A registered result in its source context

SEAM.CFIN.NESS.PARENT.01

Original ledger classification: Demand closed NOT-NEEDED [Identity/Numerical]: equilibrium J/Z witnesses carry the full 1/200 mixing at zero entropy production; the deployed wiring is PURE-I (maximally obstructed); wiring-selector contract registered; no marker move

Original claim text

NO NESS NEEDED -- THE PRICE OF THE MIXING IS EXACTLY ZERO ENTROPY PRODUCTION (demand closed as NOT-NEEDED; measured 2026-08-10, round CXXXIX(60); promoted in v908): strict theta_S (collar) hermiticity is a TWO-SEAT LINEAR LAW of the coupling -- the 1p seat A_{x+1,y} + A_{x,y+1} kills the X-, the deg-2 empty seat A_{x,y} + A_{x+1,y+1} the I-subblock coordinates; exact rank 12, kernel 12 = the {J, Z} coordinates of the 24-dim covariant coupling space = the v898 T-count. THE DEPLOYED SEAM WIRING V = A_int[C, B] IS PURE-I (every 2x2 subblock exactly -I2) = a MAXIMALLY obstructed covariant direction -- explaining the v903 strict-collar law ('30 entries, magnitude 2t') EXACTLY as 15 mixed pairs x 2 Gram positions. THE KERNEL CONTAINS EQUILIBRIUM WITNESSES: the uniform J-coupling parent V_J (kappa = m = 1/2, t = 1/20) passes strict theta_S RP in EXACT arithmetic (Grams exactly hermitian, PD by exact LDL; float lam_min 0.3064/0.1532) while its Schur compression carries the FULL canonical Pfaffian mixing -- S_J = V_J J3 V_J^T = 3J on ALL 25 channel blocks (integer identity), J coordinate EXACTLY t^2 3m/(1 - m^2) = 1/200 = the same rational floor identity as the v903 witness, Pf4 canonical 10/10; V_Z is a SECOND witness (S_Z = -3J, J coordinate -1/200). THE NESS SIDE HONEST (FINITE-NESS-NOGO): at finite size every exactly stationary quasi-free state has [h, A] = 0 => ALL block currents Phi_r = (1/4) tr(h0_r [h, A]) = 0 => sigma = beta_C Phi_C + beta_B Phi_B == 0 (exact; energy ward 7e-18) -- 'NESS with positive entropy production' is category-inapplicable; the weakest meaningful positivity = RP of the stationary covariance, EXACTLY what is tested; the two-temperature Cesaro states (frozen grid) are exactly stationary (3e-16), covariant, CAR-valid, with vanishing t = 0 product currents. THE PRICE CURVE IS FLAT-OPEN: the 15/15 canonical block census is open at EVERY drive point INCLUDING zero drive, the theta_S hermiticity defect stays PINNED (0.0982) and the PSD margin degrades monotonically -- the minimal entropy production at which the mixing gates open is EXACTLY ZERO: DRIVE BUYS NO RP, NESS-NOT-FORCED -- the demand closes as NOT-NEEDED. Kernel membership is NECESSARY, not sufficient: J/Z mixtures pass hermiticity + PD but break the canonical sign census (4/10) -- the canonical gate selects the uniform J (or Z) ray; orbit selectivity reproduced (single boundary pair: both orbits 10/10 with J coordinate exactly lambda t^2 = 1/600). THE REGISTERED NEXT CONTRACT: SEAM.STATE.WIRING.SELECTOR.01 -- is PURE-I compiler-forced? The deployed IOTA wiring comes from the vacuum-orbit construction of A_int; whether the orbit/edge rules admit a {J, Z}-kernel alternative at equal C6 covariance and equal Pf pencil is exactly answerable -- only then is it decidable whether the strict-collar obstruction is a compiler theorem or a deployment choice. The witnesses live on a DIFFERENT covariant coupling direction than the deployed A_int wiring -- whether the actual seam allows them is untouched; the v898/v903 [O] premise stays [O]. Controls: global-KMS regression reproduces the round-58/59 equilibrium obstruction (defect 0.0982); 3/3 seeded permutations break covariance + canonical census; PURE-I regression (0.1, 30 entries); the I-orbit switch-on fires WITHIN the covariant class. Zero RH content.

Original classification detail

CLOSED (NOT-NEEDED): stationary => sigma == 0 exactly and drive buys no RP; V_J/V_Z equilibrium witnesses with J coordinate exactly 1/200; PURE-I is the maximally obstructed direction -- SEAM.STATE.WIRING.SELECTOR.01 registered next

Dependencies as recorded

SEAM.CFIN.MARGINAL.STABILITY.01; SEAM.STATE.DERIVATION.01; SEAM.CFIN.KMSMIX.01; v898; v903