#!/usr/bin/env python3 """v773 -- PRIME.QFCOCYCLE.01: the closure decider of the qf offensive -- the ordered multiplicative cell cocycle on the depth-dependent slow band d(X), run under the user-frozen STAKES: if this module dies, the diagonal Gram route closes WITHOUT further variants and the sharpened Z1 contract takes over. Verdict COCYCLE-DOMAIN-ONLY (GATES 2/8 with exactly the six convergence cells the preregistered fails, GUARDS+CONTROLS 14/14): STRUCTURE WITHOUT LIMIT. WHAT HOLDS EXACTLY: (i) the Moebius/Redheffer cell identity -- growing the window by one cell is the Redheffer star action of the cell block, and its corner evaluation the exact Moebius/Riccati update G_{k+1} = G_k + Y_I D_k^{-1} Y_I^T with coefficients (U_k, W_k) EXACTLY the added source rows/columns -- holds at machine precision (max per-rung defect 9.7e-12 over 73 rungs x 5 z, independent dense-solve Ward 1.3e-13; Schur complements COMPOSE, replacing the v758-killed additive formulation); (ii) every cell Schur block is PD (min eig D_k in [0.0605, 0.0668]) and the corner update terms are PSD to -1.5e-17 -- the cocycle is a MONOTONE LOEWNER FLOW on the source; (iii) the Nevanlinna/Stieltjes domain is preserved with ZERO breaches in all 730 rung x cell tests INCLUDING both typed mode-entry transitions (d 6 -> 7 at M = 992, entering eigenvalue 9.9438e-5; d 7 -> 8 at M = 1108, 9.9460e-5; step-1 resolution 991 -> 992 and 1106 -> 1107; transition increments UNREMARKABLE -- the transitions are not the obstruction). BUT NO CONVERGENCE CELL PASSES (0/6): the corner cocycle value absorbs a FLAT ~0.1-0.2% relative update per rung (med5 ratios 1.032 / 1.014 / 0.777 at eps = 1e-1/1e-2/1e-3), and the band object falls to exactly the bar (ratios 0.496 / 0.498 / 0.514 vs 0.5) with NEGATIVE second-half slopes (b2 = -0.15..-0.16/X: increments rising toward the top -- the moving-edge activity of the 7/8 modes). Controls fire on every eps cell (Stieltjes cone broken, cell blocks leave the cone) while the identity defects stay at 5e-12 on controls: the ALGEBRA is universal, the DOMAIN is what the comb owns. PER THE FROZEN STAKES THE GRAM ROUTE CLOSES and the sharpened Z1 contract takes over, carrying the moving-edge cadence (992 / 1108 / 1276, the 8/9 crossing at 976), the ram-odd contact direction, the settled q levels (R2 0.225..0.358, R1 0.008..0.079), and the surviving domain facts (exact cocycle identity, PD cell blocks, zero domain breaches, Herglotz/Stieltjes margins). NO RH claim, no X -> infinity claim. PROVENANCE: discovery probe qf_cell_cocycle_probe.py (2026-08-05, 28.2 s, GATES 2/8, GUARDS+CONTROLS 14/14, verdict COCYCLE-DOMAIN-ONLY; ONE DECLARED IMPLEMENTATION CORRECTION carried honestly into this module: execution 1 (26.0 s) was destroyed by the numerical instability of the raw chained Banachiewicz state -- defect 6.2e13, garbage D_k margins, an implementation failure of the carried state, NOT of the identity, and not adjudicable; the state is refreshed by the exact-identity-preserving Hotelling iteration R <- R + R (I - (A - z) R) to the 1e-11 floor after each cell -- the update coefficients (U_k, W_k), every gate and every bar UNCHANGED, the identity gate remains the arbiter, and the eigh-based W~ layer reproduced IDENTICALLY between both executions). Promoted verbatim (sibling imports point at v563/v755/v766/v770; epstein_firewall_probe stays a read-only discovery import); numbers unchanged. run() encodes the preregistered 2/8 gate pattern (identity + domain pass, all six convergence cells fail) as the expected outcome (v757 precedent). Original probe docstring (verbatim): QF-OFFENSIVE strand 3, module 4 (THE LAST DECIDER) -- the ordered multiplicative cell cocycle on a depth-dependent slow band: qf_cell_cocycle_probe. STAKES (frozen up front by the user): if this module dies, the Gram route closes WITHOUT further variants and the sharpened Z1 contract takes over. The Z1 handover content in that case: the moving-edge cadence (7th threshold at M = 992, count 8 from ~1108, the 8/9 crossing at 976), the ram-odd contact direction, the settled per-function q levels (R2 family 0.225..0.358, R1 family 0.008..0.079), and whichever domain facts survive this run. Exploration only (tfpt-experiment firewall): NOT wired into run_all.py, no ledger row, no paper edit, no website edit, NO RH CLAIM, and this probe writes no files. Everything is built exclusively from the source window operator -- never from target data (AST-guarded). INPUT STATE (frozen findings, none re-adjudicated here): * v758 killed the additive cellwise-positivity formulation; qf_feshbach_effective_probe blocked the fixed-d Feshbach limit (FESHBACH-PARTIAL: d = 6 is the right well-defined object but its Cauchy tail flattens where mode 7 grazes the band edge; d = 7 converges but loses separation at the top rung; d = 8 has an internal 8/9 crossing at M = 976). The moving edge names THIS module: transport with a DEPTH-DEPENDENT band. * qf_drainage_probe: QF-SETTLES-POSITIVE (the wall is a positive per-function constant); threshold count 6 -> 7 at M = 992, -> 8 from ~1108 on the 1e8 comb. EXACT IDENTITY (derived first, then float-gated on every rung): grow the window by one cell, A_{k+1} - z = [[A_k - z, U_k], [U_k^T, W_k - z]], where (U_k, W_k) are EXACTLY the added rows/columns of the source operator between rungs k and k+1 (the new Toeplitz lag placements). Eliminating the new cell is the Redheffer star action of the cell block; on the graph of the resolvent it is the linear-fractional map [R; I] -> M_k [R; I], and its corner evaluation is the exact Moebius/Riccati update of the compressed resolvent corner G_{k+1}(z) = G_k(z) + (Y_k)_I D_k^{-1} (Y_k)_I^T, Y_k = R_k U_k, D_k = (W_k - z) - U_k^T R_k U_k, with R_k = (A_k - z)^{-1} the carried cocycle state and I the frozen NCOR-coordinate corner; the ordered product Prod_k M_k is the nested-Schur (quotient-property) composition -- Schur complements COMPOSE, they are not summed: this replaces the killed additive formulation. HONESTY (predeclared reading): for a DENSE Toeplitz source the cell coefficients are the new lags FILTERED through the carried state R_k -- the source's memory lives in the cocycle state; a strictly local new-lags-only coefficient set exists only for banded sources. All coefficients remain 100% source-native and target-free. The identity is gated on EVERY rung (defect ||(A_k - z) R_k[:, I] - E_I||_max <= IDY_BAR) and against INDEPENDENT dense solves at the Ward rungs (rel <= WARD_BAR) -- this is the module's exact-identity gate, mirroring the Feshbach reconstruction Ward. DECLARED IMPLEMENTATION CORRECTION (after the first execution; full disclosure in RESULTS): raw chained Banachiewicz updates amplified float error by ~2.3x per cell (72 cells -> defect 6.2e13) while the 4-cell control ladders stayed at 5e-12 -- a numerical failure of the carried state, NOT of the identity. The state is therefore refreshed by the exact-identity-preserving Hotelling iteration R <- R + R (I - (A - z) R) after each cell until the per-rung defect meets REFRESH_FLOOR = 1e-11 (max 3 iterations). The update coefficients (U_k, W_k), every gate and every bar are UNCHANGED; the identity gate remains the arbiter, and the eigh-based W~ layer is untouched by this correction. DEPTH-DEPENDENT BAND WITH TRANSITION MAPS (frozen band rule): the band at rung M is the THRESHOLD BAND d(M) = #{lambda_i(A_M) <= THR_NULL = 1e-4} (the deployed near-null threshold rule; measured cadence 6 -> 7 at 992, -> 8 near 1108; every change of d(M) inside the gated range is a TYPED TRANSITION, reported with the entering mode's eigenvalue). Transition maps (frozen convention): the transported frame R_k in O(d(k)) is chained by the Kato/polar factors of the band overlaps; at a dimension INCREASE d -> d' the old frame is embedded by the polar isometry J = U_thin V_thin^T of the (d' x d) overlap and the new directions enter as the sign-fixed orthonormal complement columns, R_{k+1} = [J R_k | N] in O(d'); at a (not expected) DECREASE the frame is re-anchored to I_{d'} and the transition is typed MODE-EXIT. The transported band object is W~_k(z) = R_k^T diag(1/(lambda_i(X_k) - z))_{i <= d(k)} R_k, the compressed band resolvent (the Herglotz object of the Feshbach run) in the moving d(X) frame. The cocycle and the gates run over the FULL gated range INCLUDING the transitions -- that is the point of the module. Increments across a transition are compared on the transported-old-frame corner (first d columns of R_{k+1}); transition increments are additionally listed separately. ADMISSIBLE MATRIX DOMAIN (frozen BEFORE running; the kill-#9 gate): the Nevanlinna/Stieltjes sandwich D = {Im F(z) >= -HERG_FLOOR at both complex points z = i h and -1e-3 + i h (h = 1e-2)} INTERSECT {min eig F(-eps) >= -PSD_FLOOR for eps in (1e-1, 1e-2, 1e-3)} (Stieltjes cone at the frozen real points), tested for BOTH transported objects (corner cocycle value G_k and band object W~_k) on EVERY gated rung including every transition rung. Individual cocycle factors MAY be indefinite -- ONLY domain preservation is gated (the whole philosophy: transport information, don't demand cellwise positivity); the cell margins (min eig D_k, eigenrange of the corner update term) are REPORTED, never gated. The cone test is a fixed-z statement about the compressed resolvent (like the Feshbach Q-separation) -- NOT a positive-lower-eigenvalue bound on A, which remains forbidden in gates (PD of the window stays measured output). Predeclared control honesty: real-symmetric indefinite controls KEEP the complex-point Herglotz identity (self-adjointness is not what they break); the discriminating domain clause is the Stieltjes cone at real z and/or cell-block positivity loss (D_k leaves the cone) -- exactly where 'the Herglotz sandwich' breaks for indefinite A. Domain-breach typing (frozen): 0 non-transition breaches = pass; 1..2 isolated breaches = typed exceptions (CARRIES additionally requires them transition-adjacent, i.e. within one rung of a typed transition); > 2 = SYSTEMATIC = kill. RENORMALIZED CONVERGENCE (frozen; Gate-3'-corner lesson): the gated statistic runs on RELATIVE entrywise increments rel_k = ||obj_{k+1} - obj_k||_max / N_k, N_k = max(||obj_k||_max, ||obj_{k+1}||_max), a source-native, target-free normalizer declared as part of the object definition -- this is a RENORMALIZED-OBJECT claim, NOT the absolute 2^-n contract (stated plainly). Gated cells: both objects x the three real eps (6 cells); the two complex points are REPORTED. Bars per cell (house oscillation-aware statistic): med5(LAST5)/med5(FIRST5) <= C_MED = 0.5 AND second-half falling rate b2 >= C_SLOPE = 0.02/X (hbp.fit_rate verbatim, the declared bounded-statistic slope -- no other fit enters any gate); converged-to-floor clause: a cell also passes if med5(LAST5) <= NOISE_PASS = 1e-12 (already at float noise). 72 increments, blocks FIRST5 = 1..5, LAST5 = 68..72, second half = 37..72, increment X = right-rung X. KILLS (frozen): K1 exact identity fails (any rung defect > IDY_BAR = 1e-8 or Ward residual > WARD_BAR = 1e-8); K2 SYSTEMATIC domain breach (> 2 non-transition rungs, any cell); K3 target data in the updates (AST + construction audit); K4 transport collapse (overlap sigma_min < 1e-8, a 90-degree angle); K5 an RH-strength normalizer (audit: the normalizer is the object's own entry scale, nothing else). LADDER: the 1e8 comb re-derived in-process (probes write no files); gated range GLAD = 888..1176 step 4 (73 rungs, 72 increments, cell width s = 4); step-1 spectra around every measured transition rung REPORTED (entering eigenvalue vs threshold at step-1 resolution). Guards: overlap exact, Chebyshev envelope, parent-tower prefix Ward, reproduction Ward against the Feshbach run (6/7 gap(1176) = 0.1397 +- 2e-3, nn(888) = 6, nn(1176) = 8, lambda_min(1176) = 3.8825e-6 +- 2e-8), runtime cap 1800 s predeclared. CONTROLS (mandatory, must fire; frozen fire rule): CS position-scramble (deep comb, seed 7, rungs 496..512 step 4) and CE Epstein x^2 + 5y^2 (cap 640, rungs 624..640 step 4), same cocycle machinery; FIRE = [Stieltjes cone broken: min eig G(-eps) < -1e-6 at the top rung for some gated eps] OR [cell Schur block leaves the cone: min eig D_k < 0 at real z] OR [identity defect > 1e-6] OR [init/update solve singular]. VERDICT ENUM (frozen; decision order as listed): 0. any guard fails or a control fails to fire -> printed as COCYCLE-DEAD (invalid run), exit 1, no structural claim. 1. a kill fires -> COCYCLE-DEAD: the Gram route closes without further variants; the sharpened Z1 contract takes over with the handover content named in STAKES. 2. exact identity + domain preserved (incl. transitions) + all six gated convergence cells pass -> COCYCLE-CARRIES: the wall becomes a domain-preserving transport statement; what a proof would still need is named precisely: (i) UNCONDITIONAL cell positivity -- every cell Schur block D_k in the cone from the source construction itself, replacing the measured window PD input; (ii) a Loewner-order contraction modulus for the ordered Moebius product (Birkhoff/Wojtkowski-type), giving convergence without measurement; (iii) the z -> 0 boundary transition of the limit object (Nevanlinna/Herglotz). NO RH claim at any point. 3. identity + domain hold but a convergence cell fails -> COCYCLE-DOMAIN-ONLY: structure without limit; the Gram route retains only the domain-transport statement; Z1 handover as in STAKES plus the surviving domain facts. 4. anything else -> COCYCLE-DEAD (as in 1). STOP-LIST (binding, inherited): no bare A^{-1} (every resolvent at frozen z with |z| >= 1e-3 or Im z = h, never z = 0); no PD margin or 1/eps in any gate; no fits in gates beyond the declared bounded-statistic slope; no Riemann zeros; no target data; NO RH claim. This probe writes no files. RESULTS (2026-08-05; verdict COCYCLE-DOMAIN-ONLY, GATES 2/8, GUARDS+CONTROLS 14/14, 28.2 s): * RUN LOG (honesty): execution 1 (26.0 s) was destroyed by the numerical instability of the raw chained state (defect 6.2e13, garbage D_k margins) -- implementation failure, not adjudicable, disclosed above as the DECLARED IMPLEMENTATION CORRECTION. Execution 2 with the Hotelling-refreshed state is the valid run; the eigh-based W~ layer reproduced IDENTICALLY between both executions (as declared). * THE EXACT IDENTITY HOLDS AT MACHINE PRECISION: max per-rung defect 9.7e-12 over 73 rungs x 5 z (bar 1e-8), independent dense-solve Ward 1.3e-13 (bar 1e-8). The Moebius/Redheffer cell composition with source-lag coefficients is exact as derived. Cell margins (reported): min eig D_k in [0.0605, 0.0668] -- every cell Schur block PD; corner update terms PSD to -1.5e-17: the cocycle is a MONOTONE Loewner flow on the source, exactly the structure the domain gate transports. * DOMAIN PRESERVED, ZERO BREACHES in all 730 rung x cell tests INCLUDING both typed transitions (d 6 -> 7 at M = 992, entering eigenvalue 9.9438e-5; d 7 -> 8 at M = 1108, 9.9460e-5; step-1 resolution shows the threshold crossings at 991 -> 992 and 1106 -> 1107). Margins: Stieltjes cone min eig G >= 0.709, W~ >= 9.99; Herglotz Im >= +1.22e-2 (G), >= +98.8 (W~). Transition increments are UNREMARKABLE (same size as neighboring increments) -- the transitions are NOT the obstruction. * BUT NO CONVERGENCE CELL PASSES (0/6): the corner cocycle value G absorbs a FLAT ~0.1-0.2% relative update per rung (med5 ratios 1.032 / 1.014 / 0.777 at eps = 1e-1/1e-2/1e-3 -- no decay at reachable depth, though second-half rates turn positive +0.06..+0.59/X); the band object W~ falls to EXACTLY the bar (ratios 0.496 / 0.498 / 0.514 vs 0.5) but its second-half slope is NEGATIVE (b2 = -0.15..-0.16/X: increments RISING toward the top -- the moving-edge activity of the 7/8 modes, the same signature that flattened the d = 6 Feshbach tail). * CONTROLS both fire on every eps cell (Stieltjes cone broken: min eig G = -2.2e-4 scramble / -0.385 Epstein; cell blocks leave the cone: min eig D_k = -1.3e+5 / -4.1e+2); identity defects stay at 5e-12 on controls -- the algebra is universal, the DOMAIN is what the comb owns. * CONSEQUENCE (stated plainly, per the frozen stakes): STRUCTURE WITHOUT LIMIT. The Gram route retains exactly one theorem-shaped fact -- the exact source-native cell cocycle preserves the Nevanlinna/Stieltjes domain through the full gated range including the mode-entry transitions, as a monotone Loewner flow with PD cell blocks -- but its renormalized objects do NOT converge at reachable depth: the corner updates are flat and the band increments rise with the moving edge. Per the user's frozen stakes the Gram route CLOSES without further variants and the sharpened Z1 contract takes over. Z1 HANDOVER CONTENT: the moving-edge cadence (7th threshold at M = 992, count 8 from 1107/1108, the 8/9 crossing at 976); the ram-odd contact direction; the settled per-function q levels (R2 family 0.225..0.358, R1 family 0.008..0.079); and the surviving domain facts (exact cocycle identity, PD cell blocks, zero domain breaches, Herglotz/Stieltjes margins above). NO RH claim, no X -> infinity claim. Run: experiments/tfpt-discovery/.venv/bin/python \ experiments/tfpt-discovery/qf_cell_cocycle_probe.py """ import ast import hashlib import math import os import sys import time import numpy as np import scipy.linalg as sla _HERE = os.path.dirname(os.path.abspath(__file__)) _VERIFY = os.path.abspath(os.path.join(_HERE, "..", "..", "verification")) sys.path.insert(0, _HERE) sys.path.insert(0, _VERIFY) _HERE_DISC = os.path.abspath(os.path.join(_HERE, "..", "experiments", "tfpt-discovery")) sys.path.insert(0, _HERE_DISC) import v563_paper2_readouts as core # noqa: E402 import v755_simpler_schur_recursion as srp # noqa: E402 import v766_handoff_bulk as hbp # noqa: E402 import epstein_firewall_probe as epx # noqa: E402 import v770_qf_spectral_bundle as qsb # noqa: E402 (read-only) T_START = time.time() # ------------------------------------------------ frozen specification D = srp.DGRID ATOM_MAX_DEEP = 100000000 M_CAP_DEEP = int(math.floor(math.log(ATOM_MAX_DEEP) / D)) M_TOP_DEEP = 1176 M_TOP_PAR = 824 GLAD = list(range(888, 1177, 4)) # 73 rungs, 72 increments RECON_RUNGS = (888, 968, 1048, 1128, 1176) NCOR = 8 # frozen corner size EPS_GATED = (1.0e-1, 1.0e-2, 1.0e-3) Z_REF = -1.0e-2 H_IM = 1.0e-2 ZC = (complex(0.0, H_IM), complex(-1.0e-3, H_IM)) Z_ALL = tuple(complex(-e, 0.0) for e in EPS_GATED) + ZC THR_NULL = 1.0e-4 # band rule threshold THR_DEEP = 1.0e-5 IDY_BAR = 1.0e-8 # K1 per-rung defect WARD_BAR = 1.0e-8 # K1 dense-solve Ward REFRESH_FLOOR = 1.0e-11 # state refinement target REFRESH_MAX = 3 # Hotelling iters per cell HERG_FLOOR = 1.0e-10 # domain, complex points PSD_FLOOR = 1.0e-9 # domain, Stieltjes cone BREACH_SYS = 2 # > this = systematic (K2) SVD_FLOOR = 1.0e-8 # K4 transport floor C_MED = 0.50 C_SLOPE = 0.02 NOISE_PASS = 1.0e-12 INC_FIRST5 = slice(0, 5) INC_LAST5 = slice(67, 72) INC_HALF2 = slice(36, 72) QF_FLOOR = 1.0e-15 REPRO_GAP1176 = 0.1397 REPRO_NN888 = 6 REPRO_NN1176 = 8 REPRO_LMIN1176 = 3.8825e-6 REPRO_TOL = 2.0e-3 REPRO_LTOL = 2.0e-8 COMB_DEV_BAR = 1.0e-12 PREFIX_WARD = 1.0e-12 PD_TOL = 1.0e-9 RUNTIME_CAP = 1800.0 CTRL_CONE = -1.0e-6 # control fire floor CTRL_IDY = 1.0e-6 EP_NCAP = 34000 EP_MMAX = 640 SEED = 7 BANNED = ("zetazero", "nzeros", "isprime", "primerange", "nextprime", "prevprime", "primepi", "sympy") CHECKS = [] GATES = [] def check(name, ok, detail=""): CHECKS.append((name, bool(ok))) print("[%s] %s%s" % ("PASS" if ok else "FAIL", name, (": " + detail) if detail else "")) return bool(ok) def gate(name, ok, detail=""): GATES.append((name, bool(ok))) print("[GATE %s] %s%s" % ("PASS" if ok else "FAIL", name, (": " + detail) if detail else "")) return bool(ok) def ast_firewall(): with open(os.path.abspath(__file__), "r", encoding="utf-8") as fh: tree = ast.parse(fh.read()) hits = set() for node in ast.walk(tree): name = "" if isinstance(node, ast.Name): name = node.id elif isinstance(node, ast.Attribute): name = node.attr elif isinstance(node, (ast.Import, ast.ImportFrom)): for alias in node.names: token = alias.name.split(".")[0] if any(b in token.lower() for b in BANNED): hits.add(token) if name and any(b in name.lower() for b in BANNED): hits.add(name) return sorted(hits) def freeze_spec(): hsh = hashlib.sha256() hsh.update(("qf-cell-cocycle spec: cap %d M_CAP=%d M_TOP=%d " "D=%.10f; GLAD=%s; RECON=%s; NCOR=%d; band rule = " "threshold d(M)=#{lam<=%g}, transitions typed, " "increase embed [JR|N] sign-fixed, decrease " "re-anchor; z: eps=%s zref=%g h=%g zc=%s; identity: " "G_{k+1}=G_k+Y_I D^{-1} Y_I^T, Y=RU, D=(W-z)-U^T R " "U, defect<=%g every rung, ward<=%g at RECON, " "state refreshed by Hotelling to floor %g max %d " "iters (declared correction); " "domain: Herglotz>=-%g at zc AND Stieltjes cone " ">=-%g at real eps, both objects, every rung incl " "transitions, breaches: 0 pass, <=%d typed (CARRIES " "needs transition-adjacent), > systematic kill; " "conv: relative increments, N=max neighbor " "max-entry, med5<=%g AND b2>=%g, floor %g, blocks " "[0:5][67:72][36:72], gated cells = {G,W~}x{real " "eps}, complex reported; kills: idy, systematic " "breach, AST, svd<%g, normalizer audit; repro: " "gap1176=%g nn888=%d nn1176=%d lmin=%g tol %g/%g; " "guards: comb<=%g prefix<=%g pd>-%g cap %g; " "controls: cone<%g or Dk<0 or idy>%g or singular, " "lads %s/%s ep %d/%d seed %d; verdict: invalid -> " "kills DEAD -> all pass CARRIES -> identity+domain " "DOMAIN-ONLY -> DEAD; stakes: DEAD closes the Gram " "route, Z1 contract takes over" % (ATOM_MAX_DEEP, M_CAP_DEEP, M_TOP_DEEP, D, GLAD, RECON_RUNGS, NCOR, THR_NULL, EPS_GATED, Z_REF, H_IM, ZC, IDY_BAR, WARD_BAR, REFRESH_FLOOR, REFRESH_MAX, HERG_FLOOR, PSD_FLOOR, BREACH_SYS, C_MED, C_SLOPE, NOISE_PASS, SVD_FLOOR, REPRO_GAP1176, REPRO_NN888, REPRO_NN1176, REPRO_LMIN1176, REPRO_TOL, REPRO_LTOL, COMB_DEV_BAR, PREFIX_WARD, PD_TOL, RUNTIME_CAP, CTRL_CONE, CTRL_IDY, qsb.CTRL_LAD_S, qsb.CTRL_LAD_E, EP_NCAP, EP_MMAX, SEED)).encode()) return hsh.hexdigest() # ------------------------------------------------ towers (verbatim) def build_parent_tower(): alpha = 0.5 * M_TOP_PAR * D ka, masks, dev_m = srp.channel_masks(alpha) check("G1.3 parent tower comb consistency (zeta-free Gauss " "double sieve == deployed masses, rel dev <= %.0e)" % COMB_DEV_BAR, dev_m <= COMB_DEV_BAR, "rel dev %.1e, ka=%d" % (dev_m, ka)) c = srp.continuum_lags(M_TOP_PAR) for cnl in ("ro", "re", "sp", "in"): c = c + srp.atom_channel_lags(alpha, M_TOP_PAR, masks[cnl]) return sla.toeplitz(c[:M_TOP_PAR]) def build_deep_comb(): lam_deep = core.von_mangoldt_table(ATOM_MAX_DEEP) dev = float(np.max(np.abs(lam_deep[:core.ATOM_MAX + 1] - core.LAM_TAB))) check("G1.1 deep-table overlap: deep von Mangoldt table == " "deployed core table on [0, %d] EXACTLY" % core.ATOM_MAX, dev == 0.0, "max abs dev %.1e" % dev) nn = np.nonzero(lam_deep > 0.0)[0] u_deep = np.log(nn.astype(float)) mu_deep = 2.0 * lam_deep[nn] / np.sqrt(nn.astype(float)) psi = np.cumsum(lam_deep[nn]) keep = nn.astype(float) >= core.KAPPA_X0 kappa = float(np.max(np.abs(psi[keep] - nn[keep].astype(float)) / nn[keep].astype(float))) check("G1.2 deep-range Chebyshev envelope: kappa = %.6f <= " "%.6f" % (kappa, core.KAPPA_REF + core.TOL_KAPPA), kappa <= core.KAPPA_REF + core.TOL_KAPPA) return u_deep, mu_deep def build_deep_tower(u_deep, mu_deep, T_par): alpha = 0.5 * M_TOP_DEEP * D ka = int(np.searchsorted(u_deep, 2.0 * alpha + 1.0e-14, side="right")) c_cont = srp.continuum_lags(M_TOP_DEEP) c_at, _dd = core.atom_lags_at(alpha, M_TOP_DEEP, u_deep[:ka], mu_deep[:ka]) T = sla.toeplitz((c_cont + c_at)[:M_TOP_DEEP]) dev = float(np.max(np.abs(T[:M_TOP_PAR, :M_TOP_PAR] - T_par))) check("G1.4 prefix Ward: deep tower leading %d block == parent " "tower, max abs dev %.1e <= %.0e" % (M_TOP_PAR, dev, PREFIX_WARD), dev <= PREFIX_WARD) return T, c_cont, alpha, ka # ------------------------------------------------ exact cell cocycle def ident_defect(T, z, R, M): cols = R[:, :NCOR] E = T[:M, :M] @ cols - z * cols E[np.arange(NCOR), np.arange(NCOR)] -= 1.0 return float(np.max(np.abs(E))) def cocycle_run(T, z, sizes, ward_rungs=(), margins=False): """Exact ordered cell cocycle: init resolvent at sizes[0], then 72 Moebius/Redheffer cell updates with (U, W) = the added rows/columns. Returns per-rung corners, defects, cell margins, dense-solve Ward residuals.""" cplx = (z.imag != 0.0) dt = np.complex128 if cplx else np.float64 zz = z if cplx else z.real M0 = sizes[0] A0 = np.asarray(T[:M0, :M0], dtype=dt) R = sla.solve(A0 - zz * np.eye(M0, dtype=dt), np.eye(M0, dtype=dt), assume_a="sym") dfc = ident_defect(T, zz, R, M0) for _ in range(REFRESH_MAX): if dfc <= REFRESH_FLOOR: break E0 = -(T[:M0, :M0] @ R - zz * R) E0[np.arange(M0), np.arange(M0)] += 1.0 R = R + R @ E0 dfc = ident_defect(T, zz, R, M0) Gs = [R[:NCOR, :NCOR].copy()] defects = [dfc] dk_min, upd_lo, upd_hi = [], [], [] wards = {} def ward_at(M, Rmat): A = np.asarray(T[:M, :M], dtype=dt) cols = np.eye(M, dtype=dt)[:, :NCOR] Gd = sla.solve(A - zz * np.eye(M, dtype=dt), cols, assume_a="sym")[:NCOR, :] num = float(np.max(np.abs(Gd - Rmat[:NCOR, :NCOR]))) return num / max(float(np.max(np.abs(Gd))), QF_FLOOR) if M0 in ward_rungs: wards[M0] = ward_at(M0, R) for Ma, Mb in zip(sizes, sizes[1:]): s = Mb - Ma U = np.asarray(T[:Ma, Ma:Mb], dtype=dt) W = np.asarray(T[Ma:Mb, Ma:Mb], dtype=dt) Y = R @ U Dm = (W - zz * np.eye(s, dtype=dt)) - U.T @ Y Dinv = np.linalg.inv(Dm) YD = Y @ Dinv Rn = np.empty((Mb, Mb), dtype=dt) Rn[:Ma, :Ma] = R + YD @ Y.T Rn[:Ma, Ma:] = -YD Rn[Ma:, :Ma] = -YD.T Rn[Ma:, Ma:] = Dinv R = Rn # Exact-identity-preserving state refinement (declared # implementation correction, see docstring): Hotelling # iteration R <- R + R (I - (A - z) R) until the carried # state meets the refresh floor; coefficients untouched. dfc = ident_defect(T, zz, R, Mb) for _ in range(REFRESH_MAX): if dfc <= REFRESH_FLOOR: break E = -(T[:Mb, :Mb] @ R - zz * R) E[np.arange(Mb), np.arange(Mb)] += 1.0 R = R + R @ E dfc = ident_defect(T, zz, R, Mb) Gs.append(R[:NCOR, :NCOR].copy()) defects.append(dfc) if margins and not cplx: dk_min.append(float(np.min(np.linalg.eigvalsh( 0.5 * (Dm + Dm.T))))) upd = Y[:NCOR] @ Dinv @ Y[:NCOR].T ev = np.linalg.eigvalsh(0.5 * (upd + upd.T)) upd_lo.append(float(ev[0])) upd_hi.append(float(ev[-1])) if Mb in ward_rungs: wards[Mb] = ward_at(Mb, R) return dict(Gs=Gs, defects=defects, dk_min=dk_min, upd_lo=upd_lo, upd_hi=upd_hi, wards=wards) # ------------------------------------------------ band layer def spectral_pass(T, sizes): out = {} for M in sizes: A = T[:M, :M] lam, V = np.linalg.eigh(A) out[M] = dict(lam=lam, V=qsb.sign_fix(V[:, :10]), d=int(np.sum(lam <= THR_NULL))) return out def band_transport(spec): """Chained polar transport with typed transition maps on the depth-dependent band d(M).""" ds = [spec[M]["d"] for M in GLAD] Rs = [np.eye(ds[0])] trans, sig_min = [], [] for i, (Ma, Mb) in enumerate(zip(GLAD, GLAD[1:])): da, db = ds[i], ds[i + 1] Va = spec[Ma]["V"][:, :da] Vb = spec[Mb]["V"][:Ma, :db] S = Vb.T @ Va # (db, da) if db == da: U, sv, Vt = np.linalg.svd(S) Rs.append((U @ Vt) @ Rs[-1]) sig_min.append(float(sv[-1])) elif db > da: U, sv, Vt = np.linalg.svd(S, full_matrices=True) J = U[:, :da] @ Vt N = U[:, da:db] for j in range(N.shape[1]): if N[np.argmax(np.abs(N[:, j])), j] < 0.0: N[:, j] = -N[:, j] Rs.append(np.concatenate([J @ Rs[-1], N], axis=1)) sig_min.append(float(sv[-1])) trans.append((i, Ma, Mb, da, db, "MODE-ENTRY", float(spec[Mb]["lam"][db - 1]))) else: Rs.append(np.eye(db)) sig_min.append(1.0) trans.append((i, Ma, Mb, da, db, "MODE-EXIT re-anchor", float(spec[Mb]["lam"][db - 1]))) return ds, Rs, trans, sig_min def band_obj(spec, Rs, z): out = [] for i, M in enumerate(GLAD): d = spec[M]["d"] lam = spec[M]["lam"][:d] out.append(Rs[i].T @ np.diag(1.0 / (lam - z)) @ Rs[i]) return out def rel_increments(objs, ds): rel, raw = [], [] for i in range(len(objs) - 1): c = min(ds[i], ds[i + 1]) dd = float(np.max(np.abs(objs[i + 1][:c, :c] - objs[i][:c, :c]))) nn = max(float(np.max(np.abs(objs[i]))), float(np.max(np.abs(objs[i + 1]))), QF_FLOOR) raw.append(dd) rel.append(dd / nn) return np.array(rel), np.array(raw) def conv_stat(rel, xs): med_f = float(np.median(rel[INC_FIRST5])) med_l = float(np.median(rel[INC_LAST5])) ratio = med_l / max(med_f, QF_FLOOR) rows = [dict(XmR=float(x), mx=float(max(v, QF_FLOOR))) for x, v in zip(xs[INC_HALF2], rel[INC_HALF2])] b2, _r = hbp.fit_rate(rows) ok = (ratio <= C_MED and b2 >= C_SLOPE) or med_l <= NOISE_PASS return med_f, med_l, ratio, b2, ok def herg_min(F): return float(np.min(np.linalg.eigvalsh( 0.5j * (F.conj().T - F)))) def psd_min(F): return float(np.min(np.linalg.eigvalsh( 0.5 * (F + F.T).real))) # ------------------------------------------------ controls def control_cocycle(Tc, lad, label): dets, fired = [], False for e in EPS_GATED: z = complex(-e, 0.0) try: out = cocycle_run(Tc, z, list(lad), margins=True) except np.linalg.LinAlgError: dets.append("eps=%g: singular update (fires)" % e) fired = True continue cone = psd_min(out["Gs"][-1]) dkm = min(out["dk_min"]) if out["dk_min"] else 0.0 idy = max(out["defects"]) f = cone < CTRL_CONE or dkm < 0.0 or idy > CTRL_IDY fired = fired or f dets.append("eps=%g: min eig G = %+.2e, min eig D_k = " "%+.2e, defect %.1e -> %s" % (e, cone, dkm, idy, "FIRES" if f else "quiet")) lam = np.linalg.eigvalsh(Tc[:lad[-1], :lad[-1]]) det = ("%s: %s; census %d/%d negative eigenvalues (complex-" "point Herglotz not discriminating -- predeclared)" % (label, "; ".join(dets), int(np.sum(lam < 0.0)), len(lam))) return fired, det def run_controls(c_cont, alpha_deep, ka_deep, mu_deep): print("\n-- controls (must fire: indefinite data breaks the " "Stieltjes cone / cell positivity)") rng = np.random.default_rng(SEED) pos = np.sort(rng.uniform(0.5, 2.0 * alpha_deep, ka_deep)) cat_s, _dd = core.atom_lags_at(alpha_deep, M_TOP_DEEP, pos, mu_deep[:ka_deep]) Ts = sla.toeplitz((c_cont + cat_s)[:M_TOP_DEEP]) fire_s, det_s = control_cocycle(Ts, qsb.CTRL_LAD_S, "scramble") check("CS position-scramble control fires", fire_s, det_s) r1 = epx.lattice_r1(EP_NCAP) bb = np.asarray(r1, float) / 2.0 lamE = epx.dirichlet_vonmangoldt(bb, EP_NCAP) supp = np.nonzero(np.abs(lamE) > 1.0e-9)[0] supp = supp[supp >= 2] posE = np.log(supp.astype(float)) masE = 2.0 * lamE[supp] / np.sqrt(supp.astype(float)) catE, _dd = core.atom_lags_at(0.5 * EP_MMAX * D, EP_MMAX, posE, masE) cont = srp.continuum_lags(EP_MMAX) TE = sla.toeplitz((cont + catE)[:EP_MMAX]) fire_e, det_e = control_cocycle(TE, qsb.CTRL_LAD_E, "epstein") check("CE Epstein control (x^2+5y^2) fires", fire_e, det_e) # ------------------------------------------------ run def run(): print("=" * 78) print("QF OFFENSIVE strand 3, module 4 (LAST DECIDER) -- " "ordered cell cocycle on the d(X) band, 1e8 comb") print("=" * 78) hits = ast_firewall() check("G0.1 AST firewall (K3: update coefficients are lag data " "of the source operator only)", not hits, str(hits)) spec_sha = freeze_spec() check("G0.2 construction + band rule + domain + bars + verdict " "order SHA-256-frozen BEFORE any comb data", True, "SHA256 %s..." % spec_sha[:16]) check("G0.3 reach census: M_TOP = %d <= %d; sieve cover %d <= " "%d; runtime cap %.0f s" % (M_TOP_DEEP, M_CAP_DEEP, int(math.exp(M_TOP_DEEP * D)) + 2, ATOM_MAX_DEEP, RUNTIME_CAP), M_TOP_DEEP <= M_CAP_DEEP and int(math.exp(M_TOP_DEEP * D)) + 2 <= ATOM_MAX_DEEP) u_deep, mu_deep = build_deep_comb() T_par = build_parent_tower() T, c_cont, alpha_deep, ka_deep = build_deep_tower( u_deep, mu_deep, T_par) # ---- band layer: spectra, d(X), transitions, transport spec = spectral_pass(T, GLAD) ds = [spec[M]["d"] for M in GLAD] pd_min = min(float(spec[M]["lam"][0]) for M in GLAD) check("G1.6 measured PD: lambda_min = %.3e > -%.0e on every " "gated rung (measured output, in NO gate)" % (pd_min, PD_TOL), pd_min > -PD_TOL) g1176 = (spec[1176]["lam"][6] - spec[1176]["lam"][5]) \ / spec[1176]["lam"][6] check("G1.5 reproduction Ward: 6/7 gap(1176) = %.4f vs %.4f " "(tol %.0e); nn(888) = %d (== %d), nn(1176) = %d (== " "%d); lambda_min(1176) = %.4e vs %.4e (tol %.0e)" % (g1176, REPRO_GAP1176, REPRO_TOL, ds[0], REPRO_NN888, ds[-1], REPRO_NN1176, spec[1176]["lam"][0], REPRO_LMIN1176, REPRO_LTOL), abs(g1176 - REPRO_GAP1176) <= REPRO_TOL and ds[0] == REPRO_NN888 and ds[-1] == REPRO_NN1176 and abs(spec[1176]["lam"][0] - REPRO_LMIN1176) <= REPRO_LTOL) ds, Rs, trans, sig_min = band_transport(spec) t_rungs = set() for (i, Ma, Mb, da, db, typ, lnew) in trans: t_rungs.add(Mb) print(" TYPED TRANSITION at increment %d (%d -> %d): d " "%d -> %d [%s], entering eigenvalue %.4e vs " "threshold %.0e" % (i, Ma, Mb, da, db, typ, lnew, THR_NULL)) check("K4 kill audit: transport min sigma_min = %.6f >= %.0e " "over the chained d(X) overlaps (%d typed transitions)" % (min(sig_min), SVD_FLOOR, len(trans)), min(sig_min) >= SVD_FLOOR) print(" d(X) profile: d = %d on %d rungs, 7 from M = %d, 8 " "from M = %d" % (ds[0], len(GLAD), next((M for M, d in zip(GLAD, ds) if d >= 7), -1), next((M for M, d in zip(GLAD, ds) if d >= 8), -1))) # ---- exact cocycle at all five z print("\n-- exact cell cocycle (identity gated on every rung)") coc = {} idy_worst, ward_worst = 0.0, 0.0 for z in Z_ALL: coc[z] = cocycle_run(T, z, GLAD, ward_rungs=RECON_RUNGS, margins=(abs(z - Z_REF) < 1e-15)) idy_worst = max(idy_worst, max(coc[z]["defects"])) ward_worst = max(ward_worst, max(coc[z]["wards"].values())) id_ok = gate("IDENTITY exact Moebius/Redheffer composition: " "max per-rung defect ||(A-z)R[:,I] - E_I|| = " "%.1e <= %.0e over %d rungs x %d z; max " "independent dense-solve Ward residual = %.1e <= " "%.0e at %d rungs x %d z" % (idy_worst, IDY_BAR, len(GLAD), len(Z_ALL), ward_worst, WARD_BAR, len(RECON_RUNGS), len(Z_ALL)), idy_worst <= IDY_BAR and ward_worst <= WARD_BAR) mz = coc[complex(Z_REF, 0.0)] print(" cell margins at z_ref (REPORTED, never gated): min " "eig D_k in [%.4e, %.4e]; corner update-term eigenrange " "[%.1e, %.1e]" % (min(mz["dk_min"]), max(mz["dk_min"]), min(mz["upd_lo"]), max(mz["upd_hi"]))) # ---- band objects wt = {z: band_obj(spec, Rs, z) for z in Z_ALL} # ---- domain gates print("\n-- domain preservation (Nevanlinna/Stieltjes sandwich" ", both objects, every rung incl. transitions)") breach_nt, breach_t = [], [] margins = {} for lbl, series in (("G", coc), ("W~", wt)): for z in Z_ALL: objs = series[z]["Gs"] if lbl == "G" else series[z] vals = [] for i, M in enumerate(GLAD): if z.imag > 0.0: m = herg_min(objs[i]) bad = m < -HERG_FLOOR else: m = psd_min(objs[i]) bad = m < -PSD_FLOOR vals.append(m) if bad: (breach_t if M in t_rungs else breach_nt).append((lbl, z, M, m)) margins[(lbl, z)] = (min(vals), max(vals)) for (lbl, z), (lo, hi) in margins.items(): cls = "Herglotz Im>=" if z.imag > 0.0 else "cone min eig" print(" %-2s z=%s: %s in [%+.3e, %+.3e] %s" % (lbl, ("%g%+gi" % (z.real, z.imag)) if z.imag else "%g" % z.real, cls, lo, hi, "(transitions included)" if t_rungs else "")) dom_ok = gate("DOMAIN preserved: %d non-transition breaches " "(0 required for clean pass; <= %d typed; > %d " "systematic kill) and %d transition-rung " "breaches across %d rung x cell tests" % (len(breach_nt), BREACH_SYS, BREACH_SYS, len(breach_t), 2 * len(Z_ALL) * len(GLAD)), len(breach_nt) == 0 and len(breach_t) == 0) k2_kill = len(breach_nt) > BREACH_SYS # ---- convergence of the renormalized objects print("\n-- renormalized convergence (relative entrywise " "increments; declared normalizer = neighbor max-entry)") xs = np.array([M * D for M in GLAD[1:]]) conv_ok = True for lbl, series in (("G", coc), ("W~", wt)): for z in Z_ALL: objs = series[z]["Gs"] if lbl == "G" else series[z] dloc = ds if lbl == "W~" else [NCOR] * len(GLAD) rel, raw = rel_increments(objs, dloc) med_f, med_l, ratio, b2, ok = conv_stat(rel, xs) gated = (z.imag == 0.0) line = ("%-2s z=%-8s med5 first/last = %.3e / %.3e, " "ratio %.3f, b2 %+ .3f/X, raw last %.2e" % (lbl, "%g" % z.real if not z.imag else "%g%+gi" % (z.real, z.imag), med_f, med_l, ratio, b2, raw[-1])) if gated: conv_ok &= gate("CONV %s (bars med5<=%g, " "b2>=%g, floor %g)" % (line, C_MED, C_SLOPE, NOISE_PASS), ok) else: print(" reported: %s" % line) if lbl == "W~" and gated and trans: tt = ["inc %d (M=%d): rel %.3e" % (i, Mb, rel[i]) for (i, _Ma, Mb, _a, _b, _t, _l) in trans] print(" transition increments: %s" % "; ".join(tt)) # ---- step-1 spectra around transitions (reported) print("\n-- step-1 spectra around transitions (REPORTED)") for (_i, _Ma, Mb, _da, db, _typ, _lnew) in trans: for M in range(Mb - 4, min(Mb + 5, M_TOP_DEEP + 1)): lam = np.linalg.eigvalsh(T[:M, :M]) print(" M=%d: nn=%d, lam_%d = %.4e (thr %.0e)" % (M, int(np.sum(lam <= THR_NULL)), db, lam[db - 1], THR_NULL)) # ---- K5 normalizer audit check("K5 kill audit: the convergence normalizer is the " "object's own neighbor max-entry (source-native, " "declared part of the renormalized object) -- no " "RH-strength input, no 1/eps, no PD margin in any gate", True) # ---- controls + runtime run_controls(c_cont, alpha_deep, ka_deep, mu_deep) dt = time.time() - T_START check("G0.4 runtime %.1f s <= cap %.0f s" % (dt, RUNTIME_CAP), dt <= RUNTIME_CAP) # ---- verdict guards_ok = all(ok for (n, ok) in CHECKS if not n.startswith(("CS", "CE"))) controls_ok = all(ok for (n, ok) in CHECKS if n.startswith(("CS", "CE"))) kill = (not id_ok) or k2_kill or (min(sig_min) < SVD_FLOOR) if not (guards_ok and controls_ok): verdict = "COCYCLE-DEAD (invalid run)" elif kill: verdict = "COCYCLE-DEAD" elif id_ok and dom_ok and conv_ok: verdict = "COCYCLE-CARRIES" elif id_ok and dom_ok: verdict = "COCYCLE-DOMAIN-ONLY" else: verdict = "COCYCLE-DEAD" n_gate = sum(1 for (_n, ok) in GATES if ok) n_chk = sum(1 for (_n, ok) in CHECKS if ok) print("\nVERDICT: %s" % verdict) print("GATES %d/%d, GUARDS+CONTROLS %d/%d, runtime %.1f s" % (n_gate, len(GATES), n_chk, len(CHECKS), time.time() - T_START)) if verdict == "COCYCLE-CARRIES": print("CONSEQUENCE (stated plainly): the wall is now a " "DOMAIN-PRESERVING TRANSPORT statement -- the exact " "cell cocycle composes through the full gated range " "including the typed mode-entry transitions, stays " "in the Nevanlinna/Stieltjes domain, and its " "renormalized objects converge at the frozen bars. " "WHAT A PROOF WOULD STILL NEED (named precisely): " "(i) UNCONDITIONAL cell positivity -- every cell " "Schur block D_k in the cone from the source " "construction itself, replacing the measured window " "PD input; (ii) a Loewner-order contraction modulus " "for the ordered Moebius product " "(Birkhoff/Wojtkowski-type), turning the measured " "convergence into a theorem; (iii) the z -> 0 " "boundary transition of the limit object " "(Nevanlinna/Herglotz). NO RH claim; this is a " "renormalized-object statement at reachable depth, " "not the absolute 2^-n contract.") elif verdict == "COCYCLE-DOMAIN-ONLY": print("CONSEQUENCE (stated plainly): structure without " "limit -- the exact identity and the domain " "transport hold (the failing convergence cells are " "printed above), so the Gram route retains ONLY the " "domain-transport statement. Per the frozen " "stakes: the sharpened Z1 contract takes over, " "carrying the moving-edge cadence (992 / ~1108 / " "976), the ram-odd contact direction, the settled q " "levels (0.225..0.358 / 0.008..0.079), and the " "surviving domain facts named above. NO RH claim.") else: print("CONSEQUENCE (stated plainly): the cocycle route " "dies -- per the frozen stakes the Gram route " "closes WITHOUT further variants and the sharpened " "Z1 contract takes over. Z1 handover content: the " "moving-edge cadence (7th threshold at 992, count 8 " "from ~1108, 8/9 crossing at 976), the ram-odd " "contact direction, the settled per-function q " "levels (R2 0.225..0.358, R1 0.008..0.079), and the " "domain facts that did/did not survive (see the " "margin table above). NO RH claim.") return 0 if (guards_ok and controls_ok) else 1 _run_probe = run def run(): """run_all entry point (preregistered pattern, v757/v763 precedent): guards+controls must be 14/14 and the gate table must show EXACTLY the preregistered 2/8 pattern -- IDENTITY and DOMAIN pass, all six gated convergence cells fail -- verdict COCYCLE-DOMAIN-ONLY: structure without limit; per the frozen stakes the diagonal Gram route closes and the sharpened Z1 contract takes over.""" rc = _run_probe() chk_fails = [n for (n, ok) in CHECKS if not ok] gate_fails = [n for (n, ok) in GATES if not ok] passes = [n for (n, ok) in GATES if ok] ok = (rc == 0 and not chk_fails and len(GATES) == 8 and len(gate_fails) == 6 and all(n.startswith("CONV") for n in gate_fails) and any(n.startswith("IDENTITY") for n in passes) and any(n.startswith("DOMAIN") for n in passes)) print("\n[%s] PATTERN GATE: expected the preregistered " "COCYCLE-DOMAIN-ONLY pattern (IDENTITY + DOMAIN pass, all " "six CONV cells fail, guards+controls 14/14) -- failing " "gates: %s, failing guards: %s" % ("PASS" if ok else "FAIL", [f.split()[0] for f in gate_fails], [f.split()[0] for f in chk_fails] or "none")) print("\nADJUDICATION: %s -- COCYCLE-DOMAIN-ONLY: the exact " "source-native Moebius/Redheffer cell cocycle preserves the " "Nevanlinna/Stieltjes domain through both typed mode-entry " "transitions as a monotone Loewner flow with PD cell blocks " "(structure), but no renormalized object converges at " "reachable depth (no limit) -- per the frozen stakes the " "diagonal Gram route CLOSES without further variants and " "the sharpened Z1 contract takes over. NO RH claim." % ("PASS" if ok else "FAIL")) return 0 if ok else 1 if __name__ == "__main__": import sys as _sys _sys.exit(run())