=150 2026-07-22 (XII) ( v522 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.BETA1.GSO.01: ``the clock is time-like, GSO is the gauge datum'' — a TYPED result (verdict UNDECIDED per the frozen preregistration, the mechanism identified exactly, gauge-fixed RP established under the corrected typing; the celestial/twistor story in tfpt_3 gains Step 23) — (1) the HERMITICITY WITNESS : the [formula in source] clock average violates Hermiticity EXACTLY (the one-step insertion [formula in source] has entry [formula in source] where the conjugate transpose demands [formula in source] ; entrywise census [formula in source] Hermitian-matching, [formula in source] ANTI-matching, [formula in source] violations — the pairing is complex-SYMMETRIC, strictly weaker than Hermitian: ``positivity after gauge fixing'' is not well-posed for the clock reading); (2) TIME-LIKE TYPING : ALL [formula in source] dihedral reflection axes of the NS seam circle invert the clock lift ( [formula in source] ), NONE commutes — the [formula in source] clock IS Woit's euclidean rotation; the gaugeable ( [formula in source] -compatible) part of the [formula in source] Fock tower is EXACTLY its [formula in source] -torsion [formula in source] [formula in source] the GSO/fermion-parity [formula in source] (Hermiticity census over all powers; [formula in source] the full wrap [formula in source] the [formula in source] rotation of the seam [formula in source] fermion parity); (3) the POSITIVE PART : GSO-fixed RP holds EXACTLY — [formula in source] even [formula in source] parity-projected bond-cut Gram [formula in source] PD (min eigenvalue [formula in source] at [formula in source] digits), [formula in source] complete half algebra: all odd rows/columns killed exactly, even block [formula in source] PD ( [formula in source] ), no degree truncation; the site-cut defect SURVIVES gauge fixing ( [formula in source] — the bond placement is gauge-invariant information); family A keeps failing ( [formula in source] indefinite vs family D's [formula in source] ); Kramers: [formula in source] on [formula in source] , [formula in source] restricts with [formula in source] ; Ramond control: the wrap [formula in source] ``true [formula in source] '' lift fails state invariance — the NS/ [formula in source] tower is forced; (4) KILL-TEST BOOKKEEPING: kill test (2)'s free shadow does NOT fire (no legitimate Hermitian gauge-fixed form has a negative direction), kill test (1) stays discharged also gauge-invariantly; both stay formally live on [formula in source] ; (5) TRANSPARENCY: the first frozen run scored [formula in source] (the clock-reading checks failed exactly as the mechanism predicts) and the preregistered deg-2 invariant dimension [formula in source] was a combinatorial error (correct census [formula in source] ) — documented in full, the verdict by the frozen [C-3] logic (Hermiticity failure [formula in source] UNDECIDED); CONTRACT PRECISION (iii) (prose, no marker): ``gauge-invariant subalgebra'' at the free level means the GSO/fermion-parity [formula in source] — the only [formula in source] -compatible part of the [formula in source] tower; the clock is the euclidean rotation itself (timelike), its equivariant statement moves to [formula in source] (OS quotient first, then the clock as reconstructed transfer operator); Wolfram extension (with v520/v521) [formula in source] (verified engine run); NO marker moves — WOIT.OS.TWISTOR.01 stays Open, [formula in source] proper re-routed via [formula in source] )
Research changelog · TFPT — Introduction and reading guide
v522_woit_beta1_gso_gauge.py ( WOIT.BETA1.GSO.01, 16 checks, [formula in source] 5 s; exact sympy Pfaffian–Wick [formula in source] exact [formula in source] Fractions; definiteness via [formula in source] -digit spectra, tolerance [formula in source] ; deterministic). G1 the gauge datum (Z8/NS tower, Ramond control, invariant dimensions [formula in source] ); G2 [formula in source] normalises the tower and restricts
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