A registered result in its source context

SEAM.STATE.DERIVATION.01

Original ledger classification: Measured carving [Numerical/Identity]: RP and mixing mutually exclusive; u >= t forced; the modular locus is one point; no marker move

Original claim text

THE RP/MODULAR CARVING OF THE SEAM STATE SPACE (measured 2026-08-10, round CXXIV; promoted in v903): on the v898 family the reflections and the modular route CARVE for the first time. (1) THE REFLECTION CENSUS: two spatial thetas are deployable on the 16-dim one-particle space (the sheet swap theta_S = the 16-dim lift of the v440 collar reflection, and the orientation-REVERSED 2-cycle theta_abT); the untwisted 2-cycle is NOT an OS reflection (Gram non-hermitian 0.924 already at t = 0); the v519 twist eta = +i is again FORCED. (2) THE INCOMPATIBILITY: the odd-sector Gram eigenvalues are EXACTLY +-|a_J| of the {4,5} duad (worst identity 2.2e-16) -- OS positivity <=> a_J = 0 <=> the v898 gate G3 (all 15 blocks at the floor) FALLS: reflection positivity and the block-functor mixing floor are MUTUALLY EXCLUSIVE on this family; strict RP forces t = 0 under BOTH reflections (t = 0 marginal PSD); u >= t is FORCED with u_c = t exact in the deployed region (SPEC-v2 amendment disclosed fail-first: the corner (t=1/4, beta=4) gives u_c = 0.3627 > t, law re-typed u_c >= t) -- u = 0 is RP-EXCLUDED, correcting the round-57 'u unforced' reading. (3) THE STRUCTURE OBJECT: det(A16_dep + t A_int) = (t-1)^2 (3t^2-1)^2 (9t^3+21t^2-t-1)^2 EXACT (sympy); the three positive roots organize everything measured (1p RP boundary = t/u = 1; hermitized boundary t_c(beta) -> t_gap; the ground-state modular transition at the SAME root); NO root is 1/8 -- the deployed value stays UNPINNED by state demands. (4) THE MODULAR ROUTE: D(0, beta) = |beta - 2pi|/(2pi) exact (ward 1.1e-16); the 2pi-KMS locus of the boundary reduction is EXACTLY the point (t = 0, beta = 2pi) -- the geometric temperature KILLS the mixing instead of pinning it; off-axis EMPTY. (5) THE THERMAL CURVE: order-parameter peak at beta = 1.6730 +- 5e-4 (round-57 'peak at beta = 2' corrected: coarse-grid argmax); distinguished-point census at 0.5 percent: NO HIT (DISTINGUISHED-ABSENT, typed as a reading census). The v898 [O] premise unmoved. NO RH claim. UPDATED 2026-08-27 (v972): the exclusivity is TYPED RAY- and REFLECTION-relative -- the v903 statement concerns the v898 RAY (all 33 covariant coordinates moving together), not the slice: the full 33-dim census (SEAM.STATE.RPMIXING.01) shows theta_abT kills exactly ONE coordinate (a_J, kernel value -1/(1+c^2) = -0.8240271368 at c = tanh(1/2)), leaving a 32-dim marginal RP hyperplane, and theta_S leaves a 17-dim first-order-neutral subspace with strict finite-s witnesses. The v903 anchor is reproduced exactly (odd Gram eigenvalues +-|a_J|, a_J = +0.04068013); the carving itself is UNMOVED.

Original classification detail

MEASURED: strict RP forces t = 0 (mixing and RP mutually exclusive); u >= t forced; 2pi-KMS locus = (t=0 beta=2pi); no root is 1/8

Dependencies as recorded

SEAM.CFIN.KMSMIX.01; SEAM.CFIN.WICKFUNCTOR.01; v898; v440; v519; v526