=150 2026-07-23 (II) ( v524 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.BETA2.OS.01: ``the OS quotient of the free system made explicit'' — verdict SUCCESS per the frozen preregistration, -typed per contract precision (iii); the celestial/twistor story in tfpt_3 gains Step 25 — (1) [formula in source] EXPLICIT : [formula in source] ( [formula in source] ): the [formula in source] bond-cut OS Gram exactly Hermitian, parity-block-diagonal, inertia [formula in source] PD (min eigenvalue [formula in source] at [formula in source] digits), null space [formula in source] , [formula in source] ; [formula in source] (complete half algebra): [formula in source] PD (min [formula in source] ), [formula in source] — compact euclidean time reconstructs a THERMAL (KMS) representation; exact certificate [formula in source] ; (2) the TRANSFER SEMIGROUP (Klein–Landau) : [formula in source] exactly Hermitian on all domains ( [formula in source] , dims [formula in source] ), chain identities exact, vacuum fixed; the positivity pattern [formula in source] the site/bond dichotomy: even [formula in source] PSD via the exact square identity [formula in source] ( [formula in source] ), odd [formula in source] indefinite ( [formula in source] ) — the one-step transfer is NOT positive (the chirality datum, kill-3 shadow sharpened), its even powers are; (3) THE CLOCK [formula in source] : [formula in source] : [formula in source] PD [formula in source] (min [formula in source] ), compressed spectrum [formula in source] , vacuum eigenvalue exactly [formula in source] , spectral projections [formula in source] ; [formula in source] : spectrum EXACTLY [formula in source] in both parity sectors — the silver axes of the v519 torsor return as the clock eigenvalue; the reconstructed rotation group [formula in source] unitary with the group law; (4) the v522 RESOLUTION : the census [formula in source] reproduced; EVERY anti-matching entry is a wrap overlap, every overlap-free entry matches — the pre-quotient non-Hermiticity is EXACTLY the domain/wrap artifact; on the quotient the clock has spectral calculus; pre-registered KMS deviation: no contraction on the compact circle ( [formula in source] exactly, [formula in source] ); (5) GSO/ [formula in source] : the grading survives; the perpendicular torsor mirror descends anti-unitarily ( [formula in source] ), [formula in source] on every sector (Kramers-free), [formula in source] exactly; (6) CONTROLS : site cut [formula in source] — the kill branch fires there; family A [formula in source] ; anti-chiral [formula in source] no quotient; wrong direction non-Hermitian (all mismatches wrap-overlap); KILL TESTS: (1)/(2) strengthened, (3) shadow sharpened, none fires, all seven stay live on [formula in source] ; TRANSPARENCY: run 1 [formula in source] (a sympy simplify failure on a TRUE [formula in source] product formula, fixed by a Laurent-polynomial certificate; no criterion changed); NO marker moves — WOIT.OS.TWISTOR.01 stays Open, [formula in source] is next)
Research changelog · TFPT — Introduction and reading guide
Suite. New module v524_woit_beta2_os_quotient.py ( [formula in source] checks, [formula in source] s; exact sympy [formula in source] Pfaffian-Wick [formula in source] [formula in source] -digit inertia certificates); registered in run_all.py [formula in source] script_registry.csv. Ledger. New row WOIT.BETA2.OS.01 (SUCCESS, -typed per precision (iii)); WOIT.OS.TWISTOR.01 claim/canonical status extended ( [formula in
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
documents/changelog/sections/003-source.tex · lines 294 to 314
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
- explicit script identifier v522_woit_beta1_gso_gauge.py
literal short identifier uniquely resolves in local script registry
- cross reference join tfpt_readouts_extension.wl
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
- explicit script identifier v519_woit_theta_rp_free.py
literal short identifier uniquely resolves in local script registry
- cross reference join tfpt_readouts_extension.wl
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
- explicit script identifier v524_woit_beta2_os_quotient.py
literal short identifier uniquely resolves in local script registry
- cross reference join tfpt_readouts_extension.wl
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
- explicit file citation run_all.py
literal source filename/path in TeX
- explicit file citation script_registry.csv
literal source filename/path in TeX
- explicit claim identifier status_ledger.csv
exact local ledger claim identifier
- explicit claim identifier status_ledger.csv
exact local ledger claim identifier
- explicit file citation v524_woit_beta2_os_quotient.py
literal source filename/path in TeX