A registered result in its source context

SEAM.CFIN.MARGINAL.STABILITY.01

Original ledger classification: Measured covariant exclusion [Identity/Numerical]: interior empty (exact +-a_J law), floor exchange Pf4 = (eps - 1/200)(eps + 1/200); escape only by symmetry breaking at price 2 eps; no marker move

Original claim text

STRICT 2-CYCLE RP IS IMPOSSIBLE ON THE WHOLE COVARIANT CLASS (measured 2026-08-10, round CXXXVIII(60); promoted in v908): the closure-vs-isolated dilemma of the v903 marginal witness is REFUTED AS A DILEMMA -- the theta_abT sector Grams see ONLY the channel-{4,5} 4x4 seat (ward 1e-14), covariance allows there EXACTLY the J coordinate (integer defect 2 for I/X/Z units, 0 for J; c4 = c5 forced), and the exact symbolic seat law M1 = [[aJ+aX, aI-aZ],[aI+aZ, -aJ+aX]] reduces covariantly to M1 = diag(a_J, -a_J) with det M2 = -a_J^2: strict theta_abT RP is IMPOSSIBLE on the WHOLE covariant class (the RP set = {a_J = 0} = the cone boundary, interior EMPTY); the marginal witness is NOT a limit of covariant strict equilibria (there are none) and NOT isolated (the whole s = 0 family is a positive-dimensional MARGINAL STRATUM: margin exactly 0 on all 16 CAR-valid lattice points at full 10/10 canonical mixing); the decisive scalar sup(RP-margin x mixing) = 0 EXACT. THE KERNEL ANATOMY (exact rational arithmetic): at the M2 parent the 1p Gram is IDENTICALLY 0 and the deg-2 Gram is exactly [[1, i/2], [-i/2, 1/4]] with eigenvalues {0, 5/4} -- the vacuum bound to the a-pair; both kernels forced by the SAME pure-J covariance law whose only visible coordinate a_J is exactly the strict-route obstruction. THE TRANSVERSAL ESCAPE + ITS EXACT PRICE: the ONLY hermiticity-preserving strict-enabling seat direction is the covariance-BREAKING X coordinate: at every eps > 0 the parent is STRICTLY RP (1p eigenvalues {eps, eps} exact, deg-2 det = eps^2 exact), covariance defect EXACTLY 2 eps (linear price law), mixing 10/10 with the J coordinate 1/200 UNCHANGED, margin exponent 2.000 -- TRANSVERSAL. FLOOR-EXCHANGE (the sharpest exact object): Pf4_{45}(eps) = (eps - 1/200)(eps + 1/200) and the effective 2-cycle odd Gram is diag(eps + 1/200, eps - 1/200) EXACTLY -- the canonical sign gate IS the negative effective RP margin (the same polynomial factor): one level down the exclusion survives the transversal escape, with the crossover EXACTLY at the 1/200 floor. SPEC v2 with ONE disclosed amendment (fail-first preserved: the v1 gate 'all 18 s=0 points CAR-valid' fell at the two m = 3/4 corners; v2 reads the 16 CAR-valid points, the marginality held on all 18). Reading typed: 'physical as a limit of equilibria' is unrealizable within the symmetry class -- strict 2-cycle RP needs symmetry breaking (price 2 eps) or a different reflection. Controls: the I direction violates RP for BOTH signs, Z breaks 1p hermiticity, the 1/200 identity regresses rationally, 3/3 seeded scrambles break the covariance ward. The v898/v903 [O] premise stays [O]. Zero RH content.

Original classification detail

MEASURED: strict 2-cycle RP impossible on the whole covariant class (M1 = diag(a_J, -a_J) exact); the s = 0 stratum is marginal not isolated; Pf4(eps) = (eps - 1/200)(eps + 1/200) -- crossover at the 1/200 floor

Dependencies as recorded

SEAM.STATE.DERIVATION.01; SEAM.CFIN.RP.DILATION.01; SEAM.CFIN.KMSMIX.01; v898; v903