorded statement: 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…
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
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GAUGE.DETLINE.FIXPOINT.01
Original ledger classification: Open (research contract; naive grammar extension excluded [E]; genuinely nonabelian structure required -- typed; alpha_s(M_Z) currently an external input)
Original claim text
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.
Original classification detail
Open [O] + H0 grammar kill [E] (v996): naive census-only extension of the U(1) alpha grammar to SU(2)/SU(3) excluded (sign kill, 64 conventions 0 hits); genuinely nonabelian Casimir/instanton structure required -- typed. Honest: alpha_s(M_Z) is currently an external input. ln-2 detline rate is a numerical Bismut-Freed shadow. WAVE-5 (2026-08-29, exploration probes gauge_stiffness_fixpoint/stepscaling; NOT a new module): mechanism executed at FIXED VOLUME BUT thermodynamic step-scaling DIVERGENT; typed hurdle >= 2+1D. WAVE-7 (2026-08-30, v1008): 2+1D scaffold-coherent (K=0, contractive selector, q^2 law); 4D fixpoint stays [O]. Display unmoved Open. | AFTERNOON (2026-08-30 v1011): BINDING constraint -- holonomy stiffness collapses in the confined phase; the matching point of the coupling functional must be defined in the deconfined/weak regime; charged channels enhance (~2.014x at weak g) but do not prevent collapse at minimal volume. Display stays [O].
Dependencies as recorded
ALPHA.QUILLEN.EXACT.01; SEAM.DETLINE.UNIFICATION.01; EM.FP.01
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- Research contracts
Sections that explicitly cite this claim
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- Research Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)tfpt research contracts
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)tfpt research contracts
- Research Contract — GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings from one zeta-det functional)tfpt research contracts
- Research Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)tfpt research contracts
- =150 2026-08-29 (CXLIII) (review wave 5 — two exploration probes graduate as v1002– v1003 plus three registrations: the DET16 finite-cluster hit, the two neutrino-texture structural nulls, the master scaling-limit theorem SEAM.MMST.TYPEIII.CHARGED.01, the gauge-stiffness step-scaling divergence, and the holomorphic-KMS document; suite [formula in source] , ledger [formula in source] : three new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1001). (1) v1002_ spin10_ mirror_ projector.py ( [formula in source] ): DET16 rank-one projector on the full [formula in source] cluster — [formula in source] , [formula in source] , defect [formula in source] ; [formula in source] hermitian idempotent [formula in source] , rank [formula in source] ; [formula in source] spectrum [formula in source] , gap exactly [formula in source] ; all [formula in source] [formula in source] Fock commutators [formula in source] ( [formula in source] ); parity commutator [formula in source] ; [formula in source] and [formula in source] singlets. Hopping stability on the [formula in source] -mode analogue: gap [formula in source] ( [formula in source] clusters) / [formula in source] ( [formula in source] clusters) at [formula in source] ; spectators untouched. NEW ledger row CHIRAL4D.MIRROR.DET16.01 Candidate \ (exact finite-cluster gapping; open: dynamical gauge fields, domain-wall geometry, [formula in source] D volume theorem). (2) the Casimir kill, permanent. Number-preserving Casimir projector uniqueness fails at every cluster size: one [formula in source] (none at [formula in source] ); [formula in source] half-filling multiplicity [formula in source] ; [formula in source] (exact Weyl alternation, [formula in source] ). Ledger note on CHIRAL4D.NOMIRROR.01: number-preserving Casimir projector route excluded; display stays . (3) v1003_ nu_ structural_ nulls.py ( [formula in source] ): charged-sector data [formula in source] , [formula in source] ; Schur-texture NULL — all [formula in source] preregistered [formula in source] fail, D4 reflection forces [formula in source] , hierarchy [formula in source] structurally unreachable from D4-even seam data, required [formula in source] matches none of [formula in source] comparators; orientation-doubling structure theorem — [formula in source] odd sector generically lifts the degeneracy (exact rational witness); scale NULL — [formula in source] fail, required cancellation [formula in source] not supplied, [formula in source] -branches isospectral. NEW ledger row FLAV.NU.TEXTURE.MECHANISM.01 : both nulls are binding constraints (mechanism must be D4-odd AND supply a [formula in source] even-odd cancellation; pure seam data excluded -typed). FLAV.NUSCALE.05/ .06 notes only; candidates unmoved. (4) registrations (no marker moves). NEW SEAM.MMST.TYPEIII.CHARGED.01 : ONE scaling-limit theorem [formula in source] strongly on the finite-energy core [formula in source] crossed-product continuity, from which [formula in source] , [formula in source] , type III [formula in source] , unique rotational KMS, unique CE, deck equidistribution and modular invariance follow as corollaries; children SEAM.SIMPLECURRENT.GENERATOR.01, SEAM.STATE.RPMIXING.01 continuum, ALPHA.QUILLEN.EXACT.01 rigidity, AX.P1.01 reading (listed on the parent, not back). Cited document articles/2026-08-29/holomorphic_kms_extension_en.tex ( [formula in source] pp): unconditional rotational-KMS uniqueness via KLM [formula in source] Longo–Tanimoto GIVEN the identification; P1 [formula in source] theorem-conditional on seam identification [formula in source] [formula in source] ; axiom typing UNCHANGED. GAUGE.DETLINE.FIXPOINT.01: mechanism executed at fixed volume (unique fixed point, contraction [formula in source] , exact [formula in source] and [formula in source] Dynkin ratio [formula in source] ) BUT the preregistered thermodynamic step-scaling [formula in source] is DIVERGENT ( [formula in source] oscillates [formula in source] , [formula in source] at [formula in source] ); typed hurdle: the [formula in source] D toy has no plaquette self-interaction, the real contract needs [formula in source] D; display stays . [formula in source] boundary note: unit choice closed; dimensionless hierarchies [formula in source] remain predictive obligations. Surfaces: tfpt_research_contracts (new sections MIRROR.DET16, TYPEIII.CHARGED, NU.TEXTURE.MECHANISM; DETLINE stiffness update; NOMIRROR Casimir kill); tfpt_4_frontier wave-5 paragraph; tfpt_2 (texture-mechanism note); introduction status card [formula in source] hierarchy sentence.Research changelog; TFPT — Introduction and reading guide
- =150 2026-08-30 (CXLV) (review wave 7 — four exploration strands graduate as v1006– v1009: the MMST lemma battery, the DET16 stability battery, the [formula in source] D master-object assembly scaffold, and the [formula in source] constrained minimizer; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1005). (1) v1006_ mmst_ lemma_ battery.py ( [formula in source] ): five lemmas in-house on SEAM.MMST.TYPEIII.CHARGED.01 \ — L3 crossed-product; UGF [formula in source] (measured plateau [formula in source] , max measured [formula in source] [formula in source] at [formula in source] ); TEL-a [formula in source] with exact isometries ( [formula in source] , measured envelope [formula in source] ); integer D5+A3 pairings; [formula in source] outerness in the limit [formula in source] finite-inner correction. Residual boxed: TEL-B-EXTERNAL (Hankel [formula in source] ; HS remainder sourced from the paper max [formula in source] / fit [formula in source] / v998 bound [formula in source] , not recomputed) [formula in source] ALG-EXH (two Buchholz–Verch estimates). Display stays . Cited articles/2026-08-30/mmst_charged_scaling_limit_en.tex ( [formula in source] pp) [formula in source] externalization_mmst_handoff_v2_en.html. (2) v1007_ det16_ stability_ battery.py ( [formula in source] ): T1/T2 proved (v1002); T3 Michalakis–Zwolak cited-verified (LTQO, [formula in source] , gap [formula in source] ). Counting line [formula in source] ; [formula in source] closing scan through [formula in source] ; dynamical [formula in source] uniquely gapped (full-probe min [formula in source] pinned; compressed suite). SW [formula in source] ; [formula in source] bounded. [formula in source] boxed (ordinary hopping not block-diagonal); BDL boxed (no volume-uniform gap remainder). CHIRAL4D.MIRROR.DET16.01 stays ; CHIRAL4D.NOMIRROR.01 unmoved. Cited articles/2026-08-30/det16_mirror_gap_theorem_en.tex. (3) v1008_ master_ assembly_ scaffold.py ( [formula in source] ): [formula in source] D master-object scaffold-coherent — combinatorial [formula in source] ; frozen-link [formula in source] , [formula in source] ; unique-contractive [formula in source] ; QWZ wall slope [formula in source] , DET gap [formula in source] through [formula in source] ; assembly [formula in source] [formula in source] , clock [formula in source] . [formula in source] spaces [formula in source] / [formula in source] out of suite. Decision QFT4D.LATTICE.FUNDAMENTAL.01 and GAUGE.DETLINE.FIXPOINT.01 \ unmoved. (4) v1009_ rho0_ minimizer.py ( [formula in source] ): finite uniqueness of the KMS compression (Klein); Hessian strictly positive; centre dim [formula in source] ; identity [formula in source] . TYPED: V1000_CONSEQUENCE_MISMATCH (compression kills the SK response vs frozen contrast [formula in source] ) [formula in source] CENTER_FLATNESS_PREMISE_FALSE. Canonical formula needs a weaker admissible set. FTRANSFER.SK.RHO0.01 stays . Surfaces: tfpt_research_contracts executed-update paragraphs; tfpt_4_frontier wave-7 paragraph; introduction status card; website papers.ts / VerificationDag.Research changelog; TFPT — Introduction and reading guide
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- Die gemeinsame Variationsidentität statt einzelner ExtremwerteTFPT Gesamtsynthese 2026-09-28
All 22 linked sections
- =150 2026-08-30 (CXLVI) (afternoon harvest — simplicity campaign [formula in source] [formula in source] D ladder graduate as v1010– v1011; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1009). (1) v1010_ simplicity_ bridge_ census.py ( [formula in source] ): derivation matrix over four frozen seeds, unique remainder min [formula in source] ; anchor [formula in source] is not among the three declared Milnor maps; [formula in source] four novel candidates NULL. Bridge [formula in source] CANONICAL — the bit-selector ladder forces [formula in source] and family [formula in source] forces [formula in source] column sums [formula in source] ; [formula in source] 's carrier-looking [formula in source] is inherited from [formula in source] column [formula in source] , not inserted (the v1005 circularity flag is corrected as forced provenance). Bridge [formula in source] CHOICE-but-conditionally-unique: spectrum [formula in source] alone has [formula in source] solutions; democratic-image [formula in source] carrier-anchor kernel leave exactly the corpus shift (count [formula in source] ); remaining obligation [formula in source] seam-geometric derivation of those two directional premises. Milnor strong all-structure bridge NONEXISTENT at [formula in source] (clock [formula in source] vs [formula in source] , CP rank [formula in source] vs [formula in source] ) and at every upstairs home ( [formula in source] , Gaussian [formula in source] , affine); only the coarse [formula in source] -module [formula in source] pairing bridge exists (witness constructed; [formula in source] , [formula in source] ). Ring-internal identities of v1004 (rank clock, socle CP, self-clock) unaffected. SEAM.MILNOR.LOCALRING.01 stays \ (canonical status SHARPENED); AX.P2.01 stays an axiom (pencil rehabilitated, W premises remain). (2) v1011_ 3p1d_ ladder_ battery.py ( [formula in source] ): B6–B9 compressed — minimal [formula in source] D viable (exact Gauss [formula in source] , confinement [formula in source] vs [formula in source] , exact in-face isotropy, [formula in source] ); exact tree-fixing [formula in source] with tree-independence [formula in source] ; DET survives coupling; back-reaction; periodicity restores holonomy [formula in source] ; charged channels [formula in source] at weak [formula in source] ; charge- [formula in source] control matches B8 to [formula in source] ; [formula in source] collapses above [formula in source] . BINDING: the matching point of the coupling functional must sit in the deconfined/weak regime. QFT4D.LATTICE.FUNDAMENTAL.01 Decision typing UNCHANGED (Kronecker limitation removed); GAUGE.DETLINE.FIXPOINT.01 stays \ with the matching-scale constraint recorded. Surfaces: tfpt_research_contracts executed-update paragraphs (MILNOR sharpening, P2 rehabilitation, QFT4D ladder, DETLINE matching-scale); tfpt_4_frontier [formula in source] introduction afternoon note; website papers.ts / VerificationDag.
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- Front matter / support
- Wie die vorhandenen physikalischen Herleitungen zusammen zurückwirken
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- =150 2026-08-28 (CXL) (review wave 3 — the third external bird's-eye review adjudicated and integrated: ONE new module v993 plus THREE new \ contracts plus a v986 motivation retype plus the dual-rest formula; suite [formula in source] , ledger [formula in source] ; NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v992). (1) v993_ minimal_ defect_ selector.py ( [formula in source] ): the FULL rank-8 ADE census (SNF of Cartan) with cyclic [formula in source] glue on BOTH factors selects [formula in source] uniquely ( [formula in source] aliases collapsed) — the [formula in source] architecture of v624 is an OUTPUT of (rank 8 [formula in source] cyclic [formula in source] ), not an INPUT; kill tests [formula in source] / [formula in source] (product 16, fail cyclicity) and the [formula in source] control [formula in source] ; [formula in source] exact (lattice shadow of [formula in source] ); the [formula in source] average is the UNIQUE trace-preserving finite conditional expectation (uniqueness needs the module property; kernel dim [formula in source] without it). Ledger notes on AX.P1.01/ AX.P2.01: axiom typing UNCHANGED; the equidistribution identification stays the open \ of v813; cited-not-proved remain [formula in source] and holomorphic uniqueness of [formula in source] . SEAM.SIMPLECURRENT.GENERATOR.01 canonical status grows the [formula in source] parity-shadow line. (2) Three new research contracts, all , no scripts: GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings as unique stationary points of one nonabelian zeta-det/inflow functional; generalizes ALPHA.QUILLEN.EXACT.01; honest: [formula in source] is currently an external input); GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 pole from the same spectral determinant; Einstein equation stays downstream/conditional; GRAV.NONCIRCULAR.01 binding); FTRANSFER.SK.RHO0.01 (cosmological transfers need [formula in source] , not [formula in source] alone; typed candidate [formula in source] , [formula in source] orientation picks [formula in source] ; FTRANSFER.GENERATING.01 covers equilibrium only). (3) v986 docstring retype: the [formula in source] motivation is loose ( [formula in source] ); the operator reading is the [formula in source] eigenvalue route [formula in source] ; texture data-constrains-texture; check logic and pass/fail UNCHANGED. (4) Dual rest: introduction status card (and the research-contracts keybox, with a brief frontier mirror) now carries [formula in source] (compiler) beside [formula in source] (strict-physical-TOE accounting of the 2026-08-27/28 contract wave); nothing in the second formula is claimed closed. Exploration not promoted: the wave-3 Quillen zero-mode Gram identity is a reformulation ( [formula in source] ), not a Quillen-metric object.
- Research Programme — the TFPT4D master route (one 4D transfer object instead of twenty formulas)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- =150 2026-08-28 (CXLI) (the completeness wave — four exploration probes graduate as v994– v997 (suite [formula in source] , ledger [formula in source] : eight contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v993). (1) v994_ mmst_ criteria_ battery.py ( [formula in source] ): [formula in source] of [formula in source] MMST identification criteria executed -measured — measured [formula in source] (16 Majorana copies), conformal edge spectrum [formula in source] , current normalisation [formula in source] , sector collapse [formula in source] , and the flagship: [formula in source] /GSO-projected lattice character sums reproduce the [formula in source] vacuum character [formula in source] three orders deep; C6 is now written out in articles/2026-08-28/psi_lambda_convergence_theorem_en.tex (analytic log coefficient [formula in source] vs measured [formula in source] , [formula in source] ); C7 modular invariance stays cited/open. Ledger notes on SEAM.EQUIV.MMST.01 (stays ) and SEAM.SIMPLECURRENT.GENERATOR.01 (stays ; open rest [formula in source] C7 [formula in source] net G2/G3/G4). (2) v995_ kms_ subnet_ rigidity.py ( [formula in source] ): all [formula in source] v972 mixing directions killed by KMS alone on finite [formula in source] ; covariance provably redundant; unique [formula in source] -invariant crossed-product extension [formula in source] . SEAM.STATE.RPMIXING.01 finite KMS rigidity ; type-III/continuum stays . (3) v996_ gauge_ grammar_ kill.py ( [formula in source] ): H0 structural kill — negative [formula in source] flip the stationary-root signs ( [formula in source] inverse [formula in source] , [formula in source] [formula in source] ); [formula in source] conventions [formula in source] hits; [formula in source] control [formula in source] survives all mutants; detline curvature [formula in source] exponentially with rate [formula in source] (numerical Bismut–Freed shadow). GAUGE.DETLINE.FIXPOINT.01 naive grammar excluded ; genuinely nonabelian structure required — typed; [formula in source] remains an external input; contract stays . (4) v997_ spin2_ smg_ witnesses.py ( [formula in source] ): Barnes–Rivers quadratic decomposition — [formula in source] clean (one massless TT pole, two helicities, scalaron at [formula in source] exact); the local [formula in source] Weyl [formula in source] truncation necessarily carries an opposite-residue spin-2 ghost — typed; FK SMG toy: [formula in source] unique [formula in source] -singlet ground state, Schmidt rank [formula in source] , volume-independent gap [formula in source] at [formula in source] ; [formula in source] contrast [formula in source] -degenerate; physical chiral edge keeps [formula in source] exactly. GRAV.SPIN2.EMERGENCE.01 quadratic witnesses , content pinned on the untruncated form factor; CHIRAL4D.NOMIRROR.01 SMG toy-proved , [formula in source] D [formula in source] stays ; both contracts stay . Canonical note (not a module) on FLAV.NUSCALE.05: NU_TEXTURE_CENSUS_NULL [formula in source] — frozen [formula in source] inventory provably insufficient; mechanism \ sharpened. Surfaces: tfpt_research_contracts (executed-update paragraphs at MMST/SIMPLECURRENT, RPMIXING, GAUGE.DETLINE.FIXPOINT.01, GRAV.SPIN2.EMERGENCE.01, CHIRAL4D.NOMIRROR.01, ALPHA.QUILLEN rigidity/ln-2 notes); tfpt_2 (census-null note); tfpt_4_frontier [formula in source] introduction card addendum. Exploration record: articles/2026-08-28/big_picture_simplicity_first_en.md.
- Research Contract — GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings from one zeta-det functional)
- Research Contract — GAUGE.DETLINE.FIXPOINT.01 (all three gauge couplings from one zeta-det functional)
- Full quantum gravity — induced from the boundary kernel
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- Research Contract — TFPT4D.LATTICE.ACTION.01 (the explicit finite 4D lattice action and its seven finite gates)tfpt research contracts
- Research Contract — TFPT4D.LATTICE.ACTION.01 (the explicit finite 4D lattice action and its seven finite gates)tfpt research contracts
- Research Contract — QFT4D.OS.RECON.01 (the genuine 4D Euclidean lattice package)tfpt research contracts
- Source contract and nomenclature.tfpt research contracts; tfpt research contracts; Research contracts
- Round 7: the actual DET parent, its exact factorized gap, and the local-defect obstructiontfpt research contracts; tfpt research contracts; Research contracts
- Research Contract — QFT4D.OS.RECON.01 (the genuine 4D Euclidean lattice package)Research contracts
- =150 2026-08-30 (CXLVII) (evening TOE-gate wave — four executed witnesses graduate as v1012; suite [formula in source] , ledger [formula in source] no new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1011). v1012_ toe_ gate_ witnesses.py ( [formula in source] ): T5 IR universality on the physical QWZ edge — [formula in source] (limit [formula in source] ), clustering dichotomy [formula in source] vs power-law exponent [formula in source] , Lieb–Robinson cone [formula in source] with leakage [formula in source] , cubic curvature [formula in source] with volume; TYPED SPLIT: gauge holonomy [formula in source] seam clock are not propagating modes, so the common- [formula in source] test needs dynamical gauge excitations. T8 [formula in source] eight-candidate table ALL unique; hard sectors kill the SK response ( [formula in source] ); every response-alive set is exactly [formula in source] even without [formula in source] — entropic-proximity selection is VACUOUS at finite level; verdict NO_SET_WORKS with the double diagnosis; binding requirement [formula in source] a non-entropic principle (Euclidean-cap / orientation-branch). T6 [formula in source] six-fold NULL: six pre-declared D4-odd candidates, all parity-checked, all NULL (five at [formula in source] ; [formula in source] is [formula in source] too large); the [formula in source] cancellation requires the true [formula in source] D functional — third and final scaffold-level nu-mechanism bound this week. T7 interacting TT: conserved interaction-complete lattice stress [formula in source] , TT spectral positivity exact, sum rules [formula in source] , dominant positive- [formula in source] pole persists under [formula in source] (gapped); [formula in source] trend [formula in source] suppressed [formula in source] / [formula in source] enhanced [formula in source] ; free analytic match. Missing: TFPT content, [formula in source] volume scaling, Ward identities. Ledger notes only on TFPT.TOE.COMPLETE.01, FTRANSFER.SK.RHO0.01, FLAV.NU.TEXTURE.MECHANISM.01, GRAV.SPIN2.EMERGENCE.01 (all stay ). Surfaces: tfpt_research_contracts executed-update paragraphs; tfpt_4_frontier [formula in source] introduction evening-wave note; website papers.ts / VerificationDag.Research changelog; TFPT — Introduction and reading guide
- Proof.tfpt research contracts; tfpt research contracts; Research contracts
All 12 linked sections
Registered verification modules
- v996_gauge_grammar_kill.pyRegistered verification module · frontier
Read the description recorded in the module registry
GAUGE.DETLINE.FIXPOINT.01 [O-Update: naive Grammatik-Erweiterung ausgeschlossen [E]; echt nichtabelsche Struktur noetig -- typisiert] + ALPHA.QUILLEN.EXACT.01 [O-Notiz: ln-2-Rate-Schatten] (Vollstaendigkeits-Welle 2026-08-28): H0-STRUKTURKILL -- negative b2/b3 drehen die Wurzelvorzeichen (SU(2)-Inverse -151.2, SU(3) -115.9); 64 Konventionen 0 Treffer; U(1)-Kontrolle 137.0359992168 ueberlebt alle Mutanten. Detline-Kruemmung -> 2pi exponentiell, Rate 0.6936 ~ ln 2 (numerischer Bismut-Freed-Schatten, kein Kontinuumstheorem). alpha_s(M_Z) bleibt externer Input. Python-only / Wolfram-Spiegel zurueckgestellt.
- v1008_master_assembly_scaffold.pyRegistered verification module · frontier
Read the description recorded in the module registry
QFT4D.LATTICE.FUNDAMENTAL.01 Decision / GAUGE.DETLINE.FIXPOINT.01 [O] (Review-Welle 7, 2026-08-30; 2+1D-Scaffold kohaerent): Prototyp K=0 Plaquette-Exponenten; Materie frozen-link q^2~4, K(q=0)=0, kontraktiver Selektor |R'|<1; Wand/Spiegel QWZ-Steigung ~-0.9989, DET-Gap >=1.5 bis t=0.6; Assembly Z6 (1,2,3,0), Uhr [0,1,1,2], chi_phys vs chi_mirror. Keine Marker-Bewegung. Python-only / Wolfram-Spiegel zurueckgestellt.
- v1011_3p1d_ladder_battery.pyRegistered verification module · frontier
Read the description recorded in the module registry
3+1D-Leiter B6-B9 (Nachmittag 2026-08-30): minimales 3+1D viable (Gauss 32768, Confinement, exakte Isotropie, g*~1.915); exaktes Tree-Fixing 524288 -> 4096, Tree-Unabhaengigkeit, DET unter Kopplung, Back-Reaction; Periodizitaet stellt K wieder her; geladene Kanaele ~2.014x bei schwachem g; K kollabiert in der confined Phase. BINDEND: Matching-Skala des Kopplungsfunktionals muss im deconfined/weak Regime sitzen. QFT4D.LATTICE.FUNDAMENTAL.01 bleibt Decision; GAUGE.DETLINE.FIXPOINT.01 bleibt [O]. Python-only / Wolfram zurueckgestellt.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.