A registered result in its source context
Original ledger classification: Mixed: TV interval-certified [E]; C2b scalar reduction is analytic proof plus Arb arithmetic [E]; old ALG2 implication refuted [X]; CF/DG, ALG-EXH, MMST and TOE remain Open [O].
Recorded statement: TEL-B ROUND-3 MIXED CERTIFICATE (registered 2026-09-05, v1022; no parent marker move). Native 256-bit Arb/Acb over 5812 rational cells gives TV_p(F'') <= 15.817 695 962 988 924... < 15.928 674 and K3_TV < 2.517 464 500 835. The analytic C2b scalar…
Statement, assumptions and sources
Paper context: Research contracts
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SEAM.MMST.TELB.ROUND3.01
Original ledger classification: Mixed: TV interval-certified [E]; C2b scalar reduction is analytic proof plus Arb arithmetic [E]; old ALG2 implication refuted [X]; CF/DG, ALG-EXH, MMST and TOE remain Open [O].
Original claim text
TEL-B ROUND-3 MIXED CERTIFICATE (registered 2026-09-05, v1022; no parent marker move). Native 256-bit Arb/Acb over 5812 rational cells gives TV_p(F'') <= 15.817695962988924... < 15.928674 and K3_TV < 2.517464500835. The analytic C2b scalar reduction, with executable Arb arithmetic in v1022, gives c_epsilon=0.288547359238..., c_zeta=0.110677064901..., sum=0.399224424139...<0.400. Full C2b remains open exactly at CF<=0.139/sqrt(N) and DG<=0.060/sqrt(N). The exact one-mode M2 countermodel refutes the prior ALG2 Vandermonde-to-generated-subalgebra implication; FE-GEN or a precise gauge/code projection is required, and ALG1 positivity is conditional on the same generated-sector completeness. Native python-flint==0.9.0; not Pyodide. NO RH CLAIM. ROUND-4 SUPERSESSION: v1026 closes CF/DG and the relaxed all-even-N>=16 norm below2.995906<3; the old full-C2b-open wording is historical. TV and potential inputs remain valid. v1030 gives only a conditional sector/frame interface; microscopic ALG-EXH/MMST remain OPEN.
Original classification detail
TV residual closed; C1/C2a closed by v1025; C2b reduced to CF and DG; ALG2 inference killed and replacement premise named. No parent marker move. | ROUND-4 SUPERSESSION: v1026 closes CF/DG and the relaxed all-even-N>=16 norm below2.995906<3; the old full-C2b-open wording is historical. TV and potential inputs remain valid. v1030 gives only a conditional sector/frame interface; microscopic ALG-EXH/MMST remain OPEN.
Dependencies as recorded
SEAM.MMST.TELB.C1C2A.01; SEAM.MMST.TYPEIII.CHARGED.01; TFPT.TOE.COMPLETE.01
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- Frontier and open physical interfaces
- Research contracts
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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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- Validated Fourier core and the missing finite-grid aliases.tfpt research contracts; Research contracts
- 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
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Registered verification modules
- 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.
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