A registered result in its source context

TRANSFER.COHERENT.WILSON.01

Original ledger classification: Identity [E] (executed half: unistochastic lift, Wilson code, center bridge, selectivity census) + literature [C]; branch selection and intertwiner open

Original claim text

THE COHERENT WILSON CONTRACT, executed half (registered 2026-08-27; external-review round, companion of TRANSFER.HIDDEN.CIRCULATION.01). [E] (v977, sympy-exact): (1) UNISTOCHASTICITY: the seam single step B equals |U_ij|^2 entrywise for an exact U in SU(3); the angles are forced by B (sin^2 th13 = 2/9, sin^2 th12 = 1/14, sin^2 th23 = 2/7), cos delta = -4/sqrt(65) is uniquely solved, so the complete lift set up to rephasing is the two-branch family {U, U*} with e^{i delta} = (-4 +- 7i)/sqrt(65). (2) THE WILSON DATA ARE CLASSICAL UP TO ONE SIGN: J = 1/27 exact, Re of every plaquette fixed by B through unitarity (Re Q_{12;12} = -5/324, J^2 = 1/729 from B alone) -- the classically invisible datum is the Z2 orientation bit sgn J (U* lifts the same B with J = -1/27); minimal observable = the plaquette interference readout Im(U11 U22 U12* U21*). (3) THE 5-12-13 CODE: Q_{12;12} = (-5+12i)/324, normalized (-5+12i)/13 with 5^2 + 12^2 = 13^2 (atoms 5 = g_car, 12 = dim g_SM, 13 = Delta_Q = N(3+2i)); all nine plaquettes close on four Gaussian phase types with norms exclusively {10, 13, 130, 169} = {2*5, 13, 2*5*13, 13^2}; every plaquette has Im = +-1/27; the four fundamental plaquettes generate all nine via exact B-weighted composition. (4) THE CENTER BRIDGE: disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 = 4^2 + 7^2 for the v530 atom matrix A = [[8,2],[5,3]], and e^{i delta} = (-det(A-I) +- i det A/2)/sqrt(disc chi_A) equals the transport-lift phase EXACTLY; -4+7i = (1+2i)(2+3i) with Gaussian norms 5, 13 (the v738 tower primes); NEGATIVE controls: the v530 siblings A_K (disc 48 vs identity 13) and A_Q (disc 13 vs 13/4) FAIL the identity -- the bridge selects the atom quotient A. (5) POWER LAW + RATIONALITY SELECTION: J_n^2 = (1-b)^2(1+2b-3a^2)/108 (a = (2/3)^n, b = (1/3)^n), every B^n unistochastic with its own U_n (U_6 built, |U_6|^2 = T exact); |J_6| = 0.0951088904 = 0.9884006 J_max; the uniform limit lifts to the Fourier matrix F3 at J_max = 1/(6 sqrt 3) exactly; J_n is RATIONAL ONLY at n = 1 (the deployed step hits 3(1+2b-3a^2) = 1 exactly, so J = 1/27) -- the Gaussian-Pythagorean code selects the single step. (6) NO FIXED MICROSTEP: B^2 != |U^2|^2 exact, and the Dirichlet recurrence witness n* = 967909 has min diag |U^{n*}|^2 = 0.999999 while B^{n*} is uniform to 5.6e-17 -- no single closed unitary generates the relaxing sequence; repeated steps require dephasing between steps, the six-step macro-gate U_6 is NOT U_1^6 (the coherent sharpening of the k5 clock-vs-walk verdict). (7) SELECTIVITY (hard kill passed): the obstruction certificate J^2 = -1/64 < 0 fires on the classic non-unistochastic control; mutated spectra give irrational J; census over 238 valid family points: 4 rational-J, EXACTLY ONE full 5-12-13 code point = the deployed (2/3, 1/3) (0.42% << the preregistered 10% kill). (8) PMNS NEAR-MISS stays NEGATIVE: branch phase 240.2551 deg near the deployed 240 deg (4pi/3, v270) but J_tr = -1/27 = -0.037037 != J_PMNS = -0.02965 and all three angles differ -- NO PMNS derivation. [C] literature: coherification by a reversible unitary iff unistochastic (Dunkl-Zyczkowski 0909.0116; Korzekwa et al. 1710.04228); a unitary lift carries quantum capacity log2 3. OPEN: the physical selection of sgn J; the A -> angles intertwiner (the bridge fixes the PHASE from A-invariants, the ANGLES come from B alone); any CP/time-orientation reading. Python-only per GATE.WOLFRAM.02 (SU(3)/plaquette/center-bridge symbolic algebra with nested radicals).

Original classification detail

[E] B unistochastic with exact SU(3) lift {U, U*}, J = +-1/27; 5-12-13 plaquette code (norms {10,13,130,169}); center bridge disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 with sibling negatives; rationality selection (J_n rational only at n = 1); census unique full-code point = deployed (2/3, 1/3); no fixed microstep (Dirichlet witness); [C] coherification literature; PMNS near-miss stays negative; sgn J and the intertwiner OPEN

Dependencies as recorded

TRANSFER.HIDDEN.CIRCULATION.01; DYN.UNITARY.DILATION.01; v530_center_quotient_compiler.py; v738_hecke_mod_ramified.py; v270_pmns_jarlskog_assembly.py