=150 2026-07-22 (IX) ( v519 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.THETA.FREE.01: ``the real structure exists — and free reflection positivity picks the same family''; the celestial/twistor story in tfpt_3 is now TWENTY steps — (1) THETA CLASSIFICATION COMPLETE : exactly TWO families of anti-linear structures on [formula in source] normalise the clock [formula in source] — family D ( [formula in source] , [formula in source] ): [formula in source] EXACTLY at matrix level, [formula in source] ( [formula in source] IMPOSSIBLE: [formula in source] — Kramers-free), inverts the deck, fixed set [formula in source] the great circle through the deck poles; family A ( [formula in source] ): centralises the clock projectively (NEVER inverts it), [formula in source] per [formula in source] , fixed set [formula in source] resp.\ empty; ROLE SEPARATION: family A DEFINES the euclidean section (Woit's [formula in source] side: [formula in source] , no real points — replicated exactly on [formula in source] ), family D REFLECTS it (the OS conjugation, [formula in source] conjugation with real points [formula in source] ); (2) MARK PINNING : [formula in source] preserves the [formula in source] marks iff [formula in source] — a [formula in source] -element [formula in source] -TORSOR ( [formula in source] mark axes, [formula in source] silver-midpoint axes), clock conjugation [formula in source] [formula in source] [formula in source] clock orbits; (3) SPIN/FOCK : the [formula in source] plane has no phase leaks ( [formula in source] ); exact [formula in source] : [formula in source] with [formula in source] (normalised [formula in source] ), inverts the clock tower ( [formula in source] ) and normalises the deck; the KRAMERS DICHOTOMY: the deck-induced candidate [formula in source] has [formula in source] — the v510 split/nonsplit dichotomy IS the [formula in source] vs [formula in source] dichotomy; the deck does NOT furnish [formula in source] , the seam-circle REFLECTION does; (4) KILL TEST 1 (free level) : does NOT fire — [formula in source] exists with [formula in source] AND [formula in source] and satisfies all three side conditions simultaneously (marks, deck normalisation, spin/Fock); (5) FREE RP : the NS vacuum [formula in source] has [formula in source] exactly; preconditions exact ( [formula in source] , [formula in source] , [formula in source] ; the deck FAILS anti-invariance); BOND CUT: one-particle Gram [formula in source] PD (min eigenvalue [formula in source] , [formula in source] digits), even [formula in source] sector [formula in source] PD, [formula in source] complete half-sided algebra PD (even [formula in source] odd each [formula in source] ) — RP with NO degree truncation; twist [formula in source] FORCED ( [formula in source] non-Hermitian); CONTROLS: the site cut fails exactly ( [formula in source] , inertia [formula in source] ; continuum control: Cauchy–Stieltjes strictly positive — a lattice-PLACEMENT artifact, RP selects the site placement relative to the marks); the clock-CENTRALISING family-A structure fails RP structurally ( [formula in source] ) — RP and [formula in source] select the SAME family; bonus: the anti-chiral state flips the odd sector to [formula in source] ND (the free shadow of kill test 3); / \ NOT shown: the interacting algebra [formula in source] (kill test 1 stays live there), gauge-fixed RP (kill test 2), OS reconstruction, chirality without mirrors (kill tests 3/6), [formula in source] incidence (kill test 7) — the WOIT- [formula in source] / [formula in source] roadmap named ( [formula in source] [formula in source] on the gauge-invariant subalgebra [formula in source] gauge-fixed RP on the equivariant SDYM [formula in source] sector; [formula in source] the OS quotient of the free system explicit; [formula in source] the [formula in source] duality vs [formula in source] typed; [formula in source] the chirality theorem [formula in source] the mark incidence); TWO CONTRACT PRECISIONS (prose, no marker): (i) `` [formula in source] induced by the seam reflection'' means the seam-circle REFLECTION, not the deck — the deck furnishes the [formula in source] Kramers class (the v510 bridge); (ii) the marks sit RP-side on the BOND MIDPOINTS of the [formula in source] -Majorana circle; Wolfram extension [formula in source] (verified engine run); NO marker moves — WOIT.OS.TWISTOR.01 stays Open: kill test 1 is discharged on the FREE level only and stays formally live on the interacting algebra)
Research changelog · TFPT — Introduction and reading guide
v519_woit_theta_rp_free.py ( WOIT.THETA.FREE.01, 34 checks, [formula in source] 20 s; exact sympy [formula in source] exact [formula in source] Fractions; RP definiteness via [formula in source] -digit spectra of exact Hermitian matrices, tolerance [formula in source] ; deterministic). Part W: W-S1 the two-family classification (symbolic solve); W-S2 family D (relations, Kramers-free, mark pinning, seam action, torso
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
documents/changelog/sections/004-source.tex · lines 75 to 123
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
- explicit file citation run_all.py
literal source filename/path in TeX
- cross reference join tfpt_readouts_extension.wl
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
- explicit claim identifier status_ledger.csv
exact local ledger claim identifier
- explicit file citation next.txt
literal source filename/path in TeX
- explicit file citation tfpt_readouts_extension.wl
literal source filename/path in TeX
- explicit claim identifier status_ledger.csv
exact local ledger claim identifier
- explicit script identifier v519_woit_theta_rp_free.py
literal short identifier uniquely resolves in local script registry
- explicit file citation woit_os_theta_realstructure_probe.py
literal source filename/path in TeX
- explicit file citation woit_os_theta_rp_freelevel_probe.py
literal source filename/path in TeX
- explicit file citation v519_woit_theta_rp_free.py
literal source filename/path in TeX
- explicit claim identifier status_ledger.csv
exact local ledger claim identifier
- explicit file citation script_registry.csv
literal source filename/path in TeX
- explicit script identifier v510_seam_bit_freedom.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