Follow a result back to its evidence.

SEAM.TAU.FLAG.01: the flag-transitivity equivalence web -- the tau = i attack executed on the free RP seam circle: which ESTABLISHED seam datum excludes the free-but-non-harmonic configurations? (Test family M(delta) = {+-1, +-e^(i delta)}, delta in (0, pi/2]; NO marker moves -- the bit stays [C], QGEO.REALIZE.01 and P2.TYPING.01/AX.P2.01 text-precised only.) Exact sympy + mpmath 30 digits. [E] FALSIFICATION OF BARE TRANSITIVITY: on the free RP circle V4 = {z, -z, b/z, -b/z} acts SIMPLY TRANSITIVELY on the four marks for EVERY delta (pair-exchanging inversions; complete census: deck-commuting Moebius maps = diagonal/antidiagonal) -- the expectation 'transitivity <= v216 local equality selects tau = i' is refuted; hardening: ALL undirected per-mark data (arc-pair multiset, distance multiset, cone germ) are identical for every delta -- no local jet sees the bit. [E] THE SHARP SELECTOR: FLAG transitivity (marks AND sides) <=> delta = pi/2 <=> tau = i <=> the clock -- stabiliser jump 1 -> 2, flag/arc orbits 2 -> 1, order-4 rotation (b^2 = -1 solveset {pi/2}), mark mirror z -> 1/z <=> cos delta = 0. [E] 12-FOLD EQUIVALENCE WEB (each link exact): clock rotation, D4, mark mirror, flag transitivity, three spectral degeneracies (odd-doublet split = (2/pi) ln cot(delta/2), zero only at pi/2 -- counterwitness exactly (2/pi) ln 2; arc-Laplacian degeneracy 4/pi; the v215-K3 indicator in closed form (2 sqrt 2/pi)|ln tan(delta/2)| -- the v503 lattice curve analytically), rho-twist existence ((m^2 - n^2)(t - 1/t) = 0 <=> t = 1; Atiyah-Bott rationality is delta-BLIND -- Tr(sigma e^(t Delta)) = 1 for all delta, j_cw = 148176/25 rational non-CM: rationality does NOT select), 4-cycle implementability (H4 rigidity: V4 with orders {1,2,2,2} cannot induce the cusp 4-cycle; centraliser scalar, U^2 nonscalar => no projective involution -- projective order exactly 4, Z8-shadow consistent v510), harmonic, j = 1728. [E] NEGATIVE CONTROLS: hexagonal (not concyclic, fails the preconditions); silver (harmonic but topologically dead -- position/modulus halves independent, consistent v510); 3 marks (impossible on the free circle: 0 invariant 3-subsets vs 28 invariant 4-subsets; bare n = 3 transitivity already forces equal spacing -- '4 counts': the deck-pairing makes bare transitivity free of charge). [C] THE REST (verbatim): the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit (V4 -> D4: side-indistinguishability of the four equally-decorated marks); v216 local equality does NOT deliver it (no local jet can see the side bit); its negation is now concretely measurable (odd-split (2/pi) ln cot(delta/2) != 0). Scoreboard: the counterwitness passes all 7 established unsided tests, fails all 9 clock-equivalent ones. Exact (sympy + mpmath).

Linked claims

SEAM.TAU.FLAG.01

Paper sections

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