A registered result in its source context
Original ledger classification: Proven finite no-go/boundary [E]; massless spin-2 emergence, Ward identities and universal coupling remain Open [O].
Recorded statement: GAPPED-PARENT SPIN-2 BOUNDARY (registered 2026-09-05, v1024; no parent marker move). A uniform strictly positive full-parent gap excludes a massless spin-2 pole. The exact transverse-traceless projector has direction-dependent k->0 limits…
Statement, assumptions and sources
Paper context: Research contracts
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
GRAV.PARENT.GAP.NO_GO.01
Original ledger classification: Proven finite no-go/boundary [E]; massless spin-2 emergence, Ward identities and universal coupling remain Open [O].
Original claim text
GAPPED-PARENT SPIN-2 BOUNDARY (registered 2026-09-05, v1024; no parent marker move). A uniform strictly positive full-parent gap excludes a massless spin-2 pole. The exact transverse-traceless projector has direction-dependent k->0 limits and therefore cannot be a strictly finite-range microscopic projector. A viable T7 route must use a critical physical sequence together with local tensor gauge constraints; the finite five-component symmetric-traceless target is only representation typing and is not a derived stress operator.
Original classification detail
Uniform full gap and direct finite-range TT projection are excluded as T7 mechanisms. Critical gauge-constrained escape remains open; no spin-2 closure.
Dependencies as recorded
GRAV.SPIN2.EMERGENCE.01; GRAV.WEINBERG.WITTEN.01; TFPT.TOE.COMPLETE.01
Open the original ledger source, row 778Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- 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 — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)tfpt research contracts
- Research Contract — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)Research contracts
- Research Contract — GRAV.SPIN2.EMERGENCE.01 (massless transversal spin-2 from the same spectral determinant)tfpt research contracts
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 — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )Research contracts
- Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)tfpt research contracts
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)tfpt research contracts
- Research Contract — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )tfpt research contracts
- =150 2026-09-05 (CLVII) (non-RH T1–T8 Round 3 graduates as v1022– v1025; suite [formula in source] , ledger rows [formula in source] through six narrow subcontracts; [formula in source] module checks; NO marker move; TFPT.TOE.COMPLETE.01 and every T1–T8 gate remain ). v1022_ telb_ round3_ certificates.py ( [formula in source] ; native python-flint==0.9.0, 256-bit Arb/Acb) replaces the float/Richardson TEL-B input by 5812 rational cells and the exact cut jump, proving [formula in source] and [formula in source] . Together with the stated analytic digamma/midpoint lemmas, its executable Arb arithmetic gives [formula in source] , [formula in source] and [formula in source] ; full C2b remains open exactly at CF [formula in source] and DG [formula in source] . Its exact one-mode [formula in source] countermodel refutes the former ALG2 Vandermonde-to-generated-algebra implication: FE-GEN or an exact gauge/code-projected microscopic-algebra theorem is still required, and ALG1 remains conditional on the generated projection. v1025_ telb_ c1_ c2a_ certificates.py ( [formula in source] ; native 100-bit Arb/Acb) executes the existing analytic C1/C2a proofs: [formula in source] and [formula in source] for every even [formula in source] . v1023_ derivative_ filtered_ wall.py ( [formula in source] ) proves only the finite quasi-free singular-value block: the high continuation branch is separated, but the bare [formula in source] subspace is not invariant, the low branch has [formula in source] rather than a Weyl cone, and no DET16/DET32, interacting-parent, measure/anomaly/index or [formula in source] D theorem follows. v1024_ parent_ internal_ boundaries.py ( [formula in source] ) supplies finite parent-internal T6–T8 witnesses and no-gos: a positive seam/neutrino-pair intertwiner with projective full-Fock [formula in source] lift but no mass texture; the uniform-gap and direct-TT locality obstructions but no graviton; and a gapped internal [formula in source] cap that is chosen, [formula in source] -breaking and complement-trivial, hence no global [formula in source] . T1 retains only finite axiom-core/W-bridge support while unconditional provenance and the dimension selector remain open; T3 remains at Hamiltonian-class level; T5 retains finite IR witnesses and the v1020 spectator obstruction while prime completion, OS reconstruction, confinement and scattering remain open. The common missing object is still one shared [formula in source] D parent satisfying T3–T8. Native-only handling is explicit in the website reproducer; v1022/v1025 are not represented as Pyodide certificates. NO RH CLAIM. Surfaces: tfpt_research_contracts, tfpt_4_frontier, introduction, tfpt_2_standard_model, the MMST article/PDF, ledger, generated verification maps/index, website paper/DAG/gap/FAQ mirrors and changelog.Research changelog; TFPT — Introduction and reading guide
- Neutrinostfpt 2 standard model
- Source contract and nomenclature.tfpt research contracts; tfpt research contracts; Research contracts
- NeutrinosStandard Model and flavor structure
All 14 linked sections
- Front matter / support
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)
- Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)
- Research Contract — FTRANSFER.SK.RHO0.01 (Schwinger–Keldysh completion: cosmological transfers need [formula in source] )
- Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)
Registered verification modules
- v1024_parent_internal_boundaries.pyRegistered verification module · frontier
Read the description recorded in the module registry
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.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.