2026-07-22 (I) ( v512 — the flag-transitivity equivalence web promoted as SEAM.TAU.FLAG.01: the [formula in source] attack executed on the free RP seam circle — BARE MARK-TRANSITIVITY IS FALSIFIED as a selector (on the test family [formula in source] , [formula in source] , the symmetry group is the pair-exchanging [formula in source] for EVERY [formula in source] , simply transitive on the four marks; complete census: deck-commuting M\"obius maps are diagonal/antidiagonal; hardening: ALL undirected per-mark data are identical for every [formula in source] — no local jet sees the bit), and THE SHARP SELECTOR is FLAG transitivity (marks AND their two sides indistinguishable) [formula in source] the clock — stabiliser jump [formula in source] , flag/arc orbits [formula in source] , order- [formula in source] rotation ( [formula in source] solveset [formula in source] ), mark mirror [formula in source] ; welded into a [formula in source] -FOLD EQUIVALENCE WEB (every link exact): clock rotation, [formula in source] , mark mirror, flag transitivity, three spectral degeneracies (odd-doublet split [formula in source] , zero only at [formula in source] — counterwitness exactly [formula in source] ; arc-Laplacian degeneracy [formula in source] ; the v215-K3 indicator in CLOSED FORM [formula in source] — the v503 lattice curve analytically), [formula in source] -twist existence ( [formula in source] ; Atiyah–Bott rationality [formula in source] -BLIND — [formula in source] for all [formula in source] , [formula in source] rational non-CM: rationality selects NOTHING), cusp- [formula in source] -cycle implementability (H4 rigidity: [formula in source] with orders [formula in source] cannot induce it; centraliser scalar, [formula in source] nonscalar [formula in source] no projective involution — projective order exactly [formula in source] , [formula in source] -shadow consistent v510), harmonic, [formula in source] ; NEGATIVE CONTROLS: hexagonal (not concyclic, fails preconditions), silver (harmonic but topologically dead), [formula in source] marks (impossible on the free circle: [formula in source] vs [formula in source] invariant subsets; bare [formula in source] transitivity already forces equal spacing — `` [formula in source] counts''); \ THE REST: the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit ( [formula in source] : side-indistinguishability of the four equally-decorated marks), v216 local equality does NOT deliver it, its negation is now concretely measurable; scoreboard: the counterwitness passes all [formula in source] established unsided tests, fails all [formula in source] clock-equivalent ones; Wolfram extension [formula in source] (verified engine run); NO marker moves — the bit stays , QGEO.REALIZE.01 and P2.TYPING.01/ AX.P2.01 text-precised only, SEAM.BIT.FREEDOM.01 cross-referenced)
Research changelog · TFPT — Introduction and reading guide
v512_seam_tau_flag.py ( SEAM.TAU.FLAG.01, 29 checks, [formula in source] 6 s; sympy-exact [formula in source] mpmath 30 digits [formula in source] one numpy lattice commutator; deterministic). S0 family frame (counterwitness inside the family: [formula in source] , [formula in source] , cross-ratio [formula in source] ); H1 complete symmetry census (census basis, rotation solvesets, stabiliser jump, flag/arc orbits,
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
documents/changelog/sections/005-source.tex · lines 69 to 104
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