A registered result in its source context
Original ledger classification: Candidate [C]/[N] + mechanism [O] (pentagon-class misalignment; no seesaw closure; FLAV.NUSCALE.05 unmoved)
Recorded statement: THE PENTAGON-CLASS MISALIGNMENT CANDIDATE (registered 2026-08-29, review wave 4, v1001). Candidate [C]/[N]; mechanism = the Q_+-to-flavor operator [O]; NO closure; FLAV.NUSCALE.05 unmoved. [E] U_e = I inventory theorem: no charged-lepton…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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FLAV.NUSCALE.06
Original ledger classification: Candidate [C]/[N] + mechanism [O] (pentagon-class misalignment; no seesaw closure; FLAV.NUSCALE.05 unmoved)
Original claim text
THE PENTAGON-CLASS MISALIGNMENT CANDIDATE (registered 2026-08-29, review wave 4, v1001). Candidate [C]/[N]; mechanism = the Q_+-to-flavor operator [O]; NO closure; FLAV.NUSCALE.05 unmoved. [E] U_e = I inventory theorem: no charged-lepton mass matrix in the compiler; companion algebra G-self-adjoint with eigenvalues (16/7, 4/3, 7/6). [E] misalignment U = U_v9 R13(theta, phi) solves the 13/23 pair analytically (held-out theta12 inside 1 sigma of NuFIT). [N] pentagon double hit: phi = 288 deg = 4(2pi/5) frozen => all three measured angles <= 0.56 sigma (honest max pull 0.557) at theta = 2pi/35; that theta is the unique LEE survivor of nine pre-declared candidates (LEE expectation 2.7%). [N] v3 chain SHA-16 a4c28732fa687620: Sigma = 0.0599 eV, m_beta = 9.0 meV, m_bb in [1.5, 3.8] meV, delta_CP = 287.66 deg. [N] v270-theta23 tension 1.85 sigma TYPED (TFPT-target refit pull; the pentagon phase does not recover the assembled v270 angle set). [X] census nulls: matrix 0/1607, ratio grammar null, circularity kills -- frozen 3x3 inventory insufficient. Kills: DESI floor on Sigma, DUNE delta_CP discriminates 287.7 vs 240, JUNO. y2 is DATA_CALIBRATED; no seesaw closure.
Original classification detail
[C]/[N] pentagon-class misalignment candidate (v1001): phi=288 deg, theta=2pi/35, LEE 2.7%, v3 SHA a4c28732fa687620, Sigma=0.0599 eV, m_beta=9.0 meV, m_bb [1.5,3.8] meV, delta_CP=287.66 deg; v270-theta23 tension 1.85 sigma TYPED; census 0/1607. Mechanism Q_+-to-flavor [O]. No closure. WAVE-5 (2026-08-29, v1003): both structural nulls (D4-even Schur; scale cancellation 1.885e-4) are binding on FLAV.NU.TEXTURE.MECHANISM.01 [O]. Pentagon-class candidate unmoved; no seesaw closure.
Dependencies as recorded
FLAV.NUSCALE.05; FLAV.NUSCALE.02; FLAV.NUSCALE.01; AX.P2.01
Open the original ledger source, row 765Location recorded in the ledger
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- Standard Model and flavor structure
- Frontier and open physical interfaces
- Research contracts
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)tfpt research contracts
- Neutrinos: Die vorhandenen Herleitungen gemeinsam lösenTFPT Gesamtsynthese 2026-09-28
- Neutrinostfpt 2 standard model
- NeutrinosStandard Model and flavor structure
- =150 2026-08-29 (CXLII) (review wave 4 — four exploration probes graduate as v998– v1001 plus the lattice-fundamental quasilocal-family amendment, the [formula in source] closed-metrology retype, the ALPHA.QUILLEN relative-determinant note, and the master contract TFPT.TOE.COMPLETE.01; suite [formula in source] , ledger [formula in source] : two new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v997). (1) v998_ seam_ modular_ closure.py ( [formula in source] ): two-edge HS remainder bounded by [formula in source] on the frozen plateau [formula in source] ; lattice character [formula in source] EXACT four orders [formula in source] ; [formula in source] as Eisenstein series, [formula in source] -expansion match to [formula in source] orders exact (Jacobi identity; the reviewer's C7 sharpening); [formula in source] numeric transform at [formula in source] digits with [formula in source] -weight bookkeeping. Ledger notes on SEAM.EQUIV.MMST.01 and SEAM.SIMPLECURRENT.GENERATOR.01: C7 arithmetic shadow now exact; net-level C7 stays cited/open. (2) v999_ weak_ collision_ hp.py ( [formula in source] ): the continuous-time dilation leg — generator extraction Richardson [formula in source] ; [formula in source] symbolic; [formula in source] exact; GNS splitting defect [formula in source] ; locality [formula in source] ; strong-collision singularity contrast rank [formula in source] . DYN.UNITARY.DILATION.01: the finite ladder is now COMPLETE (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time); open [formula in source] the thermodynamic field limit only; contract stays . (3) v1000_ spin2_ sk_ witnesses.py ( [formula in source] ): lattice graviton — positivity exact, [formula in source] TT helicities at all [formula in source] momenta ( [formula in source] ), [formula in source] exact; SK — KMS/FDT [formula in source] , [formula in source] -dependence contrast [formula in source] vs static [formula in source] , saddle [formula in source] -fold degenerate with [formula in source] unique in the [formula in source] lift . GRAV.SPIN2.EMERGENCE.01 quadratic Hamiltonian half executed; FTRANSFER.SK.RHO0.01 mechanism executed; both contracts stay . (4) v1001_ nu_ pentagon_ chain.py ( [formula in source] ): [formula in source] inventory theorem; misalignment [formula in source] ; pentagon double hit [formula in source] frozen, all three measured angles [formula in source] (honest max pull [formula in source] ) at [formula in source] , unique LEE survivor [formula in source] ; v3 chain SHA-16 a4c28732fa687620 with [formula in source] eV, [formula in source] meV, [formula in source] meV, [formula in source] ; v270– [formula in source] tension [formula in source] TYPED; census null [formula in source] . NEW ledger row FLAV.NUSCALE.06 Candidate \ (pentagon-class misalignment; mechanism [formula in source] the [formula in source] -to-flavor operator ; kills DESI/DUNE [formula in source] vs [formula in source] /JUNO). NO seesaw closure; FLAV.NUSCALE.05 unmoved. (5) Amendments (typed; no marker moves). QFT4D.LATTICE.FUNDAMENTAL.01: a single finite box is not a world — the fundamental object is the quasilocal consistent family [formula in source] with [formula in source] ; continuum ( [formula in source] ) optional, thermodynamic limit and controlled IR universality mandatory (dated 2026-08-29). ANCHOR.VGEO.01/ .02: display retyped from open-physics/primitive phrasing to CLOSED METROLOGY STRUCTURE ( [formula in source] unit torsor; one dimensionful calibration necessary by dimensional analysis — No-Unit v153/ v725); display stays , no physical . ALPHA.QUILLEN.EXACT.01: the correct object is the relative determinant [formula in source] ; BFK [formula in source] is [formula in source] -independent at fixed cut number so [formula in source] — no physical compensation (consistent with COMPENSATION_INTERNAL). NEW master contract TFPT.TOE.COMPLETE.01 : eight gates T1–T8 with the binding separation [formula in source] vs [formula in source] AND independent holdouts; every existing [formula in source] D/dilation/detline/SK/flavor/gravity contract is a child of one gate. Surfaces: tfpt_research_contracts (executed-update paragraphs at MMST/SIMPLECURRENT, DILATION, GRAV.SPIN2, SK.RHO0; new sections TOE.COMPLETE and NUSCALE.06; lattice-fundamental amendment; ALPHA relative-det note); tfpt_4_frontier [formula in source] introduction status card / [formula in source] row; tfpt_2 (NUSCALE.06 candidate paragraph).Research changelog; TFPT — Introduction and reading guide
- Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)Research contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Route B — leptogenesis interface ( ).Frontier and open physical interfaces
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 — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)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
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- =150 2026-08-30 (CXLIV) (review wave 6 — two exploration probes graduate as v1004– v1005 plus two registrations and display corrections: the Milnor–Frobenius–Gray finite algebra, the circularity-flagged relative pencil, the local-ring identification contract, the Weinberg–Witten spin-2 firewall, and honest rest/SM/gravity wording; suite [formula in source] , ledger [formula in source] : two new rows, existing contract rows updated, NO status-marker upgrades; Python-only / Wolfram mirror deferred as for v974–v1003). (1) v1004_ milnor_ frobenius_ gray.py ( [formula in source] ): CLASSICAL (cite, no claim) — Milnor algebra of [formula in source] dimension [formula in source] , spectral numbers [formula in source] [formula in source] exponents [formula in source] . NEW-IN-CORPUS EXACT -finite: rank clock [formula in source] table-sum [formula in source] ; [formula in source] ; self-clock iff [formula in source] ; [formula in source] unique among ordered spherical triples; Galois–Gray [formula in source] (binary Gray order [formula in source] ); CP [formula in source] socle/Frobenius; integral dual-number bridge [formula in source] free rank [formula in source] over [formula in source] , basis-dependent. INTERPRETIVE : [formula in source] . Mutants: [formula in source] [formula in source] ; [formula in source] self-clock survives but exponents fail; wrong socle rank [formula in source] . NEW ledger row SEAM.MILNOR.LOCALRING.01 : required canonical geometric/mechanical identification of the raw seam collar / [formula in source] transition bus with [formula in source] preserving dual-number action, Frobenius pairing, Gray torsor, deck action and CP (rank clock and socle-CP as outputs); kill [formula in source] second inequivalent identification or [formula in source] -equivariance failure; currently \ because Milnor algebra [formula in source] exponents are classical and the corpus map is unproven. (2) v1005_ relative_ pencil_ bridges.py ( [formula in source] ): EXACT -finite Hankel [formula in source] [formula in source] Jacobi spec [formula in source] diag [formula in source] (v106/v119) and winding spec [formula in source] [formula in source] fixed plane (v4). EXACT BUT CIRCULARITY-FLAGGED : unique [formula in source] , [formula in source] , factorisation [formula in source] , CM [formula in source] , dual number mod [formula in source] , index [formula in source] SNF [formula in source] — BUT carrier [formula in source] already sits in the column sums of [formula in source] and [formula in source] : NOT a P2 selector until [formula in source] , [formula in source] , [formula in source] are derived from seam geometry independently; AX.P2.01 typing UNCHANGED. INTERPRETIVE : Klein-four SNF [formula in source] only after [formula in source] (side-blind nulls v521, not a theorem). Mutants: [formula in source] fails; perturbed [formula in source] breaks factorisation; [formula in source] breaks Hankel. (3) registrations (no marker moves). NEW GRAV.WEINBERG.WITTEN.01 : binding firewall BEFORE any spin-2 marker move — the microscopic Hamiltonian family must NOT possess a fundamental Lorentz-covariant local conserved [formula in source] ; Lorentz, diffeomorphism Ward identities and the spin-2 mode must emerge in the SAME IR limit; acceptance [formula in source] positive TT density, two helicities, massless pole, emergent diff Ward, universal soft coupling, named evaded Weinberg–Witten premise; kill [formula in source] microscopic covariant local [formula in source] together with a massless composite spin-2 claim; child of T7, cross-link GRAV.SPIN2.EMERGENCE.01 (not back). (4) display corrections (honest wording, no claim changes). Status-at-a-glance: compiler rest [formula in source] now sits NEXT TO the strict-physical-TOE rest (ten-component [formula in source] / eight TFPT.TOE.COMPLETE.01 gates, one line). SM completeness retyped: the discrete Standard-Model structure (charges, families, flavor operators) is derived under the axioms; [formula in source] D existence, chiral measure, mirror gap, couplings and neutrino dynamics are open. Gravity display: ``parameter-free'' headlines replaced by ``the classical covariant field equation carries no free dimensionless Newton coupling under the named QFT/entanglement premises ''. Surfaces: tfpt_research_contracts (new sections MILNOR.LOCALRING, WEINBERG.WITTEN; SPIN2 firewall note; T7 child; v358/v359 keybox titles); tfpt_4_frontier wave-6 paragraph; introduction status card [formula in source] SM/gravity lines; tfpt_2 gravity heading [formula in source] conclusion; website StatusMatrix / WhatTfptClaims / ClaimStack / GravityEmergence / OpenGates / VerificationDag.Research changelog; TFPT — Introduction and reading guide
- Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)tfpt research contracts
- Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)Research contracts
Registered verification modules
- v1001_nu_pentagon_chain.pyRegistered verification module · frontier
Read the description recorded in the module registry
FLAV.NUSCALE.06 Kandidat [C]/[N] (Review-Welle 4, 2026-08-29; KEIN Schluss; Mechanismus = Q_+-zu-Flavor-Operator [O]): U_e=I Inventar + analytische 13/23-Fehlausrichtung; Pentagon-Doppel-Hit phi=288 deg=4(2pi/5), theta=2pi/35 eindeutiger LEE-Ueberlebender 2.7 %, max Pull 0.557; v3-Kette SHA-16 a4c28732fa687620: Sigma=0.0599 eV, m_beta=9.0 meV, m_bb in [1.5, 3.8] meV, delta_CP=287.66 deg; v270-theta23-Spannung 1.85 sigma GETYPT; Zensus 0/1607. Kills: DESI-Floor, DUNE delta_CP 287.7 vs 240, JUNO. FLAV.NUSCALE.05 unbewegt. Python-only / Wolfram-Spiegel zurueckgestellt.
- v1003_nu_structural_nulls.pyRegistered verification module · frontier
Read the description recorded in the module registry
FLAV.NU.TEXTURE.MECHANISM.01 [O] (Review-Welle 5, 2026-08-29; bindende Constraints, keine Texture): [E] geladener Sektor h=(1,1,1), d=(64,60,64); [X] Schur-Texture-NULL 8/8 (K,B) scheitern, D4-Spiegelung erzwingt lambda_1=lambda_3; gefordertes K ~ [3536.998, 1768.499, 1/3] trifft keinen von 9 Komparatoren; [E] Orientierungs-Verdopplung hebt Entartung generisch; [X] Skalen-NULL 12/12, 1-|c/a|=1.885e-4 von keiner gefrorenen Konstante. Mechanismus muss D4-ungerade sein UND ~2e-4-Cancellation liefern; reine Seam-Daten ausgeschlossen. Python-only / Wolfram-Spiegel zurueckgestellt.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.