A registered result in its source context

TRANSFER.HIDDEN.CIRCULATION.01

Original ledger classification: Identity [E] (executed half: fibre line, discriminator, criticality, EB no-go, KKT) + literature [C]; fibre-point selection open

Original claim text

THE HIDDEN CIRCULATION CONTRACT, executed half (registered 2026-08-27; external-review round, companion of the DYN.MARKOV.EMBED.01/DYN.UNITARY.DILATION.01 split). [E] (v976, sympy/Fraction-exact): (1) the Birkhoff fibre of the seam single step B (exact sixth root of the v221 kernel; B = (1/2)I + (1/18)P12 + (2/9)P13 + (2/9)P23 bit-exact) is EXACTLY a one-parameter line w_t, t in [0, 1/18], because the decomposition map on R[S3] has the 1-dim kernel (even - odd); the hidden parameter is the sign-character Fourier coefficient w_t-hat(sgn) = 6t; populations are exactly t-free and no fibre member is chiral (w(C123) = w(C132) forced -- the typed obstruction for any chirality reading). (2) THE DISCRIMINATOR: one-step coherence dynamics is the weighted left regular S3 representation with spectrum {1, 6t, 2/3 x2, 1/3 x2} exactly; the triangle loop current A is an exact eigen-observable Psi_t(A) = 6t A (population-blind; one step + one current readout measures t, no ancilla; one-step tomography rank 6 determines all six weights). (3) CONTRAST-QUBIT CHOI LAW: spec(Choi^{T2}) = {-3t/2, 1/6+3t/2, 1/3+3t/2, 1/2-3t/2} symbolically; CRITICALITY lambda_min = (1 - lambda2 - lambda3 - 6t)/4 with lambda2 + lambda3 = 2/3 + 1/3 = 1 EXACTLY: t = 0 sits precisely ON the entanglement-breaking boundary (mutated spectra {2/3,1/2}/{1/2,1/3} miss by -1/12/+1/12 -- criticality not generic); the squared channel is PPT on the whole range (endpoint minima 1/9, 1/12). (4) FULL-LEVEL NPT PERSISTENCE: lambda_min(Choi(Psi_t^n)^{T2}) = -(1/3)(2/3)^n, t-independent (exact eigenvalue for n in {1,2,6}; float minimum n = 1..8) -- the 3-level family is never EB at tested n (pinned by the invariant coherent state (1,1,1)/sqrt3). (5) THE NO-GO for DYN.UNITARY.DILATION.01: the deployed Kraus dilation K_ij = sqrt(T_ij)|i><j| is measure-and-prepare (one step kills every coherence, fully symbolic), its Choi is diagonal => entanglement breaking => quantum capacity 0; C_0(T) = 0 exactly (T entrywise > 0); the Kraus channel is NOT in the Birkhoff fibre. (6) BINARY MESSAGE (KKT, 50 digits): p* = (1/2, 1/2, 0) exactly capacity-achieving for BOTH T and B; C(T) = 0.00835801913781 bit, C(B) = [13 log2(13/7) - log2 7]/18 = 0.4890415237 bit, ratio 1.709%. [C] literature-typed: PPT<=>separable in 2x2 (Peres-Horodecki), separable Choi <=> EB (Horodecki-Shor-Ruskai quant-ph/0302031), EB index (Lami-Giovannetti 1411.2517) => qubit n_EB = 1 (t = 0) / 2 (t > 0). [C] VALUE COINCIDENCE (observation, NOT a theorem): the t = 0 weights (9,1,4,4)/18 = (3^2,1^2,2^2,2^2)/18 hit the v652 c = 0 defect-ladder values 2*Delta = g^2/18 including w(I) = 1/2 = 2*Delta(gt=3); multiplicity matches only at g = 2; the forcing functor (CFT defect dimension -> Birkhoff weight) is the OPEN half, named TRANSFER.DEFECT.BIRKHOFF.01. OPEN: the physical selection of a fibre point t; any 4D/flavor reading. Python-only per GATE.WOLFRAM.02 (channel/Choi/Birkhoff algebra; the exact seam rationals already mirrored).

Original classification detail

[E] the Birkhoff fibre of B is the sign-character line t in [0,1/18]; loop-current discriminator Psi_t(A) = 6t A; qubit Choi law -3t/2 with EB criticality 2/3 + 1/3 = 1; full-level NPT -(1/3)(2/3)^n; the deployed Kraus dilation is EB (Q = 0, C_0 = 0); binary-message KKT certificates; [C] defect-Birkhoff value coincidence (forcing functor OPEN as TRANSFER.DEFECT.BIRKHOFF.01)

Dependencies as recorded

DYN.UNITARY.DILATION.01; DYN.MARKOV.EMBED.01; QEC.SEAM.01; v221_seam_qecc.py; v652_orbifold_arf.py