A registered result in its source context

CARRIER.PETERSEN.RADIAL.01

Original ledger classification: Exact [E neu] finite graph/matrix structure theorems (integer/Fraction; charpolys sympy-gated) behind the carrier-geometry fence; the 10-dim multiplicity prediction typed [H neu]; carries TRANSPORT.SIXTHROOT.01 (spectral-only decider)

Original claim text

CARRIER.PETERSEN.RADIAL.01 (+ TRANSPORT.SIXTHROOT.01): the K5 edge machine, the Petersen carrier geometry with the radial dynamics whose sixth power IS the deployed transport spectrum, + the bit-exact decider on the PSD sixth root, ONE module from two probes (19/19 + 16/16 checks, ~1 s; discovery probes carrier_petersen_radial_probe.py PETERSEN-RADIAL-EXACT and transport_sixthroot_probe.py SIXTHROOT-SPECTRAL-ONLY, both 2026-08-06). PART 1, THE K5 EDGE MACHINE (all exact integer/Fraction): X = (-2,-2,-2,3,3) is the UNIQUE primitive traceless block-constant charge for the F|W = 3+2 split (sign pinned by the certified v774 table); E(K5) = 10 pairs carry the charge census {-4: 3, +1: 6, +6: 1} = the SU(5) decuple 3_{-4} + 6_{+1} + 1_{+6}, every pair cross-checked against the certified v774 hypercharge table (classes u_c/Q_up/Q_dn/e_c); under disjointness the pairs form the PETERSEN graph SRG(10,3,0,1) (charpoly (x-3)(x-1)^5(x+2)^4 exact, girth 5, |Aut| = 120 by full backtracking census = the faithful S5); the distance shells around the W vertex are (1, 3, 6) and CHARGE-PURE (+6/-4/+1 = e^c/u^c/Q), and the distance-2 shell induces a C6 -- THE FLAVOR HEXAGON AS GRAPH GEOMETRY [E neu] (explicit cycle verified edge by edge; 6 = |R+(A3)| = the transfer exponent, v124); the shell partition is EQUITABLE with quotient [[0,3,0],[1,0,2],[0,1,2]] whose eigenvector (6,-4,1) -> -2 IS the hypercharge vector, and P = Q_Pet/3 has spec(P^6) = {1, 64/729, 1/729} == the deployed TFPT transport spectrum EXACTLY (v54/v56/v171/v317; v124 lambda_n = (1-n/3)^6; GATE.METRIC.18). THE PREDICTION [H neu]: the full 10-dim Petersen walk has spec(P10^6) = {1, (1/3)^6 x5, (2/3)^6 x4} -- fast mode multiplicity 5 = g_car, slow hypercharge mode 4 = |mu4| (trace crosscheck 990 = 729 + 5 + 256); NO corpus 10-dim operator exists (T is 3-dim on the cusp space) -- a prediction, not a verification. PART 2, THE SIXTH ROOT (exact Fractions): B = (1/18)[[13,1,4],[1,13,4],[4,4,10]] -- every entry a compiler number (18 = p4(anchor), 13 = N_fam^2 + |Z2|^2, 4 = |mu4|, 10 = A_Lambda, 1 = N_Phi) -- is the UNIQUE symmetric doubly stochastic PSD sixth root with the frozen corpus-basis eigen-assignment ((1,1,1) -> 1, (1,-1,0) -> 2/3, (1,1,-2) -> 1/3; spectral reconstruction entry-exact; exactly 2 assignments in the corpus basis, a 1-parameter circle without the pin); B^6 carries the deployed spectrum exactly BUT the decider lands SPECTRAL-ONLY: B^6 is GL(3,Q)-conjugate to v486's lazy-walk M^6 (exact rational W and orthogonal O conjugations verified) and to the cusp-diagonal canonical form, yet bit-equal to NEITHER -- the corpus freezes the SPECTRUM, not the basis; the stochastic types differ (doubly vs sub-stochastic with absorbing channel). Controls fire in both parts (wrong edge 4+1 kills the (1,3,6) structure; Johnson complement kills the hexagon; both matrix perturbations break the spectrum). Typed carrier representation geometry -- ROOTCLASS-MIXED (v775) cited, no particle semantics. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. [2026-08-06 LXVI dated correction + addendum, v814: the sixth-root census missed the deployed v221 evaluation -- T_v221 (the exact spectral sum of v221's transfer (1-w)^6) == B^6 BIT-EXACTLY, so the TRANSPORT.SIXTHROOT.01 verdict upgrades from SPECTRAL-ONLY to BITEXACT-vs-v221 (the frozen SPECTRAL-ONLY stands as the probe's adjudication; ABEL-DEAD correction precedent); and the [H neu] 10-dim prediction now has a promotion-ready canonical PROPOSAL: T10 = P10^6 in the Lambda^2 basis passes all gates with the equitable v774 quotient == (Q_Pet/3)^6 bit-exact (TRANSPORT10-PROPOSED, no deploy claim), while the six-step composition is typed CLOCK-ONLY -- the deployed 6 is the clock exponent, every spatial route carries a typed obstruction.]

Original classification detail

PETERSEN-RADIAL-EXACT + SIXTHROOT-SPECTRAL-ONLY: charges (-4,+1,+6) = the SU(5) decuple against v774; Petersen SRG certified, |Aut| = 120 census; shells (1,3,6) charge-pure; the flavor hexagon = the distance-2 shell edge-by-edge; equitable quotient with hypercharge eigenvector (6,-4,1) -> -2; spec(P^6) = {1, 64/729, 1/729} = the deployed transport spectrum; 10-dim multiplicities (x5 = g_car fast, x4 = |mu4| slow) typed [H neu] -- no corpus 10-dim operator; B unique symmetric doubly stochastic PSD sixth root in the corpus basis, B^6 GL(3,Q)-conjugate to v486's M^6 and the cusp-diagonal form but bit-equal to neither -- the corpus freezes the spectrum, not the basis.

Dependencies as recorded

ARF.SPINORCOMPILER.01; v774; v54; v56; v124; v486; v327; v212; v397; v14; v700