A registered result in its source context

K5.SIXSTEP.TRANSPORT.01

Original ledger classification: Exact [E neu] operator identities and censuses (three spatial routes, sixth-power blindness, corpus census, bit-exact v221 location); [H neu] the walk-vs-clock reading and the T10 deployment proposal; dated BITEXACT correction to TRANSPORT.SIXTHROOT.01 carried

Original claim text

K5.SIXSTEP.TRANSPORT.01: the six-step composition and the 10-dim transport deploy -- the (2/3)^6 rate is canonical on three spatial routes, the deployed six is the clock exponent, and the canonical T10 proposal passes every gate, one probe (23/23 checks incl. the 3 must-fire controls, ~0.2 s; discovery probe k5_sixstep_transport_probe.py, 2026-08-06, verdicts SIXSTEP-CLOCK-ONLY / TRANSPORT10-PROPOSED). THE CORRECTION (dated note on the v808/TRANSPORT.SIXTHROOT.01 row): the deployed transport is LOCATED -- v221's transfer (1-w)^6 IS the exact spectral sum T_v221 = J/3 + (2/3)^6 u2 u2^T + (1/3)^6 u3 u3^T, and T_v221 == B^6 == (1/4374)[[1651,1267,1456],[1267,1651,1456],[1456,1456,1462]] BIT-EXACTLY -- the v808 sixth-root census missed v221, so the SIXTHROOT verdict upgrades from SPECTRAL-ONLY to BITEXACT-vs-v221 (the frozen SPECTRAL-ONLY stands as that probe's adjudication; ABEL-DEAD correction precedent). TASK A (all exact): the rate (2/3)^6 arises CANONICALLY on three independent spatial routes -- the doily alternation (three PSD double-steps duad -> syntheme -> duad: spec {1, (2/3)^6 x9, 0^5}), the hexagon compression (Pi_2 (A_Pet/3) Pi_2 == A_C6/3 with spec((A_C6/3)^6) = {(2/3)^6 x2, (1/3)^6 x4} -- BOTH deployed decay rates from pure hexagon geometry), and the hexagon circulation (((2/3) S6)^6 = (2/3)^6 I) -- but each route is blocked by a TYPED obstruction (doily: wrong space, decay multiplicity 9, no (1/3)^6 mode; hexagon: NO unit mode -- ||(A_C6/3)^6||_op = (2/3)^6 < 1 kills every norm-nonincreasing intertwiner [E neu]; radial: the bipartite sign -2/3, P NOT similar to the clock root B, and the exact conjugation S with S T_v221 S^{-1} = P^6 is deployed NOWHERE -- the missing shells -> cusp isomorphism); SIXTH-POWER BLINDNESS [E neu]: (A_C6/3)^6 and (A_{2K3}/3)^6 have IDENTICAL spectra -- the sixth power erases the cyclic geometry AND the sign, so only per-step data can distinguish walk from clock: the deployed six is the CLOCK EXPONENT (v124 lambda_n = (1-n/3)^6, v486 hand, fixed eigenbasis (1,1,1)/(1,-1,0)/(1,1,-2)). TASK B: corpus census -- NO deployed 10-dim transport operator exists (v37's Pluecker apparatus is 3x3, re-derived; v44/v45 carry Lambda^2(5) = 10 as dimension only); the CANONICAL PROPOSAL T10 = P10^6 in the Lambda^2 basis (v774 cut-code dictionary, a permutation conjugation) passes ALL gates: symmetric doubly stochastic PSD, spectrum {1^1, (1/3)^6 x5, (2/3)^6 x4} exact (multiplicities (5, 4) = (g_car, |mu4|)), the v774 class partition (e_c | u_c | Q) EQUITABLE, exact quotient == (Q_Pet/3)^6 bit-exact with the deployed spectrum {1, 64/729, 1/729} and reversibility -- a promotion-ready PROPOSAL, no deploy claim (Q6 != T_v221 bit-exact, not symmetric -- recorded: this is WHY PROPOSED, not REALIZED). Controls fire (wrong per-step rate 1/2, Johnson-complement scramble, non-equitable partition). ROOTCLASS-MIXED (v775) cited: carrier representation geometry, no physics claims beyond operator identities. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.

Original classification detail

SIXSTEP-CLOCK-ONLY + TRANSPORT10-PROPOSED: the (2/3)^6 rate canonical on three spatial routes, each with a typed obstruction; the deployed 6 is the clock exponent (sixth-power blindness makes per-step data mandatory); T_v221 == B^6 bit-exact (SIXTHROOT upgrades to BITEXACT-vs-v221, dated note on the v808 row); T10 = P10^6 in the Lambda^2 basis passes all gates -- proposal, no deploy claim; NO RH claim

Dependencies as recorded

CARRIER.PETERSEN.RADIAL.01; TRANSPORT.SIXTHROOT.01; CURVE.CODE.DOILY.01; v221; v124; v486; v37; v774; v808; v809