A registered result in its source context

CP.CHANNEL.IDENT.01

Original ledger classification: Identity [E] (exact identities and certified numerics with mutation controls -- the hexagonal channel identity sum rho^{d_k} = 4 rho / sum rho^{m_k} = 4 sympy-exact with the sheet-even/odd parity typing, arg(prod c) = 0 exactly on both magnitude sectors with the branch-order law, Tier-1 emptiness by the conjugation-commutation theorem, the frame removal Im(rho det)/det = Im rho exact with the degree +1 account, the two inequivalent Tier-2 characters as verified homomorphisms, and the Jarlskog anchor J = 3.327021e-5 = v88 at unitarity 1.1e-41) -- NARROWINGS of four existing ledger readings only; no marker moves; R1/R2 typed OPEN

Original claim text

THE CP CHANNEL / INVARIANT IDENTITIES (2026-07-29; one module, 25 checks, ~1 s; promotion of the exact cores of discovery T177 (contract CP.INVARIANT, probe cp_invariant_probe.py, 49/49, verdict DEGENERATE) -- THE CP MIRROR AS ALGEBRA: the prime-front toolkit (gauge-degree bookkeeping under declared group actions) turned on the four CP ledger rows REDTEAM.D.01 / E8.CHAN.01 / CP.MOD.01 / DUAL.FRAME.01; every statement is a NARROWING of an existing reading, executed in the same change, with NO marker moves and NO CP derivation claimed. CONTENT: (1) THE HEXAGONAL CHANNEL IDENTITY -- on the CM unit rho = e^{i pi/3} (CP.MOD.01) the E8 split 248 = 120 + 128 (E8.CHAN.01/v227) has an EXACT fiber realisation: sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly; the degrees mod 6 are four 0s and four 2s, 1 + rho^2 = rho) and sum_k rho^{m_k} = 4 (arg = 0 exactly), with the parity typing forced by integer parity -- all degrees EVEN (phase channel SHEET-EVEN under the sheet flip rho -> rho^4 = -rho), all exponents ODD (magnitude channel SHEET-ODD); CONSEQUENCE: the sheet-even phase-channel angle cannot distinguish quark from lepton (it carries pi/3, not the CP.MU6.01 sheet split); mutation controls: the identity breaks on the non-CM unit e^{i pi/5} and on a mutated degree list (30 -> 31), reality breaks on a mutated exponent list (29 -> 30); HONEST CAVEAT wired as a check: reality of the exponent sum alone is NOT hexagon-specific (the exponent residues are conjugation-closed mod 10 too) -- only the degree half (= 4 rho) is; (2) ZERO PHASE IN THE MAGNITUDE DATA + THE BRANCH-ORDER LAW (the REDTEAM.D.01 narrowing): arg(prod c) = 0 EXACTLY on both TFPT sectors (lepton triple (16/7, 4/3, 7/6), product 32/9; up-quark triple (1/2, 34/41, 4/13)) -- the CP residual is not hidden in the product -- and the mu3 branch group is EXACTLY the kernel of the magnitude data because its order divides N_fam = 3 (w^{3j} = 1; a mu4 branch already shifts the product phase by -pi/2, mutation): the residual is a FIBER datum, not a magnitude datum; (3) TIER-1 EMPTINESS BY THE BLINDNESS THEOREM: both complex kernels commute with conjugation (conj sum rho^{d_k} = 4 conj rho exactly; Im det(1, d, conj(rho) n) = -Im det(1, d, rho n) exactly), so EVERY pi/3-carrier is kappa-odd and invariant + odd forces Im F = 0: strict invariance under all four T177 groups is EMPTY on pi/3-carriers, per algebra and as preregistered; (4) THE FRAME REMOVAL (the DUAL.FRAME.01 narrowing): det(1, d, n) = 21 = N_fam * scalaron and Im det(1, d, rho n) = 21 sin(pi/3) exactly (v225 rebuilt); the orientation functional is homogeneous of DEGREE +1 in the frame normalisation (Im det(1, d, rho(t n)) = t 21 sin(pi/3) symbolically), so the NUMBER 21 sin(pi/3) is FRAME data; dividing by the oriented volume removes the frame IDENTICALLY (Im(rho v)/v = Im rho symbolically for every real v != 0): the invariant core is the fiber datum Im(rho) = sin(pi/3), the sign a declared orientation; sheet control Im det(1, d, rho^4 n) = -21 sin(pi/3); mutation: n' = (5, -8, 6) gives det = 39/2 != 21; (5) THE TWO TIER-2 CHARACTERS + THE JARLSKOG ANCHOR: P2 = arg(sum rho^{d_k}) carries (chi(kappa), chi(sigma)) = (-1, +1) and V5 = Im(rho det)/det carries (-1, -1), both verified as character HOMOMORPHISMS on the full four-element group (16 products) -- TWO INEQUIVALENT invariants carry the same value pi/3 (the DEGENERATE verdict as algebra) and NEITHER couples to the frame; the classical anchor: the TFPT CKM rebuild (s12 = lambda_C, s23 = phi0/(1+lambda_C), s13 = lambda_C^3/3, frozen delta = pi/3 + 3 lambda_C^2 per REG.FREEZE.01) is unitary to 1.1e-41 and gives J = 3.327021e-5 = the v88 lattice value; J passes rephasing invariance (incl. the mu3 branch group) and CP-oddness and fails ONLY the pi/3-carrier test (its phase content is delta, not pi/3) -- the benchmark VALIDATES the criterion instead of the value, and the full delta has NO character under the parity involution (a CP-even correction on a CP-odd angle: the CP.MOD.01 scope narrowing). NAMED LIMITS AS LOAD-BEARING CONTENT: (i) NARROWINGS ONLY -- no marker of any pre-existing contract moves, the CP residual is NOT closed, the word 'derived' appears nowhere, REG.FREEZE.01 and the 3-vs-2 lambda_C^2 coefficient question are untouched; (ii) R1 STAYS OPEN: whether a frame-coupled, scale-free, character-covariant pi/3-carrier can exist at all (the T177 obstruction: the (1, d, n) frame has only ONE oriented volume to normalise against); R2 STAYS OPEN: which of the two Tier-2 characters is physical -- the sheet-odd (orientation) reading reproduces CP.MU6.01's quark/lepton split, the sheet-even (channel) reading cannot: a structural preference, NOT a derivation; (iii) the D4 deck column of T177 is a DECLARED MODEL and is not promoted (only the model-free statements are). HONEST FENCES: no RH statement anywhere (finite exact statements about roots of unity, 3x3 determinants and one 3x3 unitary matrix); Jarlskog 1985, Wolfenstein 1983, Weyl 1946 named CLASSICAL as addresses. Discovery: T177 (experiments/tfpt-discovery/cp_invariant_probe.py, 49/49, 0.2 s, verdict DEGENERATE). UPDATE (2026-07-30, T178/v564, CP.FIBER.PIN.01): R1 is DECIDED -- the natural (metric-free) class is fiber-only BY THEOREM (one bracket generator), the metric class couples but is NON-CANONICAL (a continuum of normaliser-relative values) -- and R2 is SELECTED conditional on the classical anchor (the Jarlskog character tuple (-1,-1,-1) matches the sheet-odd orientation class only); the single-sine lemma types this row's DEGENERATE verdict as FORCED on crystallographic fibers. Markers unchanged.

Original classification detail

[E] sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly, sheet-EVEN) and sum_k rho^{m_k} = 4 (arg = 0 exactly, sheet-ODD) on the hexagonal CM unit -- the E8 channel typing has an exact fiber realisation and the phase channel is sheet-blind; arg(prod c) = 0 exactly on both TFPT sectors (the CP residual is a FIBER datum, not a magnitude datum); Tier-1 invariance EMPTY per algebra (every pi/3-carrier is kappa-odd); Im(rho det)/det = Im rho = sin(pi/3) exactly (the orientation reading is degree +1 in the frame normalisation, 21 sin(pi/3) is frame data, the sign a declared orientation); two inequivalent Tier-2 characters (-1,+1) vs (-1,-1) carry the same pi/3 (DEGENERATE), neither frame-coupled; Jarlskog anchor J = 3.327021e-5 = v88 passes (a)-(c), fails only the pi/3-carrier test. Four ledger rows narrowed, no marker moves; R1/R2 OPEN.

Dependencies as recorded

REDTEAM.D.01; E8.CHAN.01; CP.MOD.01; DUAL.FRAME.01; CP.MU6.01; FLAV.CP.01; REG.FREEZE.01; v88; v220; v225; v227; T177