A registered result in its source context
Original ledger classification: Proven subclaims [E]: C1 native interval certificate plus analytic axis bound; C2a analytic all-even-N theorem plus outward constant certificate. Parent contracts remain Open [O].
Recorded statement: TEL-B C1/C2a SUBCLAIM CONTRACT (registered 2026-09-05, v1025; no parent marker move). C1: a native 100-bit Arb/Acb certificate integrates 3888 analytic rectangles, adds a closed axis-strip majorant and the exact imaginary term 1/12,…
Statement, assumptions and sources
Paper context: Research contracts
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Read the exact registered claim and its dependencies
SEAM.MMST.TELB.C1C2A.01
Original ledger classification: Proven subclaims [E]: C1 native interval certificate plus analytic axis bound; C2a analytic all-even-N theorem plus outward constant certificate. Parent contracts remain Open [O].
Original claim text
TEL-B C1/C2a SUBCLAIM CONTRACT (registered 2026-09-05, v1025; no parent marker move). C1: a native 100-bit Arb/Acb certificate integrates 3888 analytic rectangles, adds a closed axis-strip majorant and the exact imaginary term 1/12, obtaining C_star <= 0.1520453048... < 0.1525. C2a: exact cotangent reindexing, the Peano kernel and shifted Euler summation prove N sup_k |phi_N(k)| < 0.509 for every even N>=16; v1025 outward-checks the final constants. These are subclaims of TEL-B only. C2b CF/DG, ALG-EXH, the charged/type-III scaling limit and TOE T2 remain open. Native python-flint==0.9.0; not Pyodide. NO RH CLAIM. ROUND-4 SUPERSESSION: v1026 closes the former CF/DG residual and relaxed norm; v1025 C1/C2a inputs remain valid. ALG-EXH and MMST remain OPEN.
Original classification detail
[E] subclaims only: C_star<0.1525 and sup|phi_N|<0.509/N for every even N>=16. C2b, ALG-EXH, MMST and TOE remain [O]. | ROUND-4 SUPERSESSION: v1026 closes the former CF/DG residual and relaxed norm; v1025 C1/C2a inputs remain valid. ALG-EXH and MMST remain OPEN.
Dependencies as recorded
SEAM.MMST.TYPEIII.CHARGED.01; TFPT.TOE.COMPLETE.01
Open the original ledger source, row 774Location recorded in the ledger
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- Frontier and open physical interfaces
- Research contracts
Sections that explicitly cite this claim
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- TEL-B reduction (2026-09-04)Research contracts
- TEL-B reduction (2026-09-04)tfpt research contracts
- TEL-B reduction (2026-09-04)tfpt research contracts
Navigation through a shared verification script
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- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)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
- Per-lemma statusmmst charged scaling limit en
- T2: uniform relaxed TEL-B theorem.tfpt research contracts
- T2: uniform relaxed TEL-B theorem.tfpt research contracts; Research contracts
- 2026-09-05 (CLVIII): non-RH round 4 — uniform TEL-B norm and explicit T1–T8 boundariesResearch changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)Research contracts
Registered verification modules
- v1025_telb_c1_c2a_certificates.pyRegistered verification module · frontier
Read the description recorded in the module registry
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.
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