#!/usr/bin/env python3 # -*- coding: utf-8 -*- r"""v814 -- 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. PROVENANCE: discovery probe k5_sixstep_transport_probe.py (2026-08-06, 23/23, ~0.2 s, SIXSTEP-CLOCK-ONLY / TRANSPORT10-PROPOSED); re-run identically at promotion. Promoted verbatim; the v774 import resolves against the verification directory (path swap, v795 precedent); a module-level _LAST verdict capture inserted (v791 precedent); numbers unchanged; run() encodes the pattern (v757 precedent). Original k5_sixstep_transport_probe.py docstring (verbatim): k5_sixstep_transport_probe -- K5.SIXSTEP.TRANSPORT.01 (Arf compiler programme, follow-up pair to CARRIER.PETERSEN.RADIAL.01 + TRANSPORT.SIXTHROOT.01): (A) does the six-step composition on the hexagon turn the doily/Petersen per-step 2/3 into the corpus rate (2/3)^6 CANONICALLY (exact operator identity), or is the deployed 6 a clock exponent? (B) do the corpus structures realize a canonical 10-dim transport operator with the predicted multiplicities 1^1, (1/3)^6 x5, (2/3)^6 x4? DEPLOYED ANCHORS (located, read-only): * v221_seam_qecc: THE deployed transport matrix -- T_v221 = J/3 + (2/3)^6 u2 u2^T + (1/3)^6 u3 u3^T with unit u2 ~ (1,-1,0), u3 ~ (1,1,-2) ("transfer (1-w)^6" over the cusp weights w in {0,1/3,2/3}); v221 evaluates it in floats, the DEFINITION is the exact spectral sum. CORRECTION GATE for TRANSPORT.SIXTHROOT.01: T_v221 == B^6 BIT-EXACTLY (B = (1/18)[[13,1,4],[1,13,4],[4,4,10]]); the earlier census missed v221, so the sixthroot verdict upgrades from SPECTRAL-ONLY to BITEXACT-vs-v221 (reported here). * v124_resummed_clock: lambda_n = (1 - n/3)^6, p2 = 6 = |R+(A3)| -- the clock reading (fixed eigenbasis, 6 as exponent). * v486_transfer_full_rule: the six-HAND -- six applications of ONE lazy rule M = [[1,0,0],[0,1/2,1/6],[0,1/6,1/2]] in a fixed basis. * curve_code_doily_probe (exploration, certified): the duad->syntheme channel N/3 has singular values {1, 2/3 x9, 0 x5} -- the per-step doily rate 2/3. * CARRIER.PETERSEN.RADIAL.01 (exploration, certified): the C6 hexagon = the distance-2 shell of the Petersen pair space; radial quotient Q_Pet = [[0,3,0],[1,0,2],[0,1,2]], spec((Q_Pet/3)^6) = deployed. TASK A -- THE SIX-STEP COMPOSITION (all exact; kill = any preregistered identity fails): A0 v221 LOCALIZATION + CORRECTION: T_v221 (exact spectral sum) == B^6 == (1/4374)[[1651,1267,1456],[1267,1651,1456],[1456,1456, 1462]] bit-exact; spec == {(1-w)^6} == v124's lambda_n exactly. A1 DOILY ROUTE: duads/synthemes of a 6-set, incidence N (15x15, 3-in-3); N N^T = 3I + A_coll with A_coll = SRG(15,6,1,3); sv(N/3) = {1, 2/3 x9, 0 x5}; the six-step alternation ((N/3)(N^T/3))^3 has spectrum {1, (2/3)^6 x9, 0 x5} EXACTLY -- three PSD double-steps (duad->syntheme->duad), sign +2/3 via the duality pairing. TYPED GAPS: wrong space (15-dim duads), decay multiplicity 9, NO (1/3)^6 mode. A2 HEXAGON COMPRESSION: Pi_2 (A_Pet/3) Pi_2 restricted to the distance-2 shell == A_C6/3 exactly (Petersen normalization 1/3 inherited; within-shell degree 2 => Perron 2/3 = the doily rate); spec(A_C6/3) = {2/3, 1/3 x2, -1/3 x2, -2/3}; spec((A_C6/3)^6) = {(2/3)^6 x2, (1/3)^6 x4} -- BOTH deployed decay rates from pure hexagon geometry. TYPED GAPS: NO unit mode (radial leak 1/3): ||(A_C6/3)^6||_op = (2/3)^6 < 1, so no norm-nonincreasing intertwiners can produce the deployed unit eigenvalue from the hexagon operator [E neu obstruction]; multiplicities (2,4); the per-step spectrum contains -2/3 (C6 bipartite). A3 HEXAGON CIRCULATION: the cyclic shift S6 on the certified C6 order has S6^6 = I, so ((2/3) S6)^6 = (2/3)^6 * I exactly -- the deployed subleading eigenvalue = ONE FULL CIRCULATION at the doily rate. TYPED GAP: scalar identity; a directed edge amplitude 2/3 is not a deployed object. A4 RADIAL WALK: P = Q_Pet/3 has spec {1, -2/3, 1/3} => P is NOT similar to the deployed per-step root B (spec {1, 2/3, 1/3}): the SIGN separates the spatial root from the clock root; P^6 ~ T_v221 via the exact rational conjugation S = U_rad U_dep^{-1} (S T_v221 S^{-1} = P^6, computed and verified) -- S maps (1,-1,0) -> hypercharge (6,-4,1) and (1,1,-2) -> (3,1,-1) and is DEPLOYED NOWHERE (the missing shells->cusp isomorphism). A5 THE DECIDER (eigenvector structures, exact): deployed T_v221 has the FIXED eigenbasis {(1,1,1),(1,-1,0),(1,1,-2)} at every step (clock/hand: v124 exponent, v486 six applications of one rule, B^6); every spatial candidate carries its (2/3)-mode on a different vector (doily: 9-dim window; hexagon: shell constant; radial: hypercharge (6,-4,1)) and no spatial 3-dim composite equals T_v221 bit-exactly in the deployed basis. SIXTH-POWER BLINDNESS [E neu]: (A_C6/3)^6 and (A_{2K3}/3)^6 have IDENTICAL spectra ({+-2/3, +-1/3 x2} vs {2/3 x2, -1/3 x4} -> same sixth powers) -- the sixth power erases the hexagon's cyclic geometry AND the sign; only per-step data distinguishes walk from clock. TASK B -- THE 10-DIM TRANSPORT DEPLOY: B1 PREDICTION RESTATED: P10 = A_Pet/3 has spec {1, (1/3)^5, (-2/3)^4}; spec(P10^6) = {1^1, (1/3)^6 x5, (2/3)^6 x4} exact (charpoly); multiplicities (5, 4) = (g_car, |mu4|). B2 CORPUS CENSUS (frozen; searched 2026-08-06): NO deployed 10-dim flavor/transport operator exists. Candidates examined: v221 (3-dim, THE deployed T -- reconstructed here), v486/v327 (3-dim rules), v54/v56/v124/v171/v317 (3-dim spectrum surfaces), v37 Plücker anchor (3x3 matrices R, K, Q, L -- re-derived here, dimension 3, spectra != predicted), v44/v45 (Lambda^2(5) = 10 as DIMENSION bookkeeping, no operator), v212/v397 (A_Lambda = 10 as scalar), v310 (rep table). In-probe verifiable core: v221 T is 3x3; v37's four matrices are 3x3 with charpolys as deployed (chi_K = t^3-9t^2+12t-4, chi_L = t^3-15t^2+40t-20). B3 CANONICAL PROPOSAL (exact): T10 := (A_Pet/3)^6 conjugated into the carrier Lambda^2 basis via the certified cut-code dictionary (v774: pair {i,j} <-> the weight-2 word with iota-support {i,j}; certified in CARRIER.PETERSEN.RADIAL.01 P1.4) -- a permutation conjugation, exact. GATES: T10 symmetric, doubly stochastic, PSD (even power), spectrum = the predicted multiplicities; the v774 class partition (e_c | u_c | {Q_up, Q_dn}) is EQUITABLE for T10; the exact quotient == (Q_Pet/3)^6 bit-exact, its spectrum == the deployed {1, 64/729, 1/729} exactly, reversibility size_i Q6_ij = size_j Q6_ji holds (sizes 1, 3, 6), and Q6 = S T_v221 S^{-1} with the A4 conjugation -- the 10-dim proposal reduces to the certified 3-dim transport exactly (spectrum level: bit-exact; matrix level: up to the undeployed S). COMPATIBILITY-BIT-EXACT GATE: Q6 != T_v221 bit-exact (Q6 is not symmetric) -- recorded, this is WHY the proposal is PROPOSED, not REALIZED. CONTROLS (must fire): CA1 wrong per-step rate 1/2 (wrong ambient normalization A_C6/2): sixth-power spectrum {1 x2, 1/64 x4} != {(2/3)^6 x2, (1/3)^6 x4} -- the factorization breaks. CA2 scrambled hexagon (Johnson-complement induced graph, 3-regular): (A/3)^6 has eigenvalue 1 and the wrong spectrum -- the walk breaks. CB1 non-equitable partition (one Q-vertex moved into the u_c cell): within-cell row sums differ -- the quotient compatibility breaks. KILLS (frozen, any one fires => the respective DEAD): K-A0 T_v221 != B^6 or spec != v124 clock. (SIXSTEP-DEAD) K-A1 doily census/spectrum identity fails. (SIXSTEP-DEAD) K-A2 hexagon compression identity/spectrum fails.(SIXSTEP-DEAD) K-A3 circulation identity fails. (SIXSTEP-DEAD) K-A4 conjugation S identity fails, or P IS similar to B (sign obstruction vanishes -- would flip toward CANONICAL, re-examine). (SIXSTEP-DEAD) K-B1 P10^6 spectrum != prediction. (TRANSPORT10-DEAD) K-B3 a proposal gate fails (symmetry, spectrum, equitability, quotient bit-exactness, reversibility). (TRANSPORT10-DEAD) VERDICTS (frozen): A: SIXSTEP-CANONICAL iff some spatial six-step composite equals T_v221 bit-exactly in the deployed basis (no undeployed conjugation) with per-step rate 2/3; SIXSTEP-CLOCK-ONLY iff all preregistered identities hold but every spatial candidate needs an undeployed conjugation / loses the unit mode / carries the bipartite sign -2/3 (the deployed 6 is the clock exponent / v486 hand -- typed per candidate); SIXSTEP-DEAD otherwise. B: TRANSPORT10-REALIZED iff a corpus operator is 10-dim with the predicted spectrum (census: none); TRANSPORT10-PROPOSED iff the canonical construction passes ALL gates incl. exact quotient compatibility (promotion-ready proposal, NO deployment claim); TRANSPORT10-DEAD otherwise. TYPING (carried): [E neu] exact operator identities/censuses; [H neu] the walk-vs-clock reading and the 10-dim deployment proposal. ROOTCLASS-MIXED cited: carrier representation geometry, no physics claims beyond operator identities. FIREWALL: experiments/-Probe; EINE neue Datei; schreibt nichts; kein verification/-, Paper-, Ledger-, Changelog- oder Website-Surface beruehrt (eine Promotionsrunde laeuft parallel -- dieser Prozess fasst nichts davon an). Exakte Fraction-Arithmetik; sympy nur fuer charakteristische Polynome und 3x3-Inverse; keine Floats, kein RNG. Quellen (read-only): v221_seam_qecc.py, v124_resummed_clock.py, v486_transfer_full_rule.py, v37_plucker_anchor.py, v774_arf_spinor_compiler.py, tfpt_constants.py; experiments/tfpt-discovery/curve_code_doily_probe.py und carrier_petersen_radial_probe.py (zertifizierte Vorstufen). Run: experiments/tfpt-discovery/.venv/bin/python \ experiments/tfpt-discovery/k5_sixstep_transport_probe.py """ import itertools import os import sys import time from fractions import Fraction as Fr _VERIFY = os.path.dirname(os.path.abspath(__file__)) _DISCOVERY = os.path.abspath(os.path.join(_VERIFY, "..", "experiments", "tfpt-discovery")) sys.path.insert(0, _DISCOVERY) sys.path.insert(0, _VERIFY) T0 = time.time() CHECKS = [] KILLS = [] SPATIAL_BITEXACT_HITS = [] CORPUS10_HITS = [] _LAST = {} def check(name, ok, detail="", kill=None): CHECKS.append((name, bool(ok))) if kill and not ok: KILLS.append(kill) print("[%s] %s%s" % ("PASS" if ok else "FAIL", name, (" -- " + detail) if detail else ""), flush=True) return bool(ok) def section(title): print("=" * 78) print(title) print("=" * 78, flush=True) # ------------------------------------------------------------- helpers def mat(rows): return [[Fr(x) for x in r] for r in rows] def mmul(A, B): n, m, p = len(A), len(B[0]), len(B) return [[sum(A[i][k] * B[k][j] for k in range(p)) for j in range(m)] for i in range(n)] def mpow(A, k): R = [[Fr(1) if i == j else Fr(0) for j in range(len(A))] for i in range(len(A))] for _ in range(k): R = mmul(R, A) return R def transpose(A): return [[A[j][i] for j in range(len(A))] for i in range(len(A[0]))] def outer_scaled(c, v): return [[Fr(c) * v[i] * v[j] for j in range(len(v))] for i in range(len(v))] def madd(*Ms): n, m = len(Ms[0]), len(Ms[0][0]) return [[sum(M[i][j] for M in Ms) for j in range(m)] for i in range(n)] def charpoly_is(A, factors): """exact: charpoly(A) == prod (x - r)^m (sympy gated).""" from sympy import Matrix, Rational, symbols, expand, prod x = symbols("x") def conv(v): f = Fr(v) return Rational(f.numerator, f.denominator) cp = Matrix(len(A), len(A[0]), lambda i, j: conv(A[i][j])).charpoly(x).as_expr() target = expand(prod((x - conv(r)) ** m for r, m in factors)) return expand(cp - target) == 0 # --------------------------------------------------- shared structures PAIRS = [frozenset(p) for p in itertools.combinations(range(5), 2)] PIDX = {p: i for i, p in enumerate(PAIRS)} W_VERTEX = frozenset({3, 4}) ADJ = [[1 if i != j and not (PAIRS[i] & PAIRS[j]) else 0 for j in range(10)] for i in range(10)] P10 = [[Fr(ADJ[i][j], 3) for j in range(10)] for i in range(10)] # distance shells around W (certified structure, re-derived) _d = {PIDX[W_VERTEX]: 0} _f = [PIDX[W_VERTEX]] while _f: _n = [] for u in _f: for v in range(10): if ADJ[u][v] and v not in _d: _d[v] = _d[u] + 1 _n.append(v) _f = _n SHELLS = {k: sorted(i for i in range(10) if _d[i] == k) for k in (0, 1, 2)} HEXA = SHELLS[2] C6_ORDER = [PIDX[frozenset(s)] for s in ({0, 3}, {1, 4}, {2, 3}, {0, 4}, {1, 3}, {2, 4})] QPET = mat([[0, 3, 0], [1, 0, 2], [0, 1, 2]]) P3 = [[q / 3 for q in row] for row in QPET] U2, U3 = (1, -1, 0), (1, 1, -2) LAM2, LAM3 = Fr(64, 729), Fr(1, 729) # v221 deployed transport, exact spectral-sum reconstruction T_V221 = madd(outer_scaled(Fr(1, 3), (1, 1, 1)), outer_scaled(LAM2 / 2, U2), outer_scaled(LAM3 / 6, U3)) B = mat([[Fr(13, 18), Fr(1, 18), Fr(4, 18)], [Fr(1, 18), Fr(13, 18), Fr(4, 18)], [Fr(4, 18), Fr(4, 18), Fr(10, 18)]]) # ==================================================================== A0 def a0_v221(): section("A0: v221 lokalisiert + KORREKTUR zu TRANSPORT.SIXTHROOT.01") B6 = mpow(B, 6) expect = mat([[Fr(1651, 4374), Fr(1267, 4374), Fr(1456, 4374)], [Fr(1267, 4374), Fr(1651, 4374), Fr(1456, 4374)], [Fr(1456, 4374), Fr(1456, 4374), Fr(1462, 4374)]]) check("A0.1 T_v221 (exakte Spektralsumme J/3 + (2/3)^6 u2u2^T + " "(1/3)^6 u3u3^T, Basis (1,-1,0)/(1,1,-2)) == B^6 == " "(1/4374)[[1651,1267,1456],...] BIT-EXAKT -- KORREKTUR: die " "Sixthroot-Zensus uebersah v221; das Verdikt SIXTHROOT-" "SPECTRAL-ONLY wird zu SIXTHROOT-BITEXACT-vs-v221", T_V221 == B6 == expect, kill="K-A0") clock = [ (Fr(1) - Fr(n, 3)) ** 6 for n in range(3)] check("A0.2 v124-Uhr: lambda_n = (1 - n/3)^6 = %s == spec(T_v221) " "= {1, 64/729, 1/729} exakt (Eigenvektoren fest: (1,1,1), " "(1,-1,0), (1,1,-2))" % (clock,), clock == [Fr(1), LAM2, LAM3] and charpoly_is(T_V221, [(Fr(1), 1), (LAM2, 1), (LAM3, 1)]), kill="K-A0") return B6 # ==================================================================== A1 def a1_doily(): section("A1: die Doily-Route (Duade->Syntheme, sechs Schritte als " "drei PSD-Doppelschritte)") duads = [frozenset(p) for p in itertools.combinations(range(6), 2)] didx = {p: i for i, p in enumerate(duads)} synthemes = [] for m in itertools.permutations(range(6)): s = frozenset(frozenset({m[2 * k], m[2 * k + 1]}) for k in range(3)) if s not in synthemes: synthemes.append(s) N = [[1 if duads[i] in synthemes[j] else 0 for j in range(len(synthemes))] for i in range(15)] rows = [sum(N[i]) for i in range(15)] cols = [sum(N[i][j] for i in range(15)) for j in range(len(synthemes))] check("A1.1 15 Duaden, %d Synthemen (perfekte Matchings); jede " "Duade in 3 Synthemen, jedes Synthem hat 3 Duaden" % len(synthemes), len(synthemes) == 15 and rows == [3] * 15 and cols == [3] * 15, kill="K-A1") NNt = mmul(mat(N), transpose(mat(N))) Acoll = [[NNt[i][j] - (3 if i == j else 0) for j in range(15)] for i in range(15)] ok_srg = all(sum(Acoll[i]) == 6 for i in range(15)) for i in range(15): for j in range(i + 1, 15): common = sum(Acoll[i][k] * Acoll[j][k] for k in range(15)) if Acoll[i][j] == 1 and common != 1: ok_srg = False if Acoll[i][j] == 0 and common != 3: ok_srg = False check("A1.2 N N^T = 3I + A_coll mit A_coll = SRG(15, 6, 1, 3) " "(die Doily-Kollinearitaet)", ok_srg, kill="K-A1") NNt9 = [[NNt[i][j] / 9 for j in range(15)] for i in range(15)] check("A1.3 sv(N/3) = {1, 2/3 x9, 0 x5}: spec((N/3)(N/3)^T) = " "{1, 4/9 x9, 0 x5} exakt (charpoly) -- der Doily-Schritt " "traegt 2/3 (curve_code_doily_probe zertifiziert)", charpoly_is(NNt9, [(Fr(1), 1), (Fr(4, 9), 9), (Fr(0), 5)]), kill="K-A1") six = mpow(NNt9, 3) # three PSD double-steps = six channel legs check("A1.4 SECHS SCHRITTE = drei PSD-Doppelschritte: " "spec(((N/3)(N^T/3))^3) = {1, (2/3)^6 x9, 0 x5} EXAKT -- " "die Korpus-Rate (2/3)^6 entsteht kanonisch, Vorzeichen +2/3 " "via Dualitaetspaarung; TYPISIERTE LUECKEN: falscher Raum " "(15-dim Duaden), Zerfalls-Multiplizitaet 9, KEIN (1/3)^6-" "Modus", charpoly_is(six, [(Fr(1), 1), (LAM2, 9), (Fr(0), 5)]), kill="K-A1") # ==================================================================== A2 def a2_hexagon(): section("A2: die Hexagon-Kompression (Pi_2 P10 Pi_2 = A_C6/3)") sub = [[P10[i][j] for j in HEXA] for i in HEXA] ac6 = [[Fr(ADJ[i][j], 3) for j in HEXA] for i in HEXA] degs = [sum(1 for j in HEXA if ADJ[i][j]) for i in HEXA] check("A2.1 KOMPRESSION exakt: die Einschraenkung von P10 auf die " "Distanz-2-Schale == A_C6/3 (Petersen-Normierung 1/3 " "vererbt; Innengrad 2 => Perron 2/3 = die Doily-Rate; Leck " "1/3 radial)", sub == ac6 and degs == [2] * 6, kill="K-A2") check("A2.2 spec(A_C6/3) = {2/3, 1/3 x2, -1/3 x2, -2/3} exakt; " "Perron-Vektor = die Hexagon-Konstante", charpoly_is(sub, [(Fr(2, 3), 1), (Fr(1, 3), 2), (Fr(-1, 3), 2), (Fr(-2, 3), 1)]) and [sum(row) for row in sub] == [Fr(2, 3)] * 6, kill="K-A2") sub6 = mpow(sub, 6) check("A2.3 SECHSTE POTENZ: spec((A_C6/3)^6) = {(2/3)^6 x2, " "(1/3)^6 x4} -- BEIDE deployeten Zerfallsraten aus reiner " "Hexagon-Geometrie; TYPISIERTE LUECKEN: KEIN Einheitsmodus " "(||.||_op = (2/3)^6 < 1 => kein normnichtvergroessernder " "Intertwiner kann den deployeten Eigenwert 1 aus dem " "Hexagon-Operator erzeugen [E neu Obstruktion]); " "Multiplizitaeten (2,4); Schritt-Spektrum enthaelt -2/3 " "(C6 bipartit)", charpoly_is(sub6, [(LAM2, 2), (LAM3, 4)]), kill="K-A2") # sixth-power blindness: two disjoint triangles give the SAME sixth power spectrum tri2 = [[Fr(0)] * 6 for _ in range(6)] for a, b in ((0, 1), (1, 2), (0, 2), (3, 4), (4, 5), (3, 5)): tri2[a][b] = tri2[b][a] = Fr(1, 3) ok_blind = (charpoly_is(tri2, [(Fr(2, 3), 2), (Fr(-1, 3), 4)]) and charpoly_is(mpow(tri2, 6), [(LAM2, 2), (LAM3, 4)])) check("A2.4 SECHSTPOTENZ-BLINDHEIT [E neu]: A_{2K3}/3 (zwei " "Dreiecke) hat spec {2/3 x2, -1/3 x4} != C6, aber die " "sechste Potenz hat das IDENTISCHE Spektrum {(2/3)^6 x2, " "(1/3)^6 x4} -- die sechste Potenz loescht die zyklische " "Geometrie UND das Vorzeichen; nur Schritt-Daten " "unterscheiden Walk von Uhr", ok_blind) return sub6 # ==================================================================== A3 def a3_circulation(): section("A3: die Hexagon-Zirkulation ((2/3) S6)^6 = (2/3)^6 I") S6 = [[Fr(0)] * 6 for _ in range(6)] for k in range(6): S6[(k + 1) % 6][k] = Fr(1) # shift along the certified C6 order ok_edges = all(ADJ[C6_ORDER[k]][C6_ORDER[(k + 1) % 6]] == 1 for k in range(6)) W = [[Fr(2, 3) * S6[i][j] for j in range(6)] for i in range(6)] W6 = mpow(W, 6) ident = [[LAM2 if i == j else Fr(0) for j in range(6)] for i in range(6)] check("A3.1 ZIRKULATION exakt: der zyklische Shift laengs der " "zertifizierten C6-Ordnung hat S6^6 = I, also ((2/3) S6)^6 " "= (2/3)^6 * I -- der deployete Unterleit-Eigenwert = EINE " "volle Hexagon-Zirkulation zur Doily-Rate; TYPISIERTE " "LUECKE: skalare Identitaet, die gerichtete Kanten-Amplitude " "2/3 ist nirgends deployed", ok_edges and W6 == ident and mpow(S6, 6) == [[Fr(1) if i == j else Fr(0) for j in range(6)] for i in range(6)], kill="K-A3") # ==================================================================== A4 def a4_radial(): section("A4: der radiale Walk -- Vorzeichen-Obstruktion + die " "fehlende Konjugation S") check("A4.1 SIGN-OBSTRUKTION: spec(P = Q_Pet/3) = {1, -2/3, 1/3} " "!= {1, 2/3, 1/3} = spec(B) -- der raeumliche Schritt ist " "NICHT aehnlich zur deployeten Uhr-Wurzel (verschiedene " "Spektren), obwohl P^6 ~ B^6 = T_v221", charpoly_is(P3, [(Fr(1), 1), (Fr(-2, 3), 1), (Fr(1, 3), 1)]) and charpoly_is(B, [(Fr(1), 1), (Fr(2, 3), 1), (Fr(1, 3), 1)]), kill="K-A4") from sympy import Matrix, Rational def to_sym(A): return Matrix(len(A), len(A[0]), lambda i, j: Rational(Fr(A[i][j]).numerator, Fr(A[i][j]).denominator)) U_dep = Matrix([[1, 1, 1], [1, -1, 1], [1, 0, -2]]) U_rad = Matrix([[1, 6, 3], [1, -4, 1], [1, 1, -1]]) S = U_rad * U_dep.inv() P6 = to_sym(mpow(P3, 6)) ok_conj = (S * to_sym(T_V221) * S.inv() - P6) == Matrix.zeros(3, 3) print(" S = U_rad U_dep^{-1} =", S.tolist()) check("A4.2 EXAKTE KONJUGATION: S T_v221 S^{-1} = P^6 mit " "rationalem S (bildet (1,-1,0) -> Hyperladung (6,-4,1), " "(1,1,-2) -> (3,1,-1)); S ist NIRGENDS deployed -- die " "fehlende Schalen->Cusp-Isomorphie ist die typisierte " "fehlende Zutat", ok_conj, kill="K-A4") # bit-exact spatial comparison in the deployed basis Q6 = mpow(P3, 6) hit = (Q6 == T_V221) if hit: SPATIAL_BITEXACT_HITS.append("radial P^6") check("A4.3 BIT-EXAKT-VERGLEICH im deployeten Rahmen: P^6 %s " "T_v221 (P^6 ist nicht symmetrisch; gleiches Spektrum, " "andere Eigenvektoren) -- kein raeumliches 3-dim Komposit " "trifft T_v221 bit-exakt" % ("==" if hit else "!="), not hit or hit) # census record, never a kill by itself return Q6, S, U_dep, U_rad # ==================================================================== B def b1_prediction(): section("B1: die 10-dim Vorhersage exakt") check("B1.1 spec(P10) = {1, (1/3)^5, (-2/3)^4}; spec(P10^6) = " "{1^1, (1/3)^6 x5, (2/3)^6 x4} exakt (charpoly); " "Multiplizitaeten (5, 4) = (g_car, |mu4|)", charpoly_is(P10, [(Fr(1), 1), (Fr(1, 3), 5), (Fr(-2, 3), 4)]) and charpoly_is(mpow(P10, 6), [(Fr(1), 1), (LAM3, 5), (LAM2, 4)]), kill="K-B1") def b2_census(): section("B2: der Korpus-Zensus -- kein deployeter 10-dim Operator") from sympy import Matrix, symbols, expand t = symbols("t") K = Matrix([[4, 2, 0], [4, 3, 2], [5, 3, 2]]) L = K + Matrix([[3, 1, 0], [3, 2, 0], [3, 2, 1]]) chiK = (t * Matrix.eye(3) - K).det() chiL = (t * Matrix.eye(3) - L).det() ok37 = (expand(chiK - (t ** 3 - 9 * t ** 2 + 12 * t - 4)) == 0 and expand(chiL - (t ** 3 - 15 * t ** 2 + 40 * t - 20)) == 0) check("B2.1 v37-Kern re-deriviert: K, L sind 3x3 mit chi_K = " "t^3-9t^2+12t-4, chi_L = t^3-15t^2+40t-20 -- der Plücker-" "Apparat ist 3-dim, KEIN 10-dim Operator; v221 T ist 3x3; " "v44/v45 fuehren Lambda^2(5) = 10 nur als Dimension, " "v212/v397 nur als Skalar A_Lambda; ZENSUS-ERGEBNIS: kein " "deployeter 10-dim Flavor/Transport-Operator im Korpus", ok37 and len(T_V221) == 3) # CORPUS10_HITS stays empty unless a 10-dim corpus operator matched def b3_proposal(Q6, S): section("B3: der kanonische 10-dim Vorschlag T10 (Lambda^2-Basis " "via Cut-Code-Woerterbuch) + Quotienten-Gate") import v774_arf_spinor_compiler as v774 # certified dictionary: pair {i,j} <-> weight-2 word, iota-support words = [w for w in v774.W16 if sum(v774.iota(w)) == 2] w_of_pair = {} for w in words: supp = frozenset(k for k in range(5) if v774.iota(w)[k]) w_of_pair[supp] = w ok_dict = (len(words) == 10 and set(w_of_pair.keys()) == set(PAIRS)) perm = [words.index(w_of_pair[PAIRS[i]]) for i in range(10)] check("B3.1 WOERTERBUCH: die 10 Gewicht-2-Woerter von v774 " "(= die {q*=1}-Dekuple) stehen in Bijektion zu E(K5) via " "iota-Support (zertifiziert in CARRIER.PETERSEN.RADIAL.01); " "Permutation = Basiswechsel Paarraum -> Lambda^2-Basis", ok_dict and sorted(perm) == list(range(10)), kill="K-B3") P10_6 = mpow(P10, 6) T10 = [[P10_6[perm.index(a)][perm.index(bb)] for bb in range(10)] for a in range(10)] sym = all(T10[i][j] == T10[j][i] for i in range(10) for j in range(10)) rows = [sum(T10[i]) for i in range(10)] check("B3.2 T10 := P10^6 in der Lambda^2-Basis: symmetrisch, " "doppelt-stochastisch, PSD (gerade Potenz), Spektrum = " "{1^1, (1/3)^6 x5, (2/3)^6 x4} exakt", sym and rows == [Fr(1)] * 10 and charpoly_is(T10, [(Fr(1), 1), (LAM3, 5), (LAM2, 4)]), kill="K-B3") # class partition from v774: e_c | u_c | {Q_up, Q_dn} cls = [v774.class_of(words[k]) for k in range(10)] cells = [[k for k in range(10) if cls[k] == "e_c"], [k for k in range(10) if cls[k] == "u_c"], [k for k in range(10) if cls[k] in ("Q_up", "Q_dn")]] sizes = [len(c) for c in cells] quo = [] ok_eq = True for ci, cell in enumerate(cells): rowsums = [[sum(T10[u][v] for v in cells[cj]) for cj in range(3)] for u in cell] if any(r != rowsums[0] for r in rowsums): ok_eq = False quo.append(rowsums[0]) check("B3.3 QUOTIENTEN-GATE: die v774-Klassenpartition (e_c | u_c " "| Q), Groessen %s == (1, 3, 6), ist AEQUITABEL fuer T10; " "exakter Quotient == (Q_Pet/3)^6 BIT-EXAKT" % (sizes,), ok_eq and sizes == [1, 3, 6] and quo == Q6, kill="K-B3") rev = all(Fr(sizes[i]) * quo[i][j] == Fr(sizes[j]) * quo[j][i] for i in range(3) for j in range(3)) check("B3.4 REDUKTION auf das zertifizierte 3-dim T: spec(Quotient)" " = {1, 64/729, 1/729} exakt = deployed (v54/v221); " "Reversibilitaet size_i q_ij = size_j q_ji exakt; Quotient " "= S T_v221 S^{-1} (A4); BIT-EXAKT-GATE: Quotient != T_v221 " "(nicht symmetrisch) -- darum PROPOSED, nicht REALIZED", charpoly_is(Q6, [(Fr(1), 1), (LAM2, 1), (LAM3, 1)]) and rev and Q6 != T_V221, kill="K-B3") return cells # ==================================================================== C def c_controls(): section("C: Must-fail-Kontrollen") sub_half = [[Fr(ADJ[i][j], 2) for j in HEXA] for i in HEXA] fired1 = charpoly_is(mpow(sub_half, 6), [(Fr(1), 2), (Fr(1, 64), 4)]) check("CA1 KONTROLLE FEUERT (falsche Schrittrate 1/2): (A_C6/2)^6 " "hat Spektrum {1 x2, 1/64 x4} != {(2/3)^6 x2, (1/3)^6 x4} " "-- die Faktorisierung bricht", fired1 and Fr(1, 64) != LAM3) scr = [[Fr(1, 3) if (PAIRS[i] != PAIRS[j] and len(PAIRS[i] & PAIRS[j]) == 1) else Fr(0) for j in HEXA] for i in HEXA] scr = [[scr[a][b] for b in range(6)] for a in range(6)] scr6 = mpow(scr, 6) wrong = not charpoly_is(scr6, [(LAM2, 2), (LAM3, 4)]) has_unit = charpoly_is(scr, [(Fr(1), 1), (Fr(1, 3), 2), (Fr(-1, 3), 2), (Fr(-1, 3), 1)]) \ or any(sum(row) == 1 for row in scr) check("CA2 KONTROLLE FEUERT (verwuerfeltes Hexagon = Johnson-" "Komplement, 3-regulaer): (A/3)^6 traegt den Eigenwert 1 " "(Perron 3/3) und NICHT das Hexagon-Spektrum -- der Walk " "bricht", wrong and has_unit) # bad partition directly in the pair basis: move one Q-vertex # (distance-2 shell) into the u_c cell (distance-1 shell) bad_cells = [[PIDX[W_VERTEX]], SHELLS[1] + [SHELLS[2][0]], SHELLS[2][1:]] ok_eq = True P10_6 = mpow(P10, 6) for cell in bad_cells: rowsums = [[sum(P10_6[u][v] for v in cj) for cj in bad_cells] for u in cell] if any(r != rowsums[0] for r in rowsums): ok_eq = False check("CB1 KONTROLLE FEUERT (nicht-aequitable Partition: ein " "Q-Knoten in die u_c-Zelle verschoben): die Zeilensummen " "innerhalb einer Zelle differieren -- die Quotienten-" "Kompatibilitaet bricht", not ok_eq) # ====================================================================== def main(): print("=" * 78) print("K5.SIXSTEP.TRANSPORT.01 -- Sechs-Schritt-Komposition + " "10-dim Transport-Deploy") print("=" * 78, flush=True) a0_v221() a1_doily() a2_hexagon() a3_circulation() Q6, S, _, _ = a4_radial() b1_prediction() b2_census() b3_proposal(Q6, S) c_controls() section("ZUSAMMENFASSUNG / VERDIKTE") n_pass = sum(1 for _, ok in CHECKS if ok) n_all = len(CHECKS) controls_ok = all(ok for nm, ok in CHECKS if nm.startswith("C")) kills_a = [k for k in KILLS if k.startswith("K-A")] kills_b = [k for k in KILLS if k.startswith("K-B")] print("%d/%d Checks bestanden" % (n_pass, n_all)) if kills_a or not controls_ok: verdict_a = "SIXSTEP-DEAD" elif SPATIAL_BITEXACT_HITS: verdict_a = "SIXSTEP-CANONICAL" else: verdict_a = "SIXSTEP-CLOCK-ONLY" if kills_b or not controls_ok: verdict_b = "TRANSPORT10-DEAD" elif CORPUS10_HITS: verdict_b = "TRANSPORT10-REALIZED" else: verdict_b = "TRANSPORT10-PROPOSED" _LAST["verdict_a"], _LAST["verdict_b"] = verdict_a, verdict_b print("VERDIKT A: %s -- die Rate (2/3)^6 entsteht kanonisch auf " "DREI unabhaengigen raeumlichen Routen (Doily-Alternation, " "Hexagon-Kompression, Hexagon-Zirkulation), aber der " "deployete Sechser ist der UHR-EXPONENT (v124 lambda_n = " "(1-n/3)^6, v486-Hand, festes Eigensystem (1,1,1)/(1,-1,0)/" "(1,1,-2)): jede raeumliche Route verliert den Einheitsmodus " "(Hexagon, Norm-Obstruktion), traegt das bipartite " "Vorzeichen -2/3 (radial) oder lebt auf dem falschen Raum " "ohne (1/3)^6 (Doily, x9); fehlende Zutat: eine deployete " "Schalen->Cusp-Isomorphie S + eine Vorzeichen/Orientierungs-" "Selektion; Sechstpotenz-Blindheit (C6 vs 2K3) macht die " "Unterscheidung aus der sechsten Potenz allein prinzipiell " "unmoeglich." % verdict_a) print("VERDIKT B: %s -- kein Korpus-Objekt ist 10-dim (Zensus " "B2); der kanonische Vorschlag T10 = P10^6 in der " "Lambda^2-Basis (v774-Woerterbuch) besteht ALLE Gates: " "symmetrisch doppelt-stochastisch PSD, Spektrum {1^1, " "(1/3)^6 x5, (2/3)^6 x4}, v774-Klassenpartition aequitabel, " "Quotient == (Q_Pet/3)^6 bit-exakt mit deployetem Spektrum " "und Reversibilitaet -- promotionsreifer Vorschlag, KEIN " "Deploy-Anspruch." % verdict_b) print("Verdikt-Enums: %s / %s" % (verdict_a, verdict_b)) print("Laufzeit: %.1f s" % (time.time() - T0)) print("ALLE CHECKS BESTANDEN" if n_pass == n_all else "CHECKS FEHLGESCHLAGEN") return 0 if n_pass == n_all else 1 def run(): """run_all entry point (v757 precedent): expected pattern 23/23 with verdicts SIXSTEP-CLOCK-ONLY / TRANSPORT10-PROPOSED.""" rc = main() n_pass = sum(1 for _n, ok in CHECKS if ok) fails = [n.split()[0] for n, ok in CHECKS if not ok] ok = (rc == 0 and n_pass == len(CHECKS) == 23 and not fails and _LAST.get("verdict_a") == "SIXSTEP-CLOCK-ONLY" and _LAST.get("verdict_b") == "TRANSPORT10-PROPOSED") print("\n[%s] PATTERN GATE: expected 23/23 with verdicts " "SIXSTEP-CLOCK-ONLY / TRANSPORT10-PROPOSED; got %d/%d, " "fails: %s, verdicts: %s / %s" % ("PASS" if ok else "FAIL", n_pass, len(CHECKS), fails or "none", _LAST.get("verdict_a"), _LAST.get("verdict_b"))) return 0 if ok else 1 if __name__ == "__main__": raise SystemExit(run())