Follow a result back to its evidence.

WOIT.BETA2.OS.01: the WOIT-beta2 milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed -- 'the OS quotient of the free system made explicit' (verdict SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii); 20 checks, ~5 s). [E] H_phys EXPLICIT: N = 16 (deg <= 2): the 37x37 bond-cut OS Gram is exactly Hermitian, parity-block-diagonal, inertia (37, 0, 0) PD (min eigenvalue 1.7801e-6 at 40 digits), null space {0}, dim 37 = 29 (+) 8; N = 8 (complete half algebra): (16, 0, 0) PD (min 3.3471e-3), dim 16 = 8 (+) 8 = 4^2 -- compact euclidean time reconstructs a THERMAL (KMS) representation; exact certificate sin^2(3pi/8) - sin(pi/8) sin(5pi/8) = 1/2. [E] TRANSFER SEMIGROUP (Klein-Landau): tau_k exactly Hermitian on all domains (k = 1..7, dims 29, 22, 16, 11, 7, 4, 2), chain identities exact, vacuum fixed; the positivity pattern IS the site/bond dichotomy: even k PSD via the exact square identity T(2j) = A_j*A_j ((22,0,0)/(11,0,0)/(4,0,0)), odd k indefinite ((10,12,7)/(5,6,5)/(2,2,3)) -- the one-step transfer is NOT positive (the free chirality datum, kill-test-3 shadow sharpened), its even powers ARE. [E] THE CLOCK = T^{N/4}: N = 16: tau_4 PD (11, 0, 0) (min 6.6821e-5), compressed spectrum [0.0194517, 1.64144], vacuum eigenvalue exactly 1; N = 8: spectrum EXACTLY {1, sqrt(2) - 1} = {1, 1/delta_Silver} in both parity sectors -- the silver axes of the v519 mu4 torsor return as the clock-transfer eigenvalue; spectral projections ~1e-40; the reconstructed rotation group U(s) = exp(isH) is unitary with the group law. [E] v522 RESOLUTION: the census (745, 96, 0) 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 (edge modes C(1)/C(3) = 1 + sqrt(2) = delta_S exactly, det(G - tau_4) < 0). [E] GSO/THETA: the grading survives; the perpendicular torsor mirror descends anti-unitarily (eta_perp in {+-i}), Theta_phys^2 = +1 on every sector (Kramers-free), theta_cut o theta_perp = alpha_{N/2} exactly. [E] CONTROLS: site cut indefinite ((3,3,1)/(2,2,4)) -- the contract kill branch fires there; family A (4,4,0); anti-chiral (8,8,0) no quotient; wrong direction non-Hermitian (mismatches all wrap-overlap). KILL-TEST BOOKKEEPING: (1), (2) strengthened, (3) shadow sharpened, none fires; (4)-(7) untouched; all seven stay live on A_hol. [C] FENCE: 'the clock acting unitarily' is operationalised per contract precision (iii) as the reconstructed transfer/rotation structure. TRANSPARENCY: run 1 scored 18/20 (a sympy simplify failure on a TRUE pi/16 product formula, fixed by a Laurent-polynomial certificate; no criterion changed). [O] beta3 is the next milestone; WOIT.OS.TWISTOR.01 stays [O]. Discovery provenance: experiments/tfpt-discovery/woit_os_beta2_os_quotient_probe.py (20/20, 2026-07-23). NO marker moves.

Linked claims

WOIT.BETA2.OS.01

Paper sections

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