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v898_kms_schur_mixing.py
verification/v898_kms_schur_mixing.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
r"""v898 -- SEAM.CFIN.KMSMIX.01 + SEAM.CFIN.SCHURMIX.01: THE CHANNEL-MIXING STATE THE BLOCK WICK FUNCTOR AWAITS -- the C6-covariant channel-mixing KMS state EXISTS and the Schur/Feshbach boundary elimination GENERATES all 10 carrier duads exactly, ONE module from one probe (30/30 checks, zero fails, verdict KMSMIX-MEASURED [KMSMIX-FOUND(u=1, t=1/8, beta=1), SCHURMIX-GENERATES(10/10 carrier duads, C6-covariant, J-direction, Pf4 signs canonical), RP-THETA-OPEN]; discovery probe kms_schur_mixing_probe.py, round 55, 2026-08-09, re-run identically at promotion, embedded BYTE-EXACT and executed verbatim, ~2 s). THE V896 DEMAND ('a physical channel-mixing mechanism realizing the block functor's value level') now has a CONSTRUCTED CANDIDATE STATE. (1) THE PARAMETRIZATION (exact orbit walks): the hermitian O16-commutant on the deployed 16-dim one-particle space has dimension 112 = 62 sym + 50 antisym (isotypic mults [10,0,2,2,2,0], sum m^2 ward); the Majorana-compatible Hamiltonians K = i h live in the 50-dim antisymmetric slice = 33 cross-block (EXACTLY the v896 covariant block space; the C<->B mixing block T spans 24) + 17 channel-diagonal, with exactly 2 forced zeros (the diagonal of the transposed {4,5} block). (2) THE KMS ROUTE: the FIRST point of the frozen grid, h(u=1, t=1/8) = -(A16_dep + (1/8) A_int) at beta = 1, passes ALL gates -- CAR strict (smax 0.668 < 1), exact C6 block covariance with the forced zeros, all 15 duad cross-blocks at the frozen floor, the q*/sheet grading carried EXACTLY (Ad(Gamma16)-odd support = the 5 vacuum blocks 5/5 FULL, even off-diagonal = the 10 carrier blocks 10/10 FULL), and all 15 block Wick monomials nonzero with the CANONICAL Pf4 sign pattern of the v896 block functor G_c; ROBUST at beta = 2 (all gates again); the per-orbit ray anatomy shows the tan/KMS dressing itself MIXES (odd powers of h light duads outside the seeded orbit -- the Schur mechanism operating inside the KMS route). (3) THE SCHUR ROUTE (EXACT sympy rationals): boundary elimination of the coupled diagonal state A_full = [[kappa A_CC, t V], [-t V^T, m J3]] (kappa = m = 1/2, t = 1/20; validity PROVEN exactly: ||A_full|| <= 1/2 + sqrt(15)/20 < 1) gives the EXACT identity A_eff = kappa A_CC + (t^2 m/(1-m^2)) V J3 V^T, and the census matrix S = V J3 V^T deposits NONZERO correlation on ALL 10 carrier duads (C6-covariant, uniform 3J-block: B = 3J on every carrier duad, pure J on the transposed {4,5} exactly as covariance allows, per-edge Pf4 signs MATCHING the canonical G_c) -- the SAME Schur/Feshbach elimination that creates the RH port creates the carrier channel mixing from a BARE DIAGONAL state: on both fronts (RH port, Wick functor) the real correlation lives in the ELIMINATED boundary, not the bare bulk. (4) THE FROZEN PREDICTION TABLE: the 15 block-correlation signatures of the winner (zero/nonzero pattern, canonical-unit coordinates and signs, per-edge Pf4 sign, C6 orbit, q* class) are printed as the REGISTERED prediction -- any physical seam state realizing the block functor must reproduce this pattern. (5) HONEST RP: NO spatial/OS reflection theta is deployed on the 16-dim one-particle space (v155 premise-only, v160 none, v424/v426/v440 = 8-dim collar dictionary); the Majorana real structure Theta_0 satisfies the deployed dictionary AUTOMATICALLY (conj(C_beta) = I - C_beta measured at 7.8e-61) but is particle-hole, NOT spatial; the OS-positivity under a SPATIAL theta is the NAMED OPEN CHECK RP-THETA-OPEN. CONTROLS FIRE: permuted roles break covariance (defect 0.096), grading commutation (16) and the edge law on EXACTLY 8/15; the bare diagonal state (t = 0) has 0/15 KMS cross-blocks and 0/10 Schur carrier duads. THE [O] PREMISE IS UNMOVED: these are CANDIDATE states and frozen signatures -- whether the ACTUAL seam realizes any of them is untouched; no marker moves. NO RH claim (compiler side; no primes, no zeros). Exact integer / sympy rational arithmetic in every structural decision; the only non-exact step is the certified-precision (mpmath dps 60) KMS transcendental map with FROZEN two-sided decision thresholds (nonzero >= 1e-8, zero <= 1e-40; ambiguity kills). Deterministic, no RNG. Python-only per GATE.WOLFRAM.02.
PROVENANCE: discovery probe kms_schur_mixing_probe.py (30/30,
KMSMIX-MEASURED [KMSMIX-FOUND(u=1, t=1/8, beta=1),
SCHURMIX-GENERATES(10/10), RP-THETA-OPEN], SPEC v1 frozen
2026-08-09 pre-run, no amendments; frozen expectations pre-derived
by hand before the freeze), round 55, 2026-08-09, re-run
identically at promotion. ROUND-31 EMBEDDING CONVENTION: frozen
source embedded BYTE-EXACT, executed verbatim in an isolated
namespace; printed spec SHA reproduces; byte-equality ward vs
experiments/tfpt-discovery/ inside the pattern gate. The probe
consumes tfpt_constants (READ-ONLY) and rebuilds the v880/v888/
v113/v896 machinery inline.
FIREWALL: no zeros, no prime-table oracles (AST firewall inside
the probe); NO physics-realization claim -- the [O] premise (the
boundary grammar IS a self-hosting Wick pair compiler) stays [O];
RP-THETA-OPEN is a named open check, not a gate. NO RH claim.
"""
import contextlib
import io
import os
import re
import sys
import time
import types
_HERE = os.path.dirname(os.path.abspath(__file__))
if _HERE not in sys.path:
sys.path.insert(0, _HERE)
# ------------- frozen probe source kms_schur_mixing_probe (embedded BYTE-EXACT, raw string)
_SRC_0 = r'''
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
r"""kms_schur_mixing_probe -- SEAM.CFIN.KMSMIX.01 + SEAM.CFIN.SCHURMIX.01
(EXPLORATION ONLY, experiments/; round 55, reviewer priority 5: the
PHYSICAL MECHANISM the block Wick functor awaits. Round 52
(wick_block_functor_probe) constructed the canonical C6-covariant
block object G_c on the deployed 16-dim one-particle space and
MEASURED the deployed seam vacuum SEAM-DIAGONAL -- the functor's
value level is a pure candidate awaiting a channel-mixing STATE.
THIS probe constructs that state via the two reviewer routes: (M1)
the fermionic KMS state of a C6-invariant mixing one-particle
Hamiltonian, and (M2) the Schur/Feshbach dressing -- boundary
elimination of a coupled diagonal state -- the SAME operation that
creates the RH port.)
FEASIBILITY / REDUNDANCY CHECK (done against the corpus FIRST,
2026-08-09 -- read end to end: wick_block_functor_probe (round 52),
wick_mixing_covariance_probe (round 51), seam_wick_functor_probe
(round 50), v113/v155/v160/v161, v424/v426/v440, v880/v888):
* round 52 froze the canonical block candidate G_c (all 15
cross-blocks at FLOOR = 1/200, C6-covariant, CAR-positive, chi
sign law) and typed the deployed seam SEAM-DIAGONAL; it built NO
state-generating mechanism (no Hamiltonian, no KMS, no Schur).
* v426/v440 deploy the KMS/RP dictionary (C_beta = (I+e^{beta
K})^{-1}; (LTO-RP)/BW <=> Theta K Theta = -K; Theta C_beta Theta
= I - C_beta) on an 8-dim COLLAR TOY space (4 marks x 2 sides)
-- NOT on the deployed 16-dim D5+A3 one-particle space; v155
carries reflection positivity only as the recorded [P] premise
(no operator); v160 has no reflection operator at all.
* NOTHING in the corpus parametrizes C6-invariant one-particle
Hamiltonians on the 16-dim space, computes their KMS states, or
asks whether boundary elimination (Schur) of the DEPLOYED
diagonal state generates carrier cross-blocks. That is exactly
this probe.
CAR CONVENTION (FROZEN, v113 / rounds 50-52): 16-dim real Majorana
one-particle space; channels CH(0) = Majoranas 10..15 (A3 boundary
block B, dim 6), CH(i) = {2(i-1), 2(i-1)+1} for i = 1..5 (D5 slot
pairs; carrier block C = indices 0..9). A quasifree CAR covariance
is G = (I + iA)/2 with A REAL ANTISYMMETRIC; CAR positivity 0 <= G
<= I <=> spec-norm(A) <= 1. A quadratic Majorana Hamiltonian has
one-particle operator K = i h with h REAL ANTISYMMETRIC (K
hermitian, K^T = -K); the beta-KMS covariance is C_beta = (I +
e^{beta K})^{-1}, equivalently A_beta = -tan(beta h / 2) (exact
identity: iA = 2C - I = -tanh(beta K/2), tanh(i x) = i tan(x)) --
AUTOMATICALLY 0 < C_beta < I (singular values tanh(beta s/2) < 1).
C6 acts by the round-50 lift O16 (slot pairs as units by pi = (0)
(a b)(c d e), identity on the A3 block); Gamma16 = (-I on C) (+)
(+I on B) is the q* grading operator (round 52).
THE TWO FROZEN CONSTRUCTIONS:
M1 THE KMS ROUTE. Parametrize K = i h = [[K_C, T],[T*, K_B]]
with h in the EXACT real-antisymmetric O16-commutant (the
Majorana-compatible slice of the hermitian commutant; both
dimensions measured by exact signed orbit walks: hermitian side
expected 112 = 62 sym + 50 antisym, cross/mixing part 33 =
round-52 block space, of which the C<->B mixing block T spans
24). FROZEN scan family (coarse grid + natural rays -- no
fitting):
h(u, t) = -( u * A16_dep + t * A_int ),
where A16_dep = (+)_8 J is the DEPLOYED diagonal kernel
(v113/v155 hull) and A_int is the round-52 canonical integer
covariant cross matrix (units [I2;I2;I2] / I2 / J, orientation-
propagated). The overall sign -1 is the FROZEN convention
aligning the beta -> 0+ linearization A ~ (beta/2)(u A16_dep +
t A_int) with the canonical orientation of G_c (structural
rule, frozen before first run; the + branch is reported in the
anatomy). Grid (frozen order, beta = 1 primary): (u, t) in
[(1, 1/8), (1, 1/4), (1, 1/2), (1, 1), (0, 1/4)]; winner = the
FIRST grid point passing all gates; robustness re-test of the
winner at beta = 2 (report, not gate). Gates per candidate:
(G1) CAR: 0 < C < I strict (theorem; measured ward);
(G2) exact C6 block covariance + the round-51/52 forced
zeros on the diagonal of the transposed {a,b} block;
(G3) all 15 duad cross-blocks nonzero at the frozen floor;
(G4) the q*/sheet grading carried (round-52 test: [Gamma16,
O16] = 0, edge law on all 15 messages, Ad(Gamma16)-odd
support = the 5 vacuum blocks 5/5 FULL, even off-diag =
the 10 carrier blocks 10/10 FULL);
(G5) the canonical Pfaffian/chi structure (round-52 test):
Iota/3-compressed Ahat, all 15 per-edge Pf4 nonzero,
all 15 block Wick monomials w_blk(M) = sgn(M) prod Pf4
nonzero, interleaving ward Pf(Ahat|_M) == prod Pf4, and
the SIGN MATCH sign(w_blk) == sign(w_blk of the
canonical G_c) on all 15 matchings.
TYPED: KMSMIX-FOUND(u, t, beta) / KMSMIX-OBSTRUCTED(per-point
failing gates). ANATOMY (report): per-orbit rays (u = 1, one
edge orbit of A_int at t = 1/4) -- which duads each ray LIGHTS
UP under the tan dressing (the KMS map itself mixes: odd powers
of h generate blocks outside the seeded orbit -- the Schur
mechanism inside the KMS route); the + sign branch.
M1(iv) REFLECTION POSITIVITY (typed honestly). The corpus
answer, measured by reading: NO canonical spatial/OS reflection
theta is deployed on the 16-dim one-particle space (v155:
premise only; v160: none; v424/v426/v440: the dictionary Theta
K Theta = -K, Theta C_beta Theta = I - C_beta -- deployed on an
8-dim collar toy, not on D5+A3). What CAN be tested: the
MAJORANA REAL STRUCTURE Theta_0 = complex conjugation in the
deployed Majorana basis is antiunitary, commutes with O16 and
Gamma16, and satisfies the deployed v426/v440 dictionary
AUTOMATICALLY for every K = i h (h real): Theta_0 K Theta_0 =
conj(K) = -K (BW form) and conj(C_beta) = I - C_beta (the v440
reflection relation) -- both verified on the winner. The
OS-positivity of the two-point block under a SPATIAL seam
reflection is typed as the NAMED OPEN CHECK RP-THETA-OPEN (no
deployed theta; the check awaits one). NOT a gate.
M2 THE SCHUR ROUTE (the deep cross-connection). Parent state:
the deployed DIAGONAL kernel with a C6-invariant carrier-to-
boundary coupling (the T-block of M1's parametrization, i.e.
the vacuum blocks of A_int: V = A_int[C, B]):
A_full = [[kappa A_CC, t V], [-t V^T, m J3]],
frozen kappa = m = 1/2 (the same KMS-mixing scale on both
sides; boundary invertible), t = 1/20 (validity PROVEN exactly:
||A_full|| <= max(kappa, m) + t * sqrt(lam_max(V V^T)) < 1 by
the triangle inequality + exact eigenvalue). Boundary
elimination (Schur/Feshbach -- the SAME operation that creates
the RH port): C_eff = C_CC - C_CB C_BB^{-1} C_BC. EXACT
consequence (sympy rationals):
A_eff = kappa A_CC + (t^2 m / (1 - m^2)) * S,
S := V J3 V^T (the boundary-mediated census matrix),
plus the pure-boundary pseudo-inverse variant (C_BB^+ = C_BB
for the deployed projection): A_eff+ = A_CC - (t^2/4) S (sign
flip; report). MEASURE exactly: the 10 carrier duad blocks of
S (nonzero census, C6 covariance, unit decomposition a*I2 +
b*J + traceless-sym, per-edge Pf4 signs vs canonical, {a,b}
compatibility). TYPED: SCHURMIX-GENERATES(census) /
SCHURMIX-DIAGONAL. If GENERATES: print the unified reading --
on both fronts (RH port, Wick functor) the real correlation
lives in the ELIMINATED boundary, not the bare bulk.
M3 THE 15-SIGNATURE FREEZE (deliverable): the 15 block-correlation
signatures of the best M1 candidate -- zero/nonzero pattern,
canonical-unit coordinates and signs, per-edge Pf4 sign, C6
orbit, q* class -- printed as a FROZEN prediction table (the
reviewer's 'freeze before any simulation' demand): any physical
seam state realizing the block functor must reproduce this
pattern.
C CONTROLS (must fire; frozen fire rules):
C1 PERMUTED ROLES (round-52 rule): conjugating pi by the
carrier transposition (a, c) and lifting: the covariance of
the M1 winner breaks (defect >= NZ_FLOOR); the wrong vacuum
grading Gamma' does NOT commute with the deployed O16; the
wrong vacuum Arf label breaks the message edge law on
EXACTLY 8 of 15.
C2 THE BARE DIAGONAL STATE: t = 0 (KMS of the uncoupled
deployed kernel): 0/15 cross-blocks at the floor, all 15
Wick monomials vanish (fails G3 + G5); Schur with t = 0:
A_eff = kappa A_CC exactly, 0/10 carrier cross-blocks.
FROZEN NUMERICAL PROTOCOL (the ONLY non-exact step is the
transcendental KMS map): exact integer / sympy rational arithmetic
in every structural decision (commutant walks, orbit census,
grading wiring, the ENTIRE M2 route, controls C1-wiring/C2-Schur);
the KMS map is evaluated by certified-precision mpmath at DPS =
60 via the exact hermitian eigendecomposition of K = i h (C_beta
= Q diag(1/(1 + e^{beta lam})) Q^H -- no large-exponential loss),
with the FROZEN two-sided decision thresholds: a quantity is
NONZERO iff |x| >= NZ_FLOOR = 1e-8, ZERO iff |x| <= ZTOL = 1e-40
(structural zeros and exact identities land < ~1e-58 at 60
digits; genuine grid values are >= ~1e-6); any decided quantity
in the open gap fires K2 (ambiguous -- the honest failure). Pf4
nonzero floor PF_FLOOR = 1e-16 (quadratic in block scale); Wick
monomial floor PF_FLOOR^3. No RNG, no fits.
KILLS (any one fires => typed gap):
K0 AST firewall / setup ward breaks -> PIPELINE-BROKEN
K1 commutant walk / isotypic ward incoherent -> COMMUTANT-BROKEN
K2 KMS route ward breaks (realness, antisymmetry,
covariance, CAR, threshold ambiguity) -> KMSROUTE-BROKEN
K3 Schur route exact algebra breaks -> SCHURROUTE-BROKEN
K5 freeze table incoherent with the winner -> FREEZE-BROKEN
K7 a control does not fire -> CONTROL-DEAD
VERDICT (frozen enum): KMSMIX-MEASURED [typed KMSMIX-FOUND(params)
/ KMSMIX-OBSTRUCTED(<gates>), SCHURMIX-GENERATES(<census>) /
SCHURMIX-DIAGONAL, RP-THETA-OPEN / RP-TESTED(<theta>)] (no kills;
honest OBSTRUCTED / DIAGONAL are first-class outcomes) /
KMSMIX-PARTIAL [kill tokens] / PIPELINE-BROKEN / CONTROL-DEAD.
Exit 0 iff all checks pass and no kill fired; else 1.
FIREWALL: experiments/ probe; EXPLORATION ONLY -- writes nothing
but stdout; no verification/, paper, ledger, changelog or website
surface; no .md, no commits. AST firewall: banned identifiers
zetazero / nzeros / primerange / isprime / primepi / nextprime /
prevprime (self-scan). NO physics-realization claim: the [O]
premise (the boundary grammar IS a self-hosting Wick pair
compiler) stays [O]; this probe constructs CANDIDATE states and
freezes signatures -- whether the ACTUAL seam realizes any of them
is untouched; no marker moves.
SPEC v2 AMENDMENTS (fail-first preserved): none at freeze; any
post-run amendment is documented here with the fail-first output
preserved. (Frozen expectations pre-derived by hand and cross-
checked against an independent scratch derivation of the walk
counts (52 + 10 orbits, 2 forced), the isotypic mults
[10,0,2,2,2,0], the exact Schur identity, and lam_max(V V^T) = 15
BEFORE the freeze; the probe re-measures all of them.)
Sources (read-only, machinery rebuilt inline): wick_block_functor_
probe (round 52: 16-dim layout, O16, A_int frozen rule, Gamma16,
chi/qsign/sgn, Iota/3 compression, FLOOR), wick_mixing_covariance_
probe (round 51: CAR conventions, orbit walk), v113 (Majorana CAR,
JW kernel, A16 hull), v155/v160 (RP premise census), v424/v426/
v440 (the deployed KMS/RP dictionary; 8-dim collar), v880/v888
(q*, duads, phi), tfpt_constants (N_fam, g_car).
Run:
experiments/tfpt-discovery/.venv/bin/python \
experiments/tfpt-discovery/kms_schur_mixing_probe.py
"""
import ast
import hashlib
import itertools
import os
import sys
import time
import mpmath as mp
import sympy as sp
_HERE = os.path.dirname(os.path.abspath(__file__))
_VERIFY = os.path.abspath(os.path.join(_HERE, "..", "..",
"verification"))
sys.path.insert(0, _VERIFY)
from tfpt_constants import N_fam, g_car # noqa: E402
BANNED_IDS = ("zetazero", "nzeros", "primerange", "isprime",
"primepi", "nextprime", "prevprime")
CHECKS = []
KILLS = []
T0 = time.time()
FLOOR = sp.Rational(1, 200) # round-51/52 frozen floor (G_c)
DPS = 60 # certified precision (frozen)
NZ_FLOOR = mp.mpf("1e-8") # nonzero decision floor (frozen)
ZTOL = mp.mpf("1e-40") # zero decision ceiling (frozen)
PF_FLOOR = mp.mpf("1e-16") # Pf4 nonzero floor (frozen)
mp.mp.dps = DPS
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("\n" + "=" * 74)
print("%s (t=%.1fs)" % (title, time.time() - T0))
print("=" * 74, flush=True)
def ast_scan(banned):
src = open(os.path.abspath(__file__), encoding="utf-8").read()
bad = []
for node in ast.walk(ast.parse(src)):
name = None
if isinstance(node, ast.Name):
name = node.id
elif isinstance(node, ast.Attribute):
name = node.attr
if name and name.lower() in banned:
bad.append(name)
return bad
# ---------------------------------------------------------- bit model
# (v880 / v888 conventions rebuilt inline; family/anchor basis)
def pc(v):
return bin(v).count("1")
HT = [[(pc(v) * pc(w) - pc(v & w)) % 2 for w in range(16)]
for v in range(16)]
A_BIT = 0b1000
FSIG = 0b0111
LOWIDX = {1: 0, 2: 1, 4: 2, 8: 3}
def sig(v):
"""order-3 deck sigma: (b0,b1,b2,b3) -> (b2,b0,b1,b3) (v880)."""
b = [(v >> i) & 1 for i in range(4)]
n = (b[2], b[0], b[1], b[3])
return sum(bit << i for i, bit in enumerate(n))
SIGP = tuple(sig(v) for v in range(16))
def polar_shift(c):
"""q_c(v) = C(|v|,2) + c.v mod 2 -- the 16 refinements (v880)."""
return tuple((pc(v) * (pc(v) - 1) // 2 + pc(c & v)) % 2
for v in range(16))
def iota_bits(v):
b = [(v >> i) & 1 for i in range(4)]
b.append(sum(b) % 2)
return tuple(b)
IOTA_MSG = [iota_bits(v) for v in range(16)]
def iota_support(v):
return frozenset(i + 1 for i, bit in enumerate(IOTA_MSG[v])
if bit)
def compose(p, q):
return tuple(p[q[i]] for i in range(len(q)))
def perm_order(p):
o, pp = 1, p
ident = tuple(range(len(p)))
while pp != ident:
pp = tuple(p[x] for x in pp)
o += 1
return o
def cycle_type(perm):
n = len(perm)
seen = [False] * n
cyc = []
for i in range(n):
if seen[i]:
continue
ln, j = 0, i
while not seen[j]:
seen[j] = True
j = perm[j]
ln += 1
cyc.append(ln)
return tuple(sorted(cyc))
def all_matchings(vs):
vs = sorted(vs)
if not vs:
return [frozenset()]
a = vs[0]
out = []
for b in vs[1:]:
rest = [x for x in vs if x not in (a, b)]
for sub in all_matchings(rest):
out.append(sub | {frozenset({a, b})})
return out
def fro2(M):
"""exact squared Frobenius norm of a sympy matrix."""
return sum(x * x for x in M)
def edge_orbits(perm):
"""orbits of perm on the 15 unordered duads of {0..5}, each
with the ORIENTATION-REVERSAL flag (round-51 convention)."""
n_ord = perm_order(perm)
seen = set()
out = []
for i, j in itertools.combinations(range(6), 2):
e = frozenset({i, j})
if e in seen:
continue
x, y = i, j
edges = set()
rev = False
for _k in range(n_ord):
edges.add(frozenset({x, y}))
x, y = perm[x], perm[y]
if (x, y) == (j, i):
rev = True
seen |= edges
out.append((frozenset(edges), rev, (i, j)))
return out
def pf_of(mat, idx):
"""recursive Pfaffian expansion (sympy)."""
if not idx:
return sp.Integer(1)
i0, rest0 = idx[0], idx[1:]
tot = sp.Integer(0)
for k, j in enumerate(rest0):
sub = [t for t in rest0 if t != j]
tot += sp.Integer(-1) ** k * mat[i0, j] * pf_of(mat, sub)
return tot
def pf_num(rows, idx):
"""Pfaffian of an mp-float matrix (list of lists) on idx, with
exact-zero skip (the restricted matrices are sparse by
construction)."""
memo = {}
def rec(t):
if not t:
return mp.mpf(1)
if t in memo:
return memo[t]
i0, rest = t[0], t[1:]
tot = mp.mpf(0)
for k, j in enumerate(rest):
aij = rows[i0][j]
if aij != 0:
sub = tuple(x for x in rest if x != j)
tot += (-1) ** k * aij * rec(sub)
memo[t] = tot
return tot
return rec(tuple(sorted(idx)))
DUADS_CH = sorted(itertools.combinations(range(6), 2))
J2 = sp.Matrix([[0, 1], [-1, 0]])
I2 = sp.eye(2)
IOTA6 = sp.Matrix.vstack(I2, I2, I2) # the frozen 6x2 compression
def sp_to_mp(M):
"""sympy rational matrix -> nested list of mpf (exact)."""
r, c = M.shape
return [[mp.mpf(int(M[i, j].p)) / mp.mpf(int(M[i, j].q))
if M[i, j] != 0 else mp.mpf(0)
for j in range(c)] for i in range(r)]
def main():
print("SEAM.CFIN.KMSMIX.01 + SEAM.CFIN.SCHURMIX.01 -- the "
"channel-mixing STATE (KMS + Schur routes)")
print("FROZEN_SPEC SHA-256: %s"
% hashlib.sha256(__doc__.encode("utf-8")).hexdigest())
print("NO physics-realization claim; the [O] premise stays "
"[O]; exploration only.")
# ==================================================================
section("S0 -- firewall + compiler-side setup (corpus rebuilt)")
# ==================================================================
bad = ast_scan(BANNED_IDS)
check("S0.0 AST firewall: no banned identifiers %s"
% (BANNED_IDS,), not bad, kill="K0")
refs = [polar_shift(c) for c in range(16)]
ok_ref = all(
all(q[x ^ y] ^ q[x] ^ q[y] == HT[x][y]
for x in range(16) for y in range(16)) for q in refs)
arf1 = sorted(q for q in refs if q.count(0) == 6)
siginv = [q for q in refs
if all(q[SIGP[v]] == q[v] for v in range(16))]
cand = [q for q in siginv if q[A_BIT] == 1 and q[FSIG] == 0]
check("S0.1 v880/v845 rebuilt: 16 refinements, 6 Arf-1, unique "
"q* under the frozen selector",
ok_ref and len(set(refs)) == 16 and len(arf1) == 6
and len(cand) == 1, kill="K0")
QSTAR = cand[0]
NZ = list(range(1, 16))
ovoid = [v for v in NZ if QSTAR[v] == 0]
def duad(v):
return frozenset(i for i, q in enumerate(arf1) if q[v] == 0)
DUADS_L = sorted((frozenset(d)
for d in itertools.combinations(range(6), 2)),
key=sorted)
dmap = {v: duad(v) for v in NZ}
V0 = arf1.index(QSTAR)
biject = (all(len(d) == 2 for d in dmap.values())
and sorted(dmap.values(), key=sorted) == DUADS_L)
check("S0.2 duad model: 15 messages <-> 15 duads; vacuum label "
"V0 = %d" % V0, biject and 0 <= V0 < 6, kill="K0")
phi = {}
ok_phi = True
for o in ovoid:
others = dmap[o] - {V0}
islot = frozenset(range(1, 6)) - iota_support(o)
ok_phi &= (len(others) == 1 and len(islot) == 1)
phi[next(iter(others))] = next(iter(islot))
ok_phi &= (len(phi) == 5
and set(phi.values()) == set(range(1, 6)))
check("S0.3 carrier dictionary phi (ovoid-induced) bijective: "
"%s" % (sorted(phi.items()),), ok_phi, kill="K0")
def lab(j):
return 0 if j == V0 else phi[j]
def chduad(v):
return frozenset(lab(j) for j in dmap[v])
chd = {v: chduad(v) for v in NZ}
inv_chd = {frozenset(d): v for v, d in chd.items()}
check("S0.4 the 15 messages map bijectively onto the 15 "
"channel duads (V0 -> channel 0)",
sorted(chd.values(), key=sorted) == DUADS_L, kill="K0")
# deployed C6: Sp(4,2) census + Aut pin (rounds 50-52 rebuilt)
gl_n = 0
SP6 = []
for imgs in itertools.product(range(1, 16), repeat=4):
p = [0] * 16
for v in range(1, 16):
lb = v & -v
p[v] = p[v ^ lb] ^ imgs[LOWIDX[lb]]
if len(set(p)) != 16:
continue
gl_n += 1
if all(HT[imgs[x]][imgs[y]] == 1
for x in range(4) for y in range(x + 1, 4)):
SP6.append(tuple(p))
S5P = list(itertools.permutations(range(5)))
AUT = []
for p in SP6:
if any(QSTAR[p[v]] != QSTAR[v] for v in range(16)):
continue
if compose(p, SIGP) != compose(SIGP, p):
continue
pis = [pi for pi in S5P
if all(IOTA_MSG[p[v]] == tuple(IOTA_MSG[v][pi[s]]
for s in range(5))
for v in range(16))]
if pis:
AUT.append(p)
g_pin = [p for p in AUT
if perm_order(p) == 6 and compose(p, p) == SIGP]
check("S0.5 |GL(4,2)| = %d == 20160, |Sp(4,2)| = %d == 720, "
"|Aut(C_fin)| = %d == 6, generator pin g^2 = sigma unique"
% (gl_n, len(SP6), len(AUT)),
gl_n == 20160 and len(SP6) == 720 and len(AUT) == 6
and len(g_pin) == 1, kill="K0")
GEN = g_pin[0]
a1idx = {q: i for i, q in enumerate(arf1)}
tau = [a1idx[tuple(q[GEN[v]] for v in range(16))] for q in arf1]
pia = [0] * 6
for j in range(6):
pia[tau[j]] = j
pia = tuple(pia)
PI6 = [0] * 6
for j in range(6):
PI6[lab(j)] = lab(pia[j])
PI6 = tuple(PI6)
ct6 = cycle_type(PI6)
ok_int = all(dmap[GEN[v]] == frozenset(pia[j] for j in dmap[v])
for v in NZ)
check("S0.6 DEPLOYED channel permutation pi = %s: fixes "
"channel 0, cycle type %s == (1, 2, 3); intertwines the "
"duad action on all 15" % (PI6, ct6),
PI6[0] == 0 and ct6 == (1, 2, 3) and ok_int, kill="K0")
cycles = []
seen = set()
for i in range(6):
if i in seen:
continue
cyc, j = [], i
while j not in seen:
seen.add(j)
cyc.append(j)
j = PI6[j]
cycles.append(cyc)
TWO = sorted(next(c for c in cycles if len(c) == 2))
THREE = next(c for c in cycles if len(c) == 3)
a_ch, b_ch = TWO
c_ch = THREE[0]
print(" pi cycles: fixed 0, 2-cycle %s, 3-cycle %s"
% (TWO, sorted(THREE)))
chi = {i: (-1) ** (i + 1) for i in range(1, 6)}
# deployed one-particle layout + the round-50 lift O16
CH = {0: list(range(10, 16))}
for i in range(1, 6):
CH[i] = [2 * (i - 1), 2 * (i - 1) + 1]
dims = {i: len(CH[i]) for i in CH}
CAR_IDX = list(range(10))
BND_IDX = list(range(10, 16))
def lift16(perm6):
O = sp.zeros(16)
for r in CH[0]:
O[r, r] = 1
for i in range(1, 6):
src, dst = CH[i], CH[perm6[i]]
O[dst[0], src[0]] = 1
O[dst[1], src[1]] = 1
return O
O16 = lift16(PI6)
# image map: index s in channel i, position k -> CH[pi(i)][k]
img = [0] * 16
for i in range(6):
for k, s in enumerate(CH[i]):
img[s] = CH[PI6[i]][k]
check("S0.7 deployed lift O16 orthogonal integer (slot pairs "
"as units, identity on the A3 block)",
sp.simplify(O16 * O16.T) == sp.eye(16), kill="K0")
# the round-52 canonical integer covariant cross matrix A_int
orbs = edge_orbits(PI6)
def put_ordered(A, x, y, B):
for r in range(len(CH[x])):
for c in range(len(CH[y])):
A[CH[x][r], CH[y][c]] = B[r, c]
A[CH[y][c], CH[x][r]] = -B[r, c]
A_int = sp.zeros(16)
for edges, rev, rep in orbs:
i, j = rep
if rev:
B = J2
elif i == 0:
B = IOTA6
else:
B = I2
x, y = i, j
for _k in range(perm_order(PI6)):
put_ordered(A_int, x, y, B)
x, y = PI6[x], PI6[y]
ok_aint = (sp.simplify(O16 * A_int * O16.T - A_int)
== sp.zeros(16)
and sp.simplify(A_int + A_int.T) == sp.zeros(16))
check("S0.8 round-52 canonical A_int rebuilt: integer, "
"antisymmetric, O16-covariant EXACTLY; the canonical "
"candidate G_c = (I + i FLOOR A_int)/2",
ok_aint, kill="K0")
# deployed diagonal kernel A16_dep = (+)_8 J (v113/v155 hull)
A16_dep = sp.zeros(16)
for i in range(8):
A16_dep[2 * i, 2 * i + 1] = 1
A16_dep[2 * i + 1, 2 * i] = -1
ok_dep = (sp.simplify(O16 * A16_dep * O16.T - A16_dep)
== sp.zeros(16)
and sp.simplify(A16_dep * A16_dep + sp.eye(16))
== sp.zeros(16))
n_dep_cross = sum(
1 for (i, j) in DUADS_CH
if fro2(A16_dep.extract(CH[i], CH[j])) != 0)
check("S0.9 deployed diagonal kernel A16_dep = (+)_8 J: "
"covariant, A^2 = -I (pure), cross-blocks %d/15 == 0 "
"(SEAM-DIAGONAL, round 52)" % n_dep_cross,
ok_dep and n_dep_cross == 0, kill="K0")
Gamma16 = sp.diag(*([-1] * 10 + [1] * 6))
ok_gp = (sp.simplify(Gamma16 * O16 - O16 * Gamma16)
== sp.zeros(16))
edge_law = all((QSTAR[v] == 0) == (0 in chd[v]) for v in NZ)
check("S0.10 grading operator Gamma16 = (-I on C) (+) (+I on "
"B): [Gamma16, O16] == 0 (%s); edge law q*(v)=0 iff duad "
"touches channel 0 on all 15 (%s)" % (ok_gp, edge_law),
ok_gp and edge_law, kill="K0")
vac_duads = {frozenset(chd[v]) for v in NZ if QSTAR[v] == 0}
car_duads = {frozenset(chd[v]) for v in NZ if QSTAR[v] == 1}
# canonical chi / qsign / sgn(M) machinery (round 49/52)
SYM = {}
for i in range(6):
for j in range(i + 1, 6):
SYM[(i, j)] = sp.Symbol("a_%d%d" % (i, j))
G6 = sp.Matrix(6, 6, lambda r, c:
SYM[(r, c)] if r < c
else (-SYM[(c, r)] if r > c else 0))
PF6 = sp.expand(pf_of(G6, list(range(6))))
cdict = PF6.as_coefficients_dict()
MSLOT = all_matchings(range(6))
def mono_of(m):
out = sp.Integer(1)
for e in m:
out *= SYM[tuple(sorted(e))]
return out
sgn = {}
ok_c = True
for m in MSLOT:
c = cdict.get(mono_of(m), 0)
ok_c &= (c in (1, -1))
sgn[frozenset(m)] = int(c)
def m_ist(m):
vac_e = next(e for e in m if 0 in e)
i = next(iter(vac_e - {0}))
S, T = sorted((tuple(sorted(e)) for e in m if e != vac_e))
return i, S, T
def qsign(i, S, T):
j, k, l, m4 = sorted(set(range(1, 6)) - {i})
three = [frozenset({frozenset({j, k}), frozenset({l, m4})}),
frozenset({frozenset({j, l}), frozenset({k, m4})}),
frozenset({frozenset({j, m4}), frozenset({k, l})})]
key = frozenset({frozenset(S), frozenset(T)})
return (1, -1, 1)[three.index(key)]
ok_gauge = all(
sgn[frozenset(m)]
== chi[m_ist(m)[0]] * qsign(*m_ist(m)) for m in MSLOT)
check("S0.11 symbolic scalar ward: Pf(6x6 generic) = 15 "
"monomials, sgn(M) == chi(i) * qsign(S,T), chi(i) = "
"(-1)^(i+1) (round-49 gauge)",
len(cdict) == 15 and ok_c and ok_gauge, kill="K0")
# canonical reference sign pattern (exact, from G_c = FLOOR A_int)
CH2 = {i: [2 * i, 2 * i + 1] for i in range(6)}
def compress12(A16m):
"""Iota/3 compression: 16-dim covariant -> 12-dim block
matrix (sympy)."""
Ahat = sp.zeros(12)
for (i, j) in DUADS_CH:
if i == 0:
B = (IOTA6.T * A16m.extract(CH[0], CH[j])) / 3
else:
B = A16m.extract(CH[i], CH[j])
for r in range(2):
for c in range(2):
Ahat[CH2[i][r], CH2[j][c]] = B[r, c]
Ahat[CH2[j][c], CH2[i][r]] = -B[r, c]
return Ahat
Ahat_c = compress12(FLOOR * A_int)
pf4_c = {}
for (i, j) in DUADS_CH:
Bh = Ahat_c.extract(CH2[i], CH2[j])
pf4_c[frozenset({i, j})] = -Bh.det()
wblk_c = {}
for m in MSLOT:
prod = sp.Integer(1)
for e in m:
prod *= pf4_c[frozenset(e)]
wblk_c[frozenset(m)] = sgn[frozenset(m)] * prod
ok_ref15 = (all(v != 0 for v in pf4_c.values())
and all(v != 0 for v in wblk_c.values()))
check("S0.12 canonical reference pattern (exact): all 15 Pf4 "
"and all 15 w_blk of G_c nonzero (the round-52 chi "
"structure rebuilt)", ok_ref15, kill="K0")
# ==================================================================
section("H1 -- THE COMMUTANT (hermitian side; exact orbit "
"walks)")
# ==================================================================
# signed walk on unordered index pairs (r < c): antisymmetric
# covariant dimension = orientation-consistent orbits; forced
# zeros = reversal-forced orbits.
all_pairs = [(r, c) for r in range(16) for c in range(r + 1, 16)]
visited = set()
n_anti_free = 0
n_anti_forced = 0
forced_reps = []
n_pair_orbits = 0
for p0 in all_pairs:
if p0 in visited:
continue
n_pair_orbits += 1
orb = {}
cur, s = p0, 1
forcedq = False
while True:
if cur in orb:
if orb[cur] != s:
forcedq = True
break
orb[cur] = s
r, c = img[cur[0]], img[cur[1]]
if r > c:
r, c, s = c, r, -s
cur = (r, c)
visited |= set(orb)
if forcedq:
n_anti_forced += 1
forced_reps.append(p0)
else:
n_anti_free += 1
# symmetric side: unordered-pair orbits (no sign obstruction)
# + diagonal orbits
diag_orbits = 0
seen_d = set()
for r in range(16):
if r in seen_d:
continue
diag_orbits += 1
x = r
while x not in seen_d:
seen_d.add(x)
x = img[x]
dim_anti = n_anti_free
dim_sym = n_pair_orbits + diag_orbits
dim_herm = dim_sym + dim_anti
# isotypic ward: fix counts of O16 powers -> sum of mult^2
fixs = []
pk = tuple(range(6))
for _k in range(6):
fixs.append(6 + 2 * sum(1 for i in range(1, 6)
if pk[i] == i))
pk = compose(PI6, pk)
zeta = sp.exp(2 * sp.pi * sp.I / 6)
mults = [sp.nsimplify(sp.simplify(
sp.Rational(1, 6) * sum(fixs[k] * zeta ** (-j * k)
for k in range(6))))
for j in range(6)]
sum_sq = sum(m ** 2 for m in mults)
check("H1.1 HERMITIAN-SIDE COMMUTANT of O16 (exact walks): "
"dim = %d = %d sym + %d antisym; isotypic mults %s, "
"sum m^2 = %s == dim (ward); the Majorana-compatible "
"slice K = i h is the %d-dim antisymmetric part"
% (dim_herm, dim_sym, dim_anti, mults, sum_sq, dim_anti),
sum_sq == dim_herm and sum(mults) == 16, kill="K1")
# cross / diagonal split of the antisymmetric side
ch_of = {}
for i in range(6):
for s in CH[i]:
ch_of[s] = i
visited2 = set()
n_cross_free = 0
n_diag_free = 0
for p0 in all_pairs:
if p0 in visited2:
continue
orb = {}
cur, s = p0, 1
forcedq = False
while True:
if cur in orb:
if orb[cur] != s:
forcedq = True
break
orb[cur] = s
r, c = img[cur[0]], img[cur[1]]
if r > c:
r, c, s = c, r, -s
cur = (r, c)
visited2 |= set(orb)
if not forcedq:
if ch_of[p0[0]] != ch_of[p0[1]]:
n_cross_free += 1
else:
n_diag_free += 1
check("H1.2 antisymmetric split: cross-block (mixing) part = "
"%d == 33 (the round-52 covariant block space; the "
"C<->B mixing block T spans the 2 vacuum orbits, dim "
"12 + 12 = 24), channel-diagonal part = %d (A3 antisym "
"15 + slot-orbit J's 2); forced-zero orbits = %d == 2 "
"(the diagonal of the transposed {%d,%d} block)"
% (n_cross_free, n_diag_free, n_anti_forced, a_ch, b_ch),
n_cross_free == 33 and n_diag_free == 17
and n_anti_forced == 2
and dim_anti == n_cross_free + n_diag_free, kill="K1")
# ==================================================================
section("M1 -- THE KMS ROUTE (frozen grid scan, beta = 1)")
# ==================================================================
O16_mp = sp_to_mp(O16)
Aint_mp = sp_to_mp(A_int)
Adep_mp = sp_to_mp(A16_dep)
IOTA_mp = sp_to_mp(IOTA6)
def kms_C(h_mp, beta):
"""C_beta = (I + e^{beta K})^{-1} for K = i h (h real
antisymmetric, mp rows), via the exact hermitian
eigendecomposition (certified mpmath at DPS digits).
Returns C as nested mpc lists."""
K = mp.matrix(16, 16)
for r in range(16):
for c in range(16):
if h_mp[r][c] != 0:
K[r, c] = mp.mpc(0, h_mp[r][c])
Ev, Q = mp.eighe(K)
f = [1 / (1 + mp.e ** (mp.mpf(beta) * Ev[k]))
for k in range(16)]
return [[sum(Q[r, k] * f[k] * mp.conj(Q[c, k])
for k in range(16)) for c in range(16)]
for r in range(16)]
def kms_A_from_h(h_mp, beta):
"""A_beta = -i (2 C_beta - I) = -tan(beta h / 2); returns
(A rows, wards dict)."""
C = kms_C(h_mp, beta)
A = [[mp.mpf(0)] * 16 for _ in range(16)]
im_max = mp.mpf(0)
for r in range(16):
for c in range(16):
z = -1j * (2 * C[r][c] - (1 if r == c else 0))
im_max = max(im_max, abs(mp.im(z)))
A[r][c] = mp.re(z)
anti = max(abs(A[r][c] + A[c][r])
for r in range(16) for c in range(16))
cov = max(abs(A[img[r]][img[c]] - A[r][c])
for r in range(16) for c in range(16))
H = mp.matrix(16, 16)
for r in range(16):
for c in range(16):
H[r, c] = mp.mpc(0, A[r][c])
ev = mp.eighe(H, eigvals_only=True)
smax = max(abs(x) for x in ev)
return A, {"im": im_max, "anti": anti, "cov": cov,
"smax": smax}
def h_grid(u, t):
"""frozen family h(u, t) = -(u A16_dep + t A_int), mp."""
uf = (mp.mpf(int(sp.Rational(u).p))
/ int(sp.Rational(u).q))
tf = (mp.mpf(int(sp.Rational(t).p))
/ int(sp.Rational(t).q))
return [[-(uf * Adep_mp[r][c] + tf * Aint_mp[r][c])
for c in range(16)] for r in range(16)]
def blocks_census(A):
"""per-duad Frobenius norms of the mp matrix A."""
out = {}
for (i, j) in DUADS_CH:
s = mp.mpf(0)
for r in CH[i]:
for c in CH[j]:
s += A[r][c] ** 2
out[(i, j)] = mp.sqrt(s)
return out
def compress_mp(A):
"""Iota/3 compression of an mp 16-dim covariant matrix."""
Ahat = [[mp.mpf(0)] * 12 for _ in range(12)]
for (i, j) in DUADS_CH:
if i == 0:
B = [[sum(IOTA_mp[r][rr] * A[CH[0][r]][CH[j][c]]
for r in range(6)) / 3
for c in range(2)] for rr in range(2)]
else:
B = [[A[CH[i][r]][CH[j][c]] for c in range(2)]
for r in range(2)]
for r in range(2):
for c in range(2):
Ahat[CH2[i][r]][CH2[j][c]] = B[r][c]
Ahat[CH2[j][c]][CH2[i][r]] = -B[r][c]
return Ahat
def gates(A, wards):
"""evaluate the frozen gates G1..G5 on an mp candidate;
returns (passed set, failed list, diagnostics)."""
diag = {}
failed = []
# G1 CAR strict
if not (wards["smax"] < 1 - mp.mpf("1e-6")):
failed.append("G1-CAR")
# G2 covariance + forced zeros ({a,b} block diagonal)
if not (wards["im"] < ZTOL and wards["anti"] < ZTOL
and wards["cov"] < ZTOL):
failed.append("G2-COVARIANCE")
fz = max(abs(A[CH[a_ch][k]][CH[b_ch][k]]) for k in range(2))
if not (fz < ZTOL):
failed.append("G2-FORCEDZERO")
# G3 floor census (with ambiguity band -> K2)
bn = blocks_census(A)
n_floor = sum(1 for v in bn.values() if v >= NZ_FLOOR)
ambig = [d for d, v in bn.items() if ZTOL < v < NZ_FLOOR]
diag["blocks"] = bn
diag["ambig"] = ambig
if n_floor != 15:
failed.append("G3-FLOOR(%d/15)" % n_floor)
# G4 grading fullness (odd = vacuum, even = carrier)
odd_ok, even_ok, parity_ok = 0, 0, True
for (i, j) in DUADS_CH:
so, se = mp.mpf(0), mp.mpf(0)
gi = -1 if i != 0 else 1
gj = -1 if j != 0 else 1
for r in CH[i]:
for c in CH[j]:
o = (A[r][c] - gi * gj * A[r][c]) / 2
e = (A[r][c] + gi * gj * A[r][c]) / 2
so += o ** 2
se += e ** 2
if 0 in (i, j):
odd_ok += bool(mp.sqrt(so) >= NZ_FLOOR)
parity_ok &= bool(mp.sqrt(se) < ZTOL)
else:
even_ok += bool(mp.sqrt(se) >= NZ_FLOOR)
parity_ok &= bool(mp.sqrt(so) < ZTOL)
diag["grading"] = (odd_ok, even_ok)
if not (odd_ok == 5 and even_ok == 10 and parity_ok):
failed.append("G4-GRADING(%d/5,%d/10)"
% (odd_ok, even_ok))
# G5 Pfaffian / chi structure + sign match to canonical
Ahat = compress_mp(A)
pf4 = {}
for (i, j) in DUADS_CH:
B = [[Ahat[CH2[i][r]][CH2[j][c]] for c in range(2)]
for r in range(2)]
pf4[frozenset({i, j})] = -(B[0][0] * B[1][1]
- B[0][1] * B[1][0])
diag["pf4"] = pf4
n_pf4 = sum(1 for v in pf4.values() if abs(v) >= PF_FLOOR)
wb = {}
ok_sign, ok_ward, n_wb = True, True, 0
for m in MSLOT:
prod = mp.mpf(1)
for e in m:
prod *= pf4[frozenset(e)]
w = sgn[frozenset(m)] * prod
wb[frozenset(m)] = w
if abs(w) >= PF_FLOOR ** 3:
n_wb += 1
# interleaving ward Pf(Ahat|_M) == prod Pf4
X = [[mp.mpf(0)] * 12 for _ in range(12)]
for e in m:
i, j = sorted(e)
for r in range(2):
for c in range(2):
X[CH2[i][r]][CH2[j][c]] = \
Ahat[CH2[i][r]][CH2[j][c]]
X[CH2[j][c]][CH2[i][r]] = \
-Ahat[CH2[i][r]][CH2[j][c]]
pfm = pf_num(X, range(12))
ok_ward &= bool(abs(pfm - prod)
<= mp.mpf("1e-30") * (1 + abs(prod)))
ok_sign &= bool((w > 0)
== (wblk_c[frozenset(m)] > 0))
diag["wblk"] = wb
if not (n_pf4 == 15 and n_wb == 15 and ok_ward
and ok_sign):
failed.append("G5-CHI(pf4 %d/15, wb %d/15, ward %s, "
"signmatch %s)"
% (n_pf4, n_wb, ok_ward, ok_sign))
if ambig:
failed.append("G-AMBIGUOUS%s" % ambig)
return failed, diag
SCAN = [(sp.Integer(1), sp.Rational(1, 8)),
(sp.Integer(1), sp.Rational(1, 4)),
(sp.Integer(1), sp.Rational(1, 2)),
(sp.Integer(1), sp.Integer(1)),
(sp.Integer(0), sp.Rational(1, 4))]
winner = None
win_data = None
scan_rows = []
for (u, t) in SCAN:
A, wards = kms_A_from_h(h_grid(u, t), 1)
failed, diag = gates(A, wards)
scan_rows.append(((u, t), failed))
print(" grid (u=%s, t=%s, beta=1): smax=%s %s"
% (u, t, mp.nstr(wards["smax"], 8),
"PASS all gates" if not failed
else "fails %s" % failed))
if not failed and winner is None:
winner = (u, t)
win_data = (A, wards, diag)
ok_amb = all("G-AMBIGUOUS" not in " ".join(f)
for _p, f in scan_rows)
check("M1.1 frozen grid scan complete (%d points, frozen "
"order); no threshold ambiguity fired"
% len(SCAN), ok_amb, kill="K2")
if winner is not None:
t_m1 = "KMSMIX-FOUND(u=%s, t=%s, beta=1)" % winner
else:
t_m1 = "KMSMIX-OBSTRUCTED(%s)" % (
"; ".join("(u=%s,t=%s):%s" % (p[0], p[1], f)
for p, f in scan_rows))
check("M1.2 TYPED KMS OUTCOME: %s -- the KMS state of a "
"C6-invariant mixing Hamiltonian %s the full round-52 "
"block structure (all 15 blocks at the floor, grading "
"5/5 + 10/10, all 15 Wick monomials with the canonical "
"sign pattern)"
% (t_m1, "CARRIES" if winner else "does NOT carry"),
winner is not None or "OBSTRUCTED" in t_m1,
"typed by measurement", kill="K2")
beta2_note = "not evaluated"
if winner is not None:
A2m, wards2 = kms_A_from_h(h_grid(*winner), 2)
failed2, _diag2 = gates(A2m, wards2)
beta2_note = ("PASSES all gates" if not failed2
else "fails %s" % failed2)
check("M1.3 ROBUSTNESS at beta = 2 (winner re-tested): %s"
% beta2_note, not failed2,
"report-grade robustness", kill=None)
# anatomy: per-orbit rays (report only)
print(" ANATOMY (report): per-orbit rays h = -(A16_dep + "
"1/4 E_orb) -- duads LIT (>= floor) vs duads SEEDED:")
for edges, rev, rep in orbs:
E_orb = sp.zeros(16)
i, j = rep
B = J2 if rev else (IOTA6 if i == 0 else I2)
x, y = i, j
for _k in range(perm_order(PI6)):
put_ordered(E_orb, x, y, B)
x, y = PI6[x], PI6[y]
Er = sp_to_mp(E_orb)
tf = mp.mpf(1) / 4
h_ray = [[-(Adep_mp[r][c] + tf * Er[r][c])
for c in range(16)] for r in range(16)]
Ar, _w = kms_A_from_h(h_ray, 1)
bn = blocks_census(Ar)
lit = sorted(d for d, v in bn.items() if v >= NZ_FLOOR)
seeded = sorted(tuple(sorted(e)) for e in edges)
print(" orbit rep %s (size %d%s): seeded %s -> lit "
"%d/15 %s"
% (rep, len(edges), ", reversed" if rev else "",
seeded, len(lit), lit))
check("M1.4 anatomy printed: the tan/KMS dressing itself "
"MIXES -- odd powers of h generate blocks outside the "
"seeded orbit (the Schur mechanism operating inside the "
"KMS route); report only", True, "no decision")
# ==================================================================
section("R1 -- REFLECTION POSITIVITY (the honest typed answer)")
# ==================================================================
check("R1.1 CORPUS ANSWER (measured by reading, frozen): NO "
"canonical spatial/OS reflection theta is deployed on "
"the 16-dim one-particle space -- v155 carries RP only "
"as the recorded [P] premise (no operator), v160 has no "
"reflection operator, v424/v426/v440 deploy the "
"dictionary (Theta K Theta = -K, Theta C_beta Theta = "
"I - C_beta) on an 8-dim COLLAR TOY (4 marks x 2 "
"sides), not on D5+A3", True, "typed, honest")
if winner is not None:
# Theta_0 = complex conjugation in the Majorana basis:
# Theta_0 K Theta_0 = conj(K) = -K exact-structural for
# K = i h, h real -- measured via conj(C_beta) = I - C_beta.
C = kms_C(h_grid(*winner), 1)
d_refl = mp.mpf(0)
for r in range(16):
for c in range(16):
tgt = (1 if r == c else 0) - C[r][c]
d_refl = max(d_refl, abs(mp.conj(C[r][c]) - tgt))
ok_o16 = True # conjugation commutes with real O16
check("R1.2 THE MAJORANA REAL STRUCTURE Theta_0 (antiunitary "
"conjugation in the deployed basis, commutes with "
"O16 and Gamma16): satisfies the deployed v426/v440 "
"dictionary AUTOMATICALLY -- Theta_0 K Theta_0 = "
"conj(K) = -K (BW form, structural for K = i h, h "
"real) and conj(C_beta) = I - C_beta measured on the "
"winner (defect %s < ZTOL)"
% mp.nstr(d_refl, 6),
ok_o16 and d_refl < ZTOL, kill="K2")
check("R1.3 NAMED OPEN CHECK -- RP-THETA-OPEN: Theta_0 is the "
"Majorana real structure (particle-hole), NOT a spatial "
"seam reflection; the OS-positivity of the two-point "
"block under a SPATIAL theta (the Hankel/reflection "
"Gram of v379-type) cannot be tested until a theta is "
"deployed on the 16-dim space -- typed as the named "
"open check, NOT a gate; no marker moves", True,
"typed open")
t_rp = "RP-THETA-OPEN"
# ==================================================================
section("M2 -- THE SCHUR ROUTE (exact; boundary elimination)")
# ==================================================================
# parent state: deployed diagonal + C6-invariant C<->B coupling
kap = sp.Rational(1, 2)
m_mix = sp.Rational(1, 2)
t_cpl = sp.Rational(1, 20)
A_CC = A16_dep.extract(CAR_IDX, CAR_IDX)
J3 = A16_dep.extract(BND_IDX, BND_IDX)
V = A_int.extract(CAR_IDX, BND_IDX) # the T-block (vacuum)
ok_cov_V = (sp.simplify(
O16.extract(CAR_IDX, CAR_IDX) * V - V) == sp.zeros(10, 6))
check("M2.1 the coupling T-block V = A_int[C, B] (the M1 "
"parametrization's mixing block, vacuum orbits, dim 24 "
"space; canonical element): O_C V = V (C6-invariant "
"coupling, exact)", ok_cov_V, kill="K3")
# validity of the parent state (exact triangle bound)
VVt = V * V.T
lam_max = max(VVt.eigenvals().keys(), key=lambda e: sp.N(e))
norm_bound = sp.Rational(1, 2) + t_cpl * sp.sqrt(lam_max)
check("M2.2 PARENT VALIDITY (exact): A_full = [[kappa A_CC, "
"t V], [-t V^T, m J3]], kappa = m = 1/2, t = 1/20; "
"||A_full|| <= max(kappa, m) + t sqrt(lam_max(V V^T)) = "
"1/2 + (1/20) sqrt(%s) = %s < 1 EXACT => 0 < C_full < I "
"=> the Schur complement C_eff is a valid covariance"
% (lam_max, norm_bound),
bool(norm_bound < 1), kill="K3")
# exact Schur elimination:
# C_eff = C_CC - C_CB C_BB^{-1} C_BC
# = (I + i kap A_CC)/2
# - (t^2/2)/(1-m^2) (V V^T - i m V J3 V^T)
# antisym part: A_eff = kap A_CC + (t^2 m/(1-m^2)) S,
# S = V J3 V^T (derived in the docstring; verified here)
S_mat = V * J3 * V.T
C_BB = (sp.eye(6) + sp.I * m_mix * J3) / 2
C_BB_inv = 2 * (sp.eye(6) - sp.I * m_mix * J3) / (1 - m_mix**2)
ok_inv = sp.simplify(C_BB * C_BB_inv - sp.eye(6)) == sp.zeros(6)
C_CC = (sp.eye(10) + sp.I * kap * A_CC) / 2
C_CB = sp.I * t_cpl * V / 2
C_BC = -sp.I * t_cpl * V.T / 2
C_eff = sp.expand(C_CC - C_CB * C_BB_inv * C_BC)
A_eff_formula = kap * A_CC + (t_cpl ** 2 * m_mix
/ (1 - m_mix ** 2)) * S_mat
# C_eff = R + i A_eff/2, A_eff real antisymmetric
A_eff = sp.Matrix(10, 10,
lambda r, c: sp.im(sp.expand(2 * C_eff[r, c])))
ok_schur = (sp.simplify(A_eff - A_eff_formula) == sp.zeros(10)
and sp.simplify(A_eff + A_eff.T) == sp.zeros(10))
check("M2.3 EXACT SCHUR IDENTITY: the eliminated-boundary "
"covariance C_eff = C_CC - C_CB C_BB^{-1} C_BC has "
"antisymmetric (correlation) part A_eff = kappa A_CC + "
"(t^2 m/(1-m^2)) V J3 V^T EXACTLY (%s); the census "
"matrix is S := V J3 V^T"
% ok_schur, ok_inv and ok_schur, kill="K3")
ok_cov_S = (sp.simplify(
O16.extract(CAR_IDX, CAR_IDX) * S_mat
* O16.extract(CAR_IDX, CAR_IDX).T - S_mat)
== sp.zeros(10))
n_cross = 0
print(" 10-duad census of S = V J3 V^T (carrier duads; "
"unit decomposition B = aI I2 + aJ J + sym-traceless):")
unit_rows = {}
for (i, j) in itertools.combinations(range(1, 6), 2):
B = S_mat.extract(CH[i], CH[j])
aI = (B[0, 0] + B[1, 1]) / 2
aJ = (B[0, 1] - B[1, 0]) / 2
aX = (B[0, 1] + B[1, 0]) / 2
aZ = (B[0, 0] - B[1, 1]) / 2
nz = fro2(B) != 0
n_cross += bool(nz)
unit_rows[(i, j)] = (aI, aJ, aX, aZ)
v = inv_chd[frozenset({i, j})]
print(" {%d,%d} q*=%d B = %s I2 + %s J + (X:%s, "
"Z:%s)%s"
% (i, j, QSTAR[v], aI, aJ, aX, aZ,
"" if nz else " << ZERO"))
ok_ab_unit = (unit_rows[(a_ch, b_ch)][0] == 0
and unit_rows[(a_ch, b_ch)][1] != 0)
check("M2.4 SCHUR-GENERATION CENSUS (exact): %d/10 carrier "
"cross-blocks NONZERO from the BARE diagonal state + "
"C6-invariant coupling alone; S is C6-covariant (%s); "
"the transposed {%d,%d} block is PURE J (I2 coord 0, J "
"coord %s) -- exactly the direction covariance allows "
"there" % (n_cross, ok_cov_S, a_ch, b_ch,
unit_rows[(a_ch, b_ch)][1]),
n_cross == 10 and ok_cov_S and ok_ab_unit, kill="K3")
# per-edge Pf4 signs of the dressed carrier object vs canonical
lam_eff = t_cpl ** 2 * m_mix / (1 - m_mix ** 2)
ok_pf_car = True
for (i, j) in itertools.combinations(range(1, 6), 2):
B = lam_eff * S_mat.extract(CH[i], CH[j])
pf4 = -B.det()
pf4_can = pf4_c[frozenset({i, j})]
ok_pf_car &= (sp.sign(pf4) == sp.sign(pf4_can) != 0)
t_m2 = ("SCHURMIX-GENERATES(10/10 carrier duads, C6-covariant,"
" J-direction, Pf4 signs canonical)"
if n_cross == 10 and ok_cov_S else "SCHURMIX-DIAGONAL")
check("M2.5 TYPED SCHUR OUTCOME: %s -- per-edge Pf4 = "
"-det(block) signs MATCH the canonical G_c on all 10 "
"carrier duads (%s); the pseudo-inverse (pure-boundary "
"C_BB^+ = C_BB) variant gives A_eff+ = A_CC - (t^2/4) S "
"-- same census, OPPOSITE dressing sign (report)"
% (t_m2, ok_pf_car),
t_m2.startswith("SCHURMIX-") and ok_pf_car, kill="K3")
if t_m2.startswith("SCHURMIX-GENERATES"):
print(""" THE UNIFIED READING (the reviewer's cross-connection
made concrete): the SAME Schur/Feshbach elimination that
creates the RH port (dressing by the eliminated block's
resolvent) here creates the carrier channel mixing: the
bare carrier state is EXACTLY diagonal (round 52,
SEAM-DIAGONAL), the bare boundary state is diagonal, and
the C6-invariant carrier-boundary coupling alone -- after
the boundary is ELIMINATED -- deposits nonzero correlation
on ALL 10 carrier duads with the covariant J-structure and
the canonical Pf4 signs. On both fronts the real
correlation lives in the ELIMINATED boundary, not the bare
bulk.""")
# ==================================================================
section("M3 -- THE 15-SIGNATURE FREEZE (frozen prediction "
"table)")
# ==================================================================
if winner is not None:
A, wards, diag = win_data
bn = diag["blocks"]
pf4 = diag["pf4"]
orb_of = {}
for oi, (edges, rev, rep) in enumerate(orbs):
for e in edges:
orb_of[frozenset(e)] = (oi, len(edges), rev)
print(" FROZEN 15-SIGNATURE PREDICTION TABLE (best "
"candidate: KMS %s; any physical seam state "
"realizing the block functor must reproduce the "
"zero/nonzero + sign pattern):" % (t_m1,))
print(" duad class q* orbit(size) ||B||_F"
" unit-coords (sign) sign Pf4")
ok_tab = True
for (i, j) in DUADS_CH:
v = inv_chd[frozenset({i, j})]
oi, osz, orev = orb_of[frozenset({i, j})]
if i == 0:
# coordinate along the frozen vacuum unit Iota
coord = sum(IOTA_mp[r][rr] * A[CH[0][r]][CH[j][rr]]
for r in range(6)
for rr in range(2)) / 6
coords = "Iota: %s" % mp.nstr(coord, 6)
lead = coord
else:
B = [[A[CH[i][r]][CH[j][c]] for c in range(2)]
for r in range(2)]
aI = (B[0][0] + B[1][1]) / 2
aJ = (B[0][1] - B[1][0]) / 2
coords = "I2: %s, J: %s" % (mp.nstr(aI, 6),
mp.nstr(aJ, 6))
lead = aJ if (i, j) == (a_ch, b_ch) else aI
p4 = pf4[frozenset({i, j})]
ok_tab &= bool(bn[(i, j)] >= NZ_FLOOR
and abs(p4) >= PF_FLOOR)
print(" {%d,%d} %s %d #%d(%d%s) %s [%s] "
"lead %s %s"
% (i, j, "vac" if 0 in (i, j) else "car",
QSTAR[v], oi, osz, "R" if orev else "",
mp.nstr(bn[(i, j)], 6), coords,
"+" if lead > 0 else "-",
"+" if p4 > 0 else "-"))
check("M3.1 FREEZE: all 15 signatures nonzero with signs "
"printed; coherent with the winner's gate data",
ok_tab, kill="K5")
else:
check("M3.1 FREEZE: skipped -- no KMS candidate passed "
"the gates (typed OBSTRUCTED above); the Schur-side "
"10-duad census (M2.4) stands as the frozen partial "
"signature", True, "typed", kill=None)
# ==================================================================
section("C -- controls (must fire)")
# ==================================================================
# C1 permuted roles (round-52 rule) on the M1 winner
rho = list(range(6))
rho[a_ch], rho[c_ch] = rho[c_ch], rho[a_ch]
rho = tuple(rho)
PIW = tuple(rho[PI6[rho[x]]] for x in range(6))
O16w = lift16(PIW)
imgw = [0] * 16
for i in range(6):
for k, s in enumerate(CH[i]):
imgw[s] = CH[PIW[i]][k]
if winner is not None:
A = win_data[0]
defw = max(abs(A[imgw[r]][imgw[c]] - A[r][c])
for r in range(16) for c in range(16))
else:
Ac_mp = sp_to_mp(FLOOR * A_int)
defw = max(abs(Ac_mp[imgw[r]][imgw[c]] - Ac_mp[r][c])
for r in range(16) for c in range(16))
Gw = sp.diag(*[1 if r in CH[a_ch] else -1 for r in range(16)])
gw = fro2(Gw * O16 - O16 * Gw)
w_arf = next(j for j in range(6) if lab(j) == a_ch)
mism = sum(1 for v in NZ
if (QSTAR[v] == 0) != (w_arf in dmap[v]))
check("C1 FIRES: PERMUTED ROLES (pi conjugated by the carrier "
"transposition (%d, %d), lifted): covariance of the "
"candidate breaks (max entry defect %s >= NZ_FLOOR); "
"wrong vacuum grading Gamma' does NOT commute with the "
"deployed O16 (||.||_F^2 = %s != 0); wrong vacuum Arf "
"label breaks the edge law on EXACTLY %d == 8 of 15"
% (a_ch, c_ch, mp.nstr(defw, 6), gw, mism),
defw >= NZ_FLOOR and gw != 0 and mism == 8, kill="K7")
# C2 the bare diagonal state (t = 0)
A0, wards0 = kms_A_from_h(h_grid(1, 0), 1)
bn0 = blocks_census(A0)
n0 = sum(1 for v in bn0.values() if v >= NZ_FLOOR)
Ahat0 = compress_mp(A0)
n_pf0 = 0
for (i, j) in DUADS_CH:
B = [[Ahat0[CH2[i][r]][CH2[j][c]] for c in range(2)]
for r in range(2)]
p4 = -(B[0][0] * B[1][1] - B[0][1] * B[1][0])
n_pf0 += bool(abs(p4) >= PF_FLOOR)
A_eff0 = kap * A_CC # exact Schur with t = 0
n_s0 = sum(1 for (i, j) in itertools.combinations(range(1, 6), 2)
if fro2(A_eff0.extract(CH[i], CH[j])) != 0)
check("C2 FIRES: THE BARE DIAGONAL STATE (t = 0): KMS of the "
"uncoupled deployed kernel has %d/15 cross-blocks at "
"the floor and %d/15 per-edge Pf4 nonzero (fails G3 + "
"G5); Schur with t = 0 gives A_eff = kappa A_CC exactly "
"-- %d/10 carrier cross-blocks"
% (n0, n_pf0, n_s0),
n0 == 0 and n_pf0 == 0 and n_s0 == 0, kill="K7")
# ==================================================================
section("VERDICT")
# ==================================================================
n_pass = sum(1 for _n, ok in CHECKS if ok)
n_tot = len(CHECKS)
controls_ok = all(ok for nm, ok in CHECKS if nm.startswith("C"))
if not controls_ok:
VERDICT = "CONTROL-DEAD"
elif "K0" in KILLS:
VERDICT = "PIPELINE-BROKEN"
elif KILLS:
VERDICT = "KMSMIX-PARTIAL [%s]" % ", ".join(
sorted(set({"K1": "COMMUTANT-BROKEN",
"K2": "KMSROUTE-BROKEN",
"K3": "SCHURROUTE-BROKEN",
"K5": "FREEZE-BROKEN"}.get(k, k)
for k in KILLS)))
else:
VERDICT = "KMSMIX-MEASURED [%s, %s, %s]" % (t_m1, t_m2,
t_rp)
print("%d/%d checks passed" % (n_pass, n_tot))
print("VERDICT: %s" % VERDICT)
print("""
REPORT (exploration only -- no promotion, no edits):
* THE PARAMETRIZATION (H1): the hermitian O16-commutant on the
deployed 16-dim space has dimension %d = %d sym + %d antisym
(exact orbit walks; isotypic ward sum m^2); the Majorana-
compatible Hamiltonians K = i h live in the %d-dim
antisymmetric slice = 33 cross (the round-52 covariant block
space; the C<->B mixing block T spans 24) + 17 diagonal; the
only forced zeros remain the 2 diagonal coordinates of the
transposed {%d,%d} block.
* THE KMS ROUTE (M1): %s. beta = 2 robustness: %s. The KMS
dressing A = -tan(beta h/2) is itself a mixing machine: the
per-orbit ray anatomy shows odd powers of h lighting duads far
outside the seeded orbit -- the Schur mechanism operating
inside the KMS route.
* THE RP ANSWER (R1, honest): NO deployed spatial/OS reflection
theta exists on the 16-dim one-particle space (v155 premise-
only, v160 none, v426/v440 = 8-dim collar dictionary). The
Majorana real structure Theta_0 satisfies the deployed
v426/v440 dictionary automatically (conj(C_beta) = I - C_beta
measured); the OS-positivity of the two-point block under a
SPATIAL theta is the named open check RP-THETA-OPEN.
* THE SCHUR ROUTE (M2, exact): %s. From the bare DEPLOYED
diagonal state + the C6-invariant coupling alone, boundary
elimination deposits S = V J3 V^T on ALL 10 carrier duads
(C6-covariant, J-direction, {%d,%d}-compatible, canonical Pf4
signs) -- the reviewer's cross-connection made concrete: on
both fronts (RH port, Wick functor) the real correlation
lives in the ELIMINATED boundary, not the bare bulk.
* THE FREEZE (M3): the 15 block-correlation signatures of the
best candidate printed as the frozen prediction table.
* The [O] premise (the boundary grammar IS a self-hosting Wick
pair compiler) stays [O]; these are CANDIDATE states + frozen
signatures; no marker moves.
Runtime: %.1f s""" % (dim_herm, dim_sym, dim_anti, dim_anti,
a_ch, b_ch, t_m1, beta2_note, t_m2,
a_ch, b_ch, time.time() - T0))
print("ALL CHECKS PASSED" if n_pass == n_tot
else "CHECKS FAILED: %d" % (n_tot - n_pass))
return 0 if (n_pass == n_tot and not KILLS) else 1
if __name__ == "__main__":
raise SystemExit(main())
'''
# --------------------------------------------------------------- harness
_PF_RE = re.compile(r"^\s*\[(PASS|FAIL)\]\s+(\S+)", re.M)
_VD_RE = re.compile(r"VERDICT[:\]]")
def _probe_file(name):
cand = os.path.abspath(os.path.join(
_HERE, os.pardir, "experiments", "tfpt-discovery", name + ".py"))
return cand if os.path.isfile(cand) else None
def _census(out):
marks = _PF_RE.findall(out)
fails = sorted({tok for st, tok in marks if st == "FAIL"})
verdict = ""
for line in out.splitlines():
if _VD_RE.search(line):
verdict = line.strip()
return len(marks), fails, verdict
def _exec_probe(name, src, run_entry=True):
"""Execute one embedded frozen probe source BYTE-EXACT in its own
module namespace (round-31 convention); capture and re-emit
stdout; return (stdout, exit_code, byte_equal_or_None)."""
if src[:1] == "\n":
src = src[1:]
path = _probe_file(name)
same = None
if path is not None:
with open(path, encoding="utf-8") as fh:
same = (fh.read() == src)
fname = path or os.path.abspath(__file__)
mod = types.ModuleType(name)
mod.__file__ = fname
sys.modules[name] = mod
buf = io.StringIO()
code = 0
with contextlib.redirect_stdout(buf):
try:
exec(compile(src, fname, "exec"), mod.__dict__)
entry = mod.__dict__.get("main") or mod.__dict__.get("run")
if run_entry and callable(entry):
rc = entry()
code = 0 if rc is None else int(rc)
except SystemExit as exc:
code = 0 if exc.code is None else int(exc.code)
except Exception: # regression guard
import traceback
traceback.print_exc(file=sys.stdout)
code = 99
out = buf.getvalue()
sys.stdout.write(out)
sys.stdout.flush()
return out, code, same
def _gate(name, out, code, same, exp_n, exp_fails, exp_verdict,
exp_code, gates):
n, fails, verdict = _census(out)
ok = (n == exp_n and fails == list(exp_fails)
and exp_verdict in verdict and code == exp_code
and same is not False)
gates.append(ok)
prov = ("byte-exact vs experiments source" if same is True else
"embedded copy (source file not present)" if same is None
else "SOURCE MISMATCH")
print("\n[%s] PATTERN GATE %s: %d checks (exp %d) | FAILs %s "
"(exp %s) | exit %d (exp %d) | %s\n verdict line: %s"
% ("PASS" if ok else "FAIL", name, n, exp_n,
",".join(fails) if fails else "none",
",".join(exp_fails) if exp_fails else "none",
code, exp_code, prov, verdict), flush=True)
return ok
_PLAN = (
('kms_schur_mixing_probe', _SRC_0, 30, (), 'KMSMIX-MEASURED', 0),
)
def run():
t0 = time.time()
print("=" * 74)
print('v898 -- SEAM.CFIN.KMSMIX.01 + SEAM.CFIN.SCHURMIX.01: the channel-mixing state the block Wick functor awaits -- the C6-covariant mixing KMS state EXISTS (u=1, t=1/8, beta=1; all 15 blocks, grading 5/5+10/10, canonical Pf4 signs; beta=2 robust) and the exact Schur elimination GENERATES all 10 carrier duads from the bare diagonal state; RP-THETA-OPEN named; the [O] premise unmoved')
print("(frozen probes embedded byte-exact and executed verbatim; NO RH claim)")
print("=" * 74, flush=True)
gates = []
for name, src, exp_n, exp_fails, exp_verdict, exp_code in _PLAN:
print("\n" + "-" * 74)
print("EMBEDDED FROZEN PROBE: %s" % name)
print("-" * 74, flush=True)
out, code, same = _exec_probe(name, src)
_gate(name, out, code, same, exp_n, exp_fails,
exp_verdict, exp_code, gates)
ok = all(gates)
print("\n" + "=" * 74)
print("v898: %d/%d pattern gates passed | runtime %.1f s"
% (sum(gates), len(gates), time.time() - t0))
print('the mixing mechanism has a constructed candidate: KMS state + exact Schur generation; the 15-signature table is the registered prediction')
print("[%s] v898 VERDICT GATE" % ("PASS" if ok else "FAIL"))
return 0 if ok else 1
if __name__ == "__main__":
raise SystemExit(run())
Recorded source fingerprint
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