#!/usr/bin/env python3 """v780 -- PRIME.Z1.COMPACTNESS.01: the sharpened-Z1 trilogy -- edge signature, boundary triple, variable-edge M-function -- ONE module from three probes (v518 precedent; gates 3/4 + 1/4 + legs 3/6 with EXACTLY the preregistered fails; guards+controls 20/20 + 23/23 + 23/23; ~270 s -- parts 2 and 3 re-derive the 1e9 comb in-process, full frozen ladders kept per the v677/v772 suite precedent; discovery probes z1_edge_signature_probe.py Z1-SIGNATURE-PARTIAL, z1_boundary_triple_probe.py Z1-TRIPLE-PARTIAL, z1_variable_edge_mfunction_probe.py Z1-VAREDGE-PARTIAL, all 2026-08-05). MODULE 1 (the gate): the N2 GNS/Jacobi family carries THREE of the four measured handover signatures natively in its self-adjoint frame -- edge collisions at the right depth (min boundary-pair gap 0.0032 vs source 0.0039), the ram-odd contact direction in its threshold band (cos up to 0.9971, 5/5 on LAST5; the first genuinely positive structural transfer onto the N2 family), settled positive couplings (14/14 type P) -- but NOT the widening cadence: its edge census is regular quadrature filling (DX ~ 0.4485, the free-Jacobi type; structural identification: the Gram window operator IS the Toeplitz Gram of the N2 unified Weil measure), so the cell structure must be IMPORTED as boundary data. MODULE 2 (the import): the finite boundary triple (A = 2 - J_K, imported Gram band) is EXACTLY Herglotz through all typed transitions (min eig Im H = +0.216; gate a) -- the frame survives -- but delivery/cell/trace fail at 5.88/no-response/0.388 with the root cause MEASURED: the Gram near-kernel packets are delocalized (cell-mass exactly 0.500 beyond the K = M/2 GNS window on every gate rung), so the truncation + polar whitening turns the loss into quasi-generic boundary noise; still arithmetic-specific (5.9 vs GOE 13.0 vs random 132.5); full-depth GNS is provably out of reach by deepening (lags to 2M = X 27.75, e^27.75 atoms). MODULE 3 (the yield): with the RAW mu-weighted import (no whitening; candidate A/B trigger executed as frozen, both at 0.92 -- typed UNRESOLVED-BY-THIS-METRIC with the disclosed discrimination loss, far from dead-grade 10): the Herglotz family is BOUNDED (grid-sup ratio 0.936, it falls) and EQUICONTINUOUS (derivative ratio 0.807) through all three typed transitions; the entry mass is SUMMABLE (c_mass max 0.032 << bar 1.0 -- the user kill 'nicht summierbare Eintrittsmasse' is far away; entry masses constant to 1%); the entry residues are predominantly RANK-ONE (ratios 0.796/0.869/0.804 -- the 0.997-contact prediction confirmed in the raw metric) with an O(20%) non-PSD rebalancing drift (P1 PSD half typed too strong); the moment functionals do NOT settle (median tail osc 22.1) -- same root cause as the delivery: the import noise. THE MEASURED UNIFICATION (the round's real yield): PRIME.KMS.INDUCTIVE_STATE.02 and PRIME.Z1.OPERATOR.01 SHARE their compactness theorem -- the cluster-existence half is CARRIED (bounded mass + bounded/equicontinuous family = Helly/Montel at finite level) -- and SHARE their single remaining obstruction: state SELECTION (the moment tracks must settle) == import-faithful boundary coupling (a coupling of the Gram band to the bulk that does not pass through the lossy K = M/2 half-window frame). Both contract rows carry the dated cross-referenced note; the merged target is named Z1-COMPACTNESS. NOT claimed: anything beyond X = 20.3125, limit existence, eps-uniformity, continuum self-adjointness, spectral reality, RH. No marker move. Python-only per GATE.WOLFRAM.02. PROVENANCE: discovery probes z1_edge_signature_probe.py (2026-08-05, 27.1 s, gates 3/4 A-fail, 20/20; the Z1-C avatar construction correction -- census 5-dim ro-negative FRAME instead of the invalid single-vector first run -- carried verbatim in the docstring, all bars unchanged), z1_boundary_triple_probe.py (2026-08-05, 118.6 s, gates 1/4 a-pass, 23/23, single preregistered execution) and z1_variable_edge_mfunction_probe.py (2026-08-05, 115.5 s, legs 3/6 DEL/P1/CL-fail, 23/23, single preregistered execution, candidate B after the frozen trigger); all three re-run identically at promotion. Promoted verbatim as ONE module; transforms: sibling imports remapped to the promoted twins (simpler_schur_recursion_probe -> v755, handoff_bulk_probe -> v766, qf_spectral_bundle_probe -> v770; epstein_firewall_probe stays a read-only discovery import -- v773 precedent), parts 2/3 wrapped in function scopes, and run() encodes the three preregistered partial patterns (v757 precedent). Numbers unchanged. Original edge-signature probe docstring (verbatim): SHARPENED-Z1 kickoff -- the first Z1 gate: does the N2 Hilbert-Polya truncation family (the deployed zeta-free GNS/Jacobi family of the glued object, v714/v716-v721/v727-v734) exhibit the SAME moving-edge / near-kernel signature that the closed diagonal- Gram route measured on its window operator? z1_edge_signature_probe. Exploration only (tfpt-experiment firewall): NOT wired into run_all.py, no ledger row, no paper edit, no website edit, NO RH CLAIM, no spectral-reality claim beyond measurement, and this probe writes no files. It never reads a zero ordinate; the construction path is AST-firewalled against prime/zero identifiers exactly as in the parent probes. STRUCTURAL IDENTIFICATION (stated first, it frames the whole gate): the closed Gram route's source window operator is T = Toeplitz(continuum + atoms) on the dyadic grid D = 1/64, and srp.continuum_lags(M) == core.arch_lags + stage2.pole_lags_closed: the source tower IS the Toeplitz Gram matrix of the N2 unified Weil measure p = car + cat + cp. The N2 truncation family (v718 machinery: Wheeler modified-Chebyshev -> monic (aM, gM) -> orthonormal Jacobi J_K, eigenvalues = Gauss nodes) is the GNS representation of the multiplication/shift operator of the SAME measure. This probe therefore does NOT ask "same object?" (that is exact and guarded); it asks whether the MEASURED handover constraints of the Gram route survive the passage into the candidate's self-adjoint operator frame J_K -- the frame in which any Z1 boundary-triple / Weyl-M-function module would have to work. A match = the candidate family carries the threshold structure natively; a failure = the structure is Gram-frame-specific and the constraint list rules the family out as-is. INPUT STATE (frozen findings, none re-adjudicated here): * qf_edge_separation_probe (EDGE-KEEPS-MOVING, 1e9 comb): source near-kernel (thr 1e-4) mode entries at M = 888 / 992 / 1108 / 1276 (X = 13.875 / 15.5 / 17.3125 / 19.9375), inter-entry gaps DX = 1.625 / 1.8125 / 2.625 -- WIDENING cadence (ratios 1.11538, 1.44828), rel spread 0.381; avoided 7/8 crossing with min rel gap 0.0039 at M = 1240; separated dimension oscillates (6 separated under a 7/8/9 cluster at the top). * qf_drainage_probe (QF-SETTLES-POSITIVE 14/14, 1e8 comb): settled per-function band weights (R2 family 0.225..0.358, R1 family 0.008..0.079); entry anchors 888:6 / 992:7 / count 8 from ~1108; 6/7 gap bottoms 0.1008 (~1100), recovers 0.1397 at 1176; lambda_min(1176) = 3.882e-6. * qf_representation_census_probe (QF-REPRESENTATION-OPEN): exactly ONE near-null direction is rung-stably (cos = 0.992..0.999, typ. 0.997) the ram-odd most-negative wavepacket direction; the E_7 (+) E_{-2} identification failed the census. * note_hilbert_polya_truncations / v718: the N2 family's GNS nodes converge onto the frozen targets (100% of 377 at tol 0.25, ladder rate -1.61); pole band tau < GAMMA1 = 14.10 is the trivial-mode/threshold band of the family (27 nodes at h = 1433); Wheeler validity + Levinson PD measured on all windows. CANDIDATE FAMILY (frozen; deployed construction reused read-only, zeta-free by design, verified by the AST guard): at dyadic rung M (X = M*D), the candidate operator is the K-point GNS truncation J_K of the unified window measure with K = M/2: Chebyshev moments p[:M] -> jac.wheeler(p[:M], K) -> orthonormal Jacobi (bJ = aM, aJ = sqrt(gM[1:K])) -- v718 gns_nodes machinery verbatim. DECLARED frame choice: the per-window D(h) of the deployed frame-A ladder is replaced by the source's dyadic D = 1/64 so that the candidate's ladder lives on the SAME X axis as the measured source cadence; the K-ladder at fixed measure is exactly v718's "pure GNS ladder". Deep comb cap ATOM_MAX_DEEP = 1e8 (drainage cap, frozen), M_TOP = 1176, ladder LAD = 648..1176 step 4 (133 rungs, K = 324..588), census pre-rung M_PRE = 644. THE GNS FRAME MAP (frozen; needed to transplant contact + drainage): the ON polynomial basis of J_K is the Cholesky-ON basis of the cos-basis Gram G_c[j,k] = (p_|j-k| + p_{j+k})/2 (the even folding of the Toeplitz Gram under x = 2 cos theta); for a coefficient vector f the GNS coordinates are c = L^T f (G_c = L L^T) and ||f||_mu = ||L^T f||. Frame Ward G1.7: at M_WARD = 648 the tridiagonalization L^{-1} A_x L^{-T} of the multiplication matrix A_x[j,k] = must reproduce the Wheeler (aM, sqrt gM) tridiagonal (max abs dev <= 1e-3, consistency Ward -- catches a wrong frame, not a precision claim; the norm-chain L[k,k] = ||pi_k||/2 is REPORTED). CANDIDATE EDGE BAND (frozen): the threshold/boundary band of the family is the pole band of the N2 note: nodes with tau = arccos(x/2)/D < TAU_EDGE = 14.10 (the deployed v718 GAMMA1 pole-band boundary, DECLARED; classical annotation: this equals the smooth-density edge -- it enters ONLY as a fixed census line applied identically to candidate and every control, and the cadence gate compares RATIOS, insensitive to the line's placement). Census count n_edge(M) = #{tau_j < TAU_EDGE}; entry rung of level n = first LAD rung with count >= n (baseline = count at M_PRE). SIGNATURE GATES (all frozen BEFORE the first run; the comparison object is the SOURCE cadence ratio sequence, never absolute positions): Z1-A MOVING-EDGE CADENCE: >= 4 entries (>= 3 gaps) on LAD; the LAST three inter-entry gaps g1, g2, g3 must WIDEN (g1 < g2 < g3, g1 > 0) AND their ratios r1 = g2/g1, r2 = g3/g2 must match the source ratios (1.11538, 1.44828) within RATIO_BAR = 0.25 relative each (|r_i / r_i^src - 1| <= 0.25). Z1-B AVOIDED CROSSING AT THE BAND EDGE: boundary-pair gap profile g(M) = (tau_{ne+1} - tau_{ne}) / tau_{ne+1} (last node inside / first outside); PASS iff some rung within |X - X_entry| <= 1.0 of a measured entry has g <= DIP_BAR = 0.25 x median(g over LAD) (source analog: 7/8 dip 0.0039 vs O(0.05) typical, ratio ~0.08). Z1-C RAM-ODD CONTACT DIRECTION: candidate avatar of the ram-odd negative wavepacket frame = the 5 MOST NEGATIVE eigenvectors of Toeplitz(c_ro)[:K,:K] (the census C1 E_{-2} avatar dimension; c_ro = hand-built ramified-odd comb: atoms u = (2k+1) log 2, masses 2 log2 * 2^{-(2k+1)/2} -- the srp ro channel, Ward-checked against srp masks at parent reach); contact = largest principal cosine between orth(L^T W_ro) and the edge-band eigenspace of J_K; PASS iff cos >= CONTACT_BAR = 0.95 on >= 4 of the LAST5 rungs (source: 0.997 rung-stable). [CONSTRUCTION CORRECTION, documented: the first run (2026-08-05a) used a single-vector avatar (lowest ro eigenvector only) and its G1.10b anchor fired at 0.9534 -- the census contact 0.992..0.999 is measured against the 5-dim ro-negative FRAME, not one vector; the avatar was corrected once to the census frame object, all bars unchanged, and the rerun is the adjudicating run. The invalid first run made no signature statement; under the wrong single-vector avatar its C gate read cos 0.22..0.37 on LAST5 (fail), so the correction changes the measured object, not the bar.] Z1-D SETTLED COUPLING LEVELS (drainage transplanted): q_f(M) = ||U_edge^T L^T f||^2 / ||L^T f||^2 for the 14 frozen battery functions (hbp.battery verbatim, NPAD = 128), mu-normalized (DECLARED: GNS-native normalization -- level IDENTITY with the source's settled levels is NOT gated, only the settles-positive property); drainage P bars verbatim on PARENT5/MID5/TOP5/HALF2: |b| <= 0.05 per X unit, level >= 1e-3, TOP5 rel spread <= 0.15; PASS iff 14/14 type P. GUARDS (must pass or the run is invalid): G0.1 AST firewall (banned: zetazero/nzeros/isprime/primerange/ nextprime/prevprime/primepi/sympy); G0.2 SHA-256 freeze of battery bytes + ladders + bars + anchors BEFORE any comb data is built here; G0.3 reach census + runtime cap 1200 s; G1.1 deep-table overlap == deployed core table EXACTLY; G1.2 Chebyshev envelope kappa <= KAPPA_REF + 1e-6 on [100, 1e8]; G1.3 parent tower comb consistency (<= 1e-12); G1.4 prefix Ward deep tower leading 824-block == parent tower (<= 1e-12); G1.5 source anchor reproduction (Gram side, same object): (a) near-null counts 884:5, 888:6, 988:6, 992:7, 1104:7, 1108:8; (b) 7/8 gap(1176) = 0.0613 +- 2e-4, lambda_min(1176) = 3.882e-6 +- 2e-8; (c) drainage settled levels med5(TOP5) reproduce the nine frozen values +- 2e-3; G1.6 Wheeler validity: kbad None on EVERY LAD rung AND Gauss moment reconstruction rel dev <= 1e-8 at M = 648/888/1176; G1.7 GNS frame Ward (above, <= 1e-3); G1.8 Cholesky PD of G_c on every LAD rung; G1.9 boundedness: every q_f in [-1e-12, 1 + 1e-9], every contact cos <= 1 + 1e-12; G1.10 ro-comb Ward: hand ro lags == srp ro channel lags at parent reach (<= 1e-12) AND source-side contact anchor at M = 972: max principal cosine near-kernel(6) vs the 5-dim ram-odd negative frame >= 0.97 (census frozen band 0.992..0.999). CONTROLS (mandatory, must fire): CG STRUCTURAL (the discriminating control): a generic random self-adjoint family of the SAME dimensions -- 3 GOE principal -truncation families H_K = (A + A^T)[:K,:K] / sqrt(2K) (seeds 11/12/13) PLUS the free Chebyshev Jacobi (bJ = 0, aJ = 1, nodes 2cos(j pi/(K+1))) -- each run through the IDENTICAL edge census on the identical ladder; FIRE iff 0/4 instances pass the Z1-A cadence bars (a cadence any operator family shows is worthless; the free family is the constant-density null anchor, ratios == 1). CS position scramble (uniform (0.5, 2 alpha), masses kept, seed 7, deep comb) on rungs 888..1176 step 32: FIRE iff the candidate construction breaks (Wheeler kbad) on some rung OR the census completes without passing the Z1-A bars. CE Epstein x^2 + 5y^2 (epstein_firewall_probe read-only, cap M = 640) on rungs 400..640 step 8: same fire rule. A control that survives AND passes Z1-A has spuriously converged: the run is INVALID. VERDICT ENUM (frozen; decision order as listed): 0. any guard fails or a control spuriously matches -> printed as Z1-GATE-INVALID, exit 1, no signature statement follows. 1. Z1-SIGNATURE-MATCH = A and B and C and D all pass: the candidate family carries the measured threshold structure; the next Z1 module is named: the Weyl-M-function / boundary-triple construction on the candidate's edge band. 2. Z1-SIGNATURE-PARTIAL = at least one of A/B/C/D passes (named exactly); the passing signatures define the surviving interface, the failing ones the missing structure. 3. Z1-SIGNATURE-ABSENT = none of A/B/C/D passes: the candidate family lacks the measured threshold structure as-is; what any future Z1 candidate must add is stated from the failure anatomy. STOP-LIST (binding, inherited): no zeros / prime tables anywhere in the construction path; no bare A^{-1}; no PD-margin or 1/eps in any gate; no fits inside gates beyond the declared bounded-statistic slope (drainage P clause verbatim); the cadence gate is fit-free; NO RH claim. This probe writes no files. Runtime cap 1200 s. RESULTS (2026-08-05, adjudicating preregistered run, 24.1 s; GATES A/B/C/D = FAIL/PASS/PASS/PASS -> 3/4; GUARDS+CONTROLS 20/20; verdict Z1-SIGNATURE-PARTIAL, the failing signature is exactly the widening cadence): * Z1-A FAILS -- THE CANDIDATE EDGE IS QUADRATURE FILLING, NOT A WIDENING CADENCE. The edge census rises 22 -> 40 over K = 324..588 with 18 entries at an almost perfectly REGULAR spacing DX = 0.4375/0.5000 (mean 0.4485; grid note: gaps are quantized by the step-4 rung grid, resolution 0.0625). The last-3 gaps 0.4375/0.5000/0.4375 give ratios 1.143/0.875 vs source 1.115/1.448: the FIRST ratio matches (dev 0.025) but the widening clause fails and dev2 = 0.396 > 0.25. Scale observation (reported): candidate mean DX = 0.4485 is ~3.6x denser than the source's first gap 1.625 -- consistent with v718's node/zero density 3.37: the candidate edge fills at the Gauss-quadrature density, and that filling is REGULAR -- exactly what the free-Jacobi null anchor shows (its ratios are 1.000/1.000). The widening moving-edge cadence of the Gram near-kernel has no analog among the Gauss nodes. * Z1-B PASSES -- WITH ITS CO-LOCATION CLAUSE VACUOUS, TYPED HONESTLY: at the candidate's entry density (0.44 X between entries < 2 x the +-1.0 X window) every rung is entry- adjacent, so the gate reduces to its dip-depth clause. That clause is genuinely carried: the boundary-pair gap profile (ladder median 0.0353) collapses to 0.0032 at M = 896 (0.090 x median) and 0.0043 around M = 1096 (0.123 x median) -- edge-node collisions of the SAME depth as the source's 7/8 crossing minimum 0.0039. Observation (reported, no gate, post-hoc): the two deepest dips sit at M = 896 and ~1096, within one or two rung-steps of the SOURCE's Gram landmarks (6th-mode entry 888; 6/7-gap bottom 1096..1100, 8th entry 1108) -- the candidate's edge collisions echo the source's mode-entry depths even though its own census is regular. * Z1-C PASSES 5/5 -- THE RAM-ODD CONTACT SURVIVES THE PASSAGE INTO THE OPERATOR FRAME: largest principal cosine between orth(L^T W_ro) (the mu-normalized 5-dim ram-odd negative frame) and the edge-band eigenspace of J_K = 0.9890 / 0.9860 / 0.9775 / 0.9662 / 0.9667 on LAST5 (ladder median 0.9456, max 0.9971; chance floor ~ 0.26; source Gram-frame contact 0.997, anchor reproduced here at 0.9931). The one- dimensional qf/deck-odd contact that the census found in the Gram near-kernel is PRESENT in the candidate's threshold band -- the first genuinely positive structural transfer of the handover list onto the N2 family. * Z1-D PASSES 14/14 -- SETTLED POSITIVE COUPLINGS IN THE CANDIDATE FRAME: all functions type P (rates |b| <= 0.017/X, TOP5 spreads <= 0.014, levels 0.0047..0.6450). Honest anatomy: the mu-normalized hierarchy INVERTS the Gram wall's -- hats dominate (R2:hat(R/2,R/2) 0.6450 vs source 0.3127; R1:hat(R/4,R/4) 0.0222 vs 0.0082) while boxes collapse (R2:box[0,R] 0.0098 vs 0.3583): the edge band couples strongly to smooth localized packets and weakly to sharp boxes once the GNS metric reweights. * CONTROLS ALL FIRE: CG 0/4 -- the three GOE truncation families produce 0..1 usable entry gaps (erratic edge, no cadence statement possible), the free Chebyshev Jacobi gives perfectly regular ratios 1.000/1.000 and fails the widening clause exactly as the candidate does; CS scramble: Wheeler breakdown kbad = 16 on all 10 control rungs (the scrambled measure is not a state -- v718's Levinson breakdown in the Wheeler chain); CE Epstein: Wheeler breakdown kbad = 27 on all 31 control rungs. GUARDS 20/20: deep table exact, kappa 0.038821, prefix Ward 2.0e-14, source anchors ALL reproduced (counts 884:5/888:6/988:6/992:7/1104:7/1108:8, 7/8 gap(1176) 0.0613, lambda_min 3.8825e-6, drainage levels worst dev 4.9e-5, contact anchor 0.9931), Wheeler valid on all 134 rungs (recon dev <= 1.6e-13), frame Ward 5.2e-13, ro Ward 0.0, Cholesky PD 134/134, boundedness clean. * CONSEQUENCE FOR THE Z1 PROGRAMME (stated plainly): the N2 truncation family carries three of the four measured handover signatures natively in its self-adjoint frame -- edge collisions at the right depth (B), the ram-odd contact direction in its threshold band (C, cos 0.977..0.989), and settled positive battery couplings (D) -- but NOT the widening moving-edge cadence (A): the candidate's edge census is regular quadrature filling, indistinguishable in cadence TYPE from the free Chebyshev Jacobi (equilibrium filling), and the widening 1.625/1.8125/2.625 lives only in the Gram near-kernel entries. For the boundary-triple / Weyl-M-function module this splits the work precisely: the candidate edge band is a legitimate carrier of the contact and coupling structure (C, D) and exhibits collision events (B), but the CELL STRUCTURE of the Z1 contract -- the entry rungs 888/992/1108/1276 with their widening cadence -- must be imported as boundary data from the Gram near-kernel (the cell-cocycle surface), not read off J_K's spectrum. A Z1 candidate built as "J_K + boundary triple over the Gram near-kernel band" is consistent with everything measured here; a Z1 candidate that expects the bulk spectrum alone to produce the cadence is ruled out at the frozen bars. NOT claimed: any statement beyond X = 18.375, eps-uniformity, spectral reality, RH. Run: experiments/tfpt-discovery/.venv/bin/python \ experiments/tfpt-discovery/z1_edge_signature_probe.py Original boundary-triple probe docstring (verbatim): SHARPENED-Z1 module 2 -- the boundary triple: J_K bulk + Gram near-kernel boundary space; does its Weyl M-function deliver the qf block, show the cell structure at the measured entry rungs, and does the relative trace object of the pair track the deployed Weil functional? z1_boundary_triple_probe. Exploration only (tfpt-experiment firewall): NOT wired into run_all.py, no ledger row, no paper edit, no website edit, NO RH CLAIM, no spectral-reality claim beyond measurement, and this probe writes no files. The construction path is AST-firewalled against prime/zero identifiers; everything below is source-native (built from the unified window measure and its Gram/GNS frames only). INPUT STATE (frozen findings, none re-adjudicated here): * z1_edge_signature_probe (Z1-SIGNATURE-PARTIAL, gates B/C/D): the N2 GNS/Jacobi family carries edge collisions (min boundary-pair gap 0.0032 vs source 0.0039), the ram-odd contact in its threshold band (cos 0.977..0.989 on LAST5), and settled positive battery couplings (14/14 P) -- but NOT the widening moving-edge cadence (its edge census is regular quadrature filling). Constraint stated there: the cell structure must be imported as boundary data from the Gram near-kernel; this module is that construction. * qf_edge_separation_probe (1e9 comb): source near-kernel entries at M = 888/992/1108/1276; avoided 7/8 crossing, gap 0.0039 at M = 1240; anchors 6/7 gap(1096) = 0.1008, 6/7(1176) = 0.1397, 7/8(1176) = 0.0613, lambda_min(1176) = 3.882e-6, deep count 1 throughout. * qf_cell_cocycle_probe (COCYCLE-DOMAIN-ONLY): the frozen band rule d(M) = #{lam <= 1e-4} with typed transitions; the Kato/polar transported frame with dimension embedding R' = [J R | N] at entries (J = thin-SVD polar isometry of the band overlap, N = sign-fixed orthonormal complement); the Nevanlinna/Stieltjes domain points z = i h, -1e-3 + i h (h = 1e-2) and eps in (1e-1, 1e-2, 1e-3). These conventions are reused verbatim. * qf_feshbach_effective_probe / qf_edge_separation_probe: the transported effective block F~_X(z) = R^T [Lambda_d(X) - z - C_d(z)] R with the MEASURED Schur correction C_d(z) = E_c^T diag(1/(lam_c - z)) E_c (machine scale, P A Q = 0 coupling Ward) -- rebuilt here rung by rung, the reference object of the delivery gate. COMPUTE-BUDGET DECLARATION (checked BEFORE this spec was frozen; machine facts only, no spectra consulted): hw.memsize = 512 GB, 32 cores -- this is the benchmark machine of the edge probe (1e9 sieve 12.3 s / 13.5 GB peak; tents 8.0e5 atoms/s). The deep cap is therefore frozen at ATOM_MAX_DEEP = 1e9 so that the 9th entry at M = 1276 is inside the gated ladder; M_TOP = 1300 (X = 20.3125, sieve cover exp(20.3125) + 2 = 661,740,976 <= 1e9; M_CAP = floor(64 ln 1e9) = 1326). Runtime cap 1800 s predeclared. CONSTRUCTION (all frozen before the first run): BULK: the N2 truncation family exactly as in the signature probe: at dyadic rung M (D = 1/64, X = M*D), K = M/2, Chebyshev moments p[:M] -> jac.wheeler -> orthonormal Jacobi J_K (v696/ v718 machinery verbatim); GNS frame map c = L^T f with G_c[j,k] = (p_|j-k| + p_{j+k})/2 = L L^T (frame Ward at M = 888 as before). DECLARED THRESHOLD DICTIONARY: the bulk operator of the triple is A_X := 2 I - J_K -- positive, with its threshold at 0 = the band edge x = 2 (the edge whose census carried the signature probe's gates B/C). The Gram route's spectral parameter z -> 0- (below its near-kernel at 0) and the triple's z -> 0- (below the bulk threshold at 0) are identified at the SAME z; this dictionary is DECLARED, not derived -- gate (b) is precisely the measurement of it. BOUNDARY SPACE: per rung, the transported Gram near-kernel band: d(M) = #{lam_i(T[:M,:M]) <= THR_NULL = 1e-4} (cocycle band rule verbatim; typed transitions expected exactly at the frozen entries 992 / 1108 / 1276); band basis V_d sign-fixed, chained frame R by Kato/polar links, dimension embedding R' = [J R | N] at entries (cocycle convention verbatim); transported cell basis B_X = V_d R (reference coordinates). IMPORT into the candidate frame: U_X = L^T B_X[:K] (the predeclared cell->cos avatar of the parent probes), polar factorization U = Q^ P (Q^ = the mu-orthonormal boundary frame, P = the import distortion, reported); import floor sigma_min(U) >= 1e-8 else typed IMPORT-COLLAPSE (delivery structurally impossible in the candidate frame). WEYL M-FUNCTION (frozen convention, stated exactly): H_X(z) := Q^_X^T (A_X - z)^{-1} Q^_X (Herglotz leg) S_X(z) := H_X(z)^{-1} (delivered block) -- the Krein/Weyl M-function of the finite restriction- extension pair: S_X(z) equals the Schur complement of A - z onto the boundary space in any adapted orthonormal frame (block-inverse identity), so S is the triple's effective boundary operator and F~ is its Gram-route counterpart; both anti-Herglotz, both evaluated on the frozen z set ZSET = (-1e-1, -1e-2, -1e-3, i h, -1e-3 + i h), h = 1e-2, Z_REF = -1e-2 (edge-probe reference cell). Wards: banded- solve residual <= 1e-9; S H = I <= 1e-8; H against a dense eigendecomposition evaluation at rungs 888 and 1272 (<= 1e-9). GATES (frozen; oscillation-aware where profiles are gated): (a) HERGLOTZ: min eig Im H_X(z) >= -1e-8 at both complex z on EVERY rung (structural; exact for a self-adjoint pair -- a violation beyond 1e-6 is DEAD-grade). Im S <= +1e-8 (anti-Herglotz) reported as Ward. (b) QF-BLOCK DELIVERY (the identification gate): rho_b(X) = ||S_X(Z_REF) - F~_X(Z_REF)||_F / ||F~_X(Z_REF)||_F, both in the SAME transported reference coordinates; PASS iff med5 over GATE_BLOCK = 1256..1272 (the last five rungs of the completed d = 8 run) <= B_MATCH = 0.25; STRUCTURAL FAIL (DEAD-grade) iff med5 > B_DEAD = 10 or import collapse -- i.e. the boundary space does not ride the bulk threshold at all. Full z-profile, eigenvalue tables and import health reported; the d = 9 frontier tail reported unadjudicated. (c) CELL STRUCTURE: relative max-entry increments of S(Z_REF) along the chained ladder (cocycle normalizer verbatim: rel_k = ||S_{k+1} - S_k||_max / max(||S_k||_max, ||S_{k+1}||_max); at a transition the compare is on the transported-old-frame corner S'[:d,:d], cocycle convention). Contrast statistic: rho(e) = rel(entry increment at e) / median(rel over all non-transition increments), for the frozen entry set E_TEST = (992, 1108, 1276). PASS iff min_e rho(e) >= C_RESP = 3.0 AND at most 1 non-transition increment reaches min_e rel(e). (All non-transition increments serve as the contrast population -- deterministic and stronger than a random-rung sample; deviation from the task wording declared.) Known risk, typed up front: the Gram census entries are threshold bookkeeping, while the band's dynamical events are the crossings (gap bottoms 1096..1100, 1240); if the response sits there instead, (c) fails with that named lesson. (d) TRACE-FORMULA PRECURSOR (measurement, typed so): battery autocorrelation polynomials g_f(x) = a_0(f) + 2 sum_d a_d(f) T_d(x/2) (hbp battery verbatim, NPAD = 128; a_d(f) = autocorrelation lags of the padded cell vector). Ward (Gauss/Weil identity, the finite trace formula of the bulk): the GNS state omega(g_f) = sum_j p_0 U[0,j]^2 g_f(x_j) equals the deployed Weil-functional evaluation w_f = a_0 p_0 + 2 sum_d a_d p_d at rel dev <= 1e-8 (checked at rungs 888/1108/1300). GATE (the pair leg): the DECOUPLED system (bulk with the boundary condition cutting the boundary space off: J_D = P J P + P_perp J P_perp, P = Q^ Q^^T) must still track Weil: err_d(X) = sum_f |omega_D(g_f) - w_f| / sum_f |w_f|; PASS iff med5(GATE_BLOCK) <= D_LEVEL = 0.05 AND the second-half trend is falling-or-flat (hbp.fit_rate b >= -0.01 per X; b > 0 = falling, reported). GUARDS (must pass or the run is invalid): G0.1 AST firewall; G0.2 SHA-256 freeze of battery bytes + ladders + bars + anchors BEFORE any comb data is built; G0.3 reach census + runtime cap; G1.1 deep-table overlap == deployed EXACTLY; G1.2 Chebyshev envelope kappa <= KAPPA_REF + 1e-6 over [100, 1e9]; G1.3 parent tower comb consistency (<= 1e-12); G1.4 prefix Ward (<= 1e-12); G1.5 source anchors: (a) counts 884:5 888:6 988:6 992:7 1104:7 1108:8 1272:8 1276:9 (the 9th entry INSIDE the ladder); (b) 6/7 gap(1096) = 0.1008, 6/7(1176) = 0.1397, 7/8(1176) = 0.0613, 7/8(1240) = 0.0039 (each +- 2e-4); lambda_min(1176) = 3.882e-6 +- 2e-8; (c) drainage settled levels med5(1160..1176) reproduce the nine frozen values +- 2e-3; (d) measured transition set == frozen E_TEST; G1.6 Wheeler kbad None on every rung + Gauss moment reconstruction <= 1e-8 at 888/1108/1300; G1.7 GNS frame Ward at 888 (<= 1e-3); G1.8 Cholesky PD every rung + measured Gram PD lambda_min > -1e-9; G1.9 coupling Ward max |E_c| <= 1e-8 and transport Wards (sigma_min >= 1e-8, ||R^T R - I|| <= 1e-10); G1.10 resolvent/Schur Wards as declared above; G1.11 Gauss/Weil state identity <= 1e-8. CONTROLS (mandatory, must fire): CS position scramble (1e9 comb, masses kept, seed 7, rungs 888..1300 step 48): FIRE iff the bulk construction breaks (Wheeler kbad) on some rung -- measured signature of a non-state measure (v718 Levinson breakdown). CE Epstein x^2 + 5y^2 (cap M = 640, rungs 400..640 step 8): same fire rule. CB GOE BULK (seed 11): the SAME imported boundary frames Q^_X, bulk replaced by A_goe = 2 I - (A + A^T)[:K,:K]/sqrt(2K) (principal-truncation family); evaluated at z = -1e-1 (clear of the GOE edge fluctuation scale K^{-2/3}). FIRE iff rho_b^goe = med5(GATE_BLOCK) of ||S_goe - F~(-1e-1)||_F / ||F~(-1e-1)||_F > B_MATCH -- a generic bulk must NOT deliver the qf block. DECLARED DEVIATION from the task wording ("no cell response at the entry rungs"): the (c)-response travels with the boundary path Q^_X, which CB shares by design, so gating CB on absent response would let a boundary-driven response invalidate the run spuriously; the GOE cell-response contrast IS computed and REPORTED, and its reading (bulk-mediated vs boundary-driven response) is typed into the verdict either way. CW WRONG BOUNDARY (seed 20260805): 6 fixed random orthonormal cell vectors (R^888, zero-padded), same import pipeline, on the d = 6 run 888..988 plus the 992 transition evaluation; FIRE iff [med5 of rho_b^cw over the last 5 rungs of the d = 6 run > B_MATCH] AND [the CW contrast at 992 < C_RESP] -- a random band must neither deliver the block nor respond at the entry. VERDICT ENUM (frozen; decision order as listed): 0. any guard fails or a control fails to fire -> printed as Z1-TRIPLE-INVALID, exit 1, no structural statement follows. 1. Z1-TRIPLE-DEAD = (a) violated beyond 1e-6 OR (b) structural fail (med5 rho_b > 10, or import collapse): the sharpened Z1 form is wrong as constructed; what the failure teaches is typed from the anatomy (which frame kills it). 2. Z1-TRIPLE-CARRIES = (a) and (b) and (c) and (d) all pass: the sharpened Z1 object exists at finite level -- the boundary triple with Gram-band boundary data delivers the qf block, shows the cell structure, and its relative trace object tracks Weil; what a proof-grade Z1 still needs is named: (i) a continuum boundary triple whose minimal/maximal domains reproduce this finite pair with a self-adjointness proof, (ii) the z -> 0 Nevanlinna boundary limit of M (the cocycle module's open leg), (iii) the relative trace formula at theorem level (Krein spectral shift vs the Weil measure, currently a measured tracking). 3. Z1-TRIPLE-PARTIAL = anything else: the passing legs are named as the surviving interface, the failing legs as the missing structure. STOP-LIST (binding, inherited): no zeros/prime tables anywhere; no bare A^{-1} (every resolvent at frozen z with |z| >= 1e-3 or Im z = h); no PD-margin or 1/eps in any gate; no fits in gates beyond the declared bounded-statistic slope (hbp.fit_rate, gate d); the delivery and contrast gates are fit-free; NO RH claim. This probe writes no files. Runtime cap 1800 s. RESULTS (2026-08-05; single preregistered execution, no reruns, 118.3 s; GUARDS+CONTROLS 23/23 -- the run is VALID; GATES 1/4, a = PASS, b/c/d = FAIL; b not structural: med5 rho_b = 5.88 < dead-grade 10; verdict Z1-TRIPLE-PARTIAL): * CONSTRUCTION CLEAN THROUGH EVERY WARD: 1e9 comb (kappa 0.038821, 34.4M atoms to e^20.3125), all edge-probe anchors reproduce EXACTLY on the extended ladder (counts incl. the 9th entry at 1276; 7/8 gap(1240) = 0.0039; lambda_min(1176) = 3.8825e-6; drainage dev 4.9e-5), typed transitions at 992/1108/1276 with entering eigenvalues 9.944e-5/9.946e-5/ 9.975e-5; resolvent/Schur/dense-H/Gauss-Weil Wards all <= 2.3e-12. Notably the transported band SUBSPACE moves smoothly (chain sigma_min = 0.9979 over all 103 links, including through the 7/8 crossing region): the Gram-side boundary path is tame; everything rough below is import- side. * (a) HERGLOTZ PASSES EXACTLY: min eig Im H = +0.216 over all 104 rungs x both complex z (floor -1e-8 never approached); Im S anti-Herglotz Ward clean (max eig -1.0e-2 < 0). The pair (A = 2 - J_K, imported Gram band) is a genuine finite Weyl/Krein triple on every rung including all three typed transitions. * (b) DELIVERY FAILS AT med5 rho_b = 5.88 (bar 0.25, dead 10) -- WITH A SPLIT SPECTRUM ANATOMY. At the top gate rung (M = 1272, d = 8): eig S(-1e-2) = 0.0101/0.0102/0.0105/ 0.0106 | 0.0184/0.0214 | 0.0485/0.1611 vs F~ = 0.0100.. 0.0101. HALF the boundary directions ride the bulk threshold at the qf scale (within 1..6% of eps) -- the identification dictionary is not empty -- but two directions carry 5x..16x eps of bulk energy and dominate the Frobenius statistic. The z-ladder types it as a genuine mismatch, not a cell artifact (rho = 1.00 at z = -1e-1, 5.33 at -1e-2, 41.3 at -1e-3: grows exactly as 1/|z| -- a fixed energy excess). Import anatomy (the cause, measured): cell-mass of the transported band in the first K = M/2 cells is 0.500 on every gate rung (the near-null packets are DELOCALIZED across the full M-cell window), and sigma_min(U) = 2.4e-4.. 1e-3: the [:K] truncation keeps half of each packet, and the polar whitening renormalizes near-collapsed mu-norm remnants by ~1e3 into O(1) boundary directions that then behave quasi-generically. Candidate-vs-generic separation is still real and large: 5.9 (candidate) vs 13.0 (GOE bulk, coarse cell) vs 132.5 (random boundary) -- the arithmetic import retains structure, but not at the frozen identification bar. * (c) NO CELL RESPONSE -- and NOT at the crossings either: the predeclared risk fired in a sharper form. Entry contrasts rho(992/1108/1276) = 1.54/2.02/1.04 (bar 3.0), 49 of 100 within-run increments comparable; the S-path roughness is BROADBAND (median rel increment 0.25 per rung; top-5 at M = 996/920/1116/936/1004, not concentrated at entries or at the 1096..1100 / 1240 crossing rungs). Since the Gram boundary path itself is smooth (sigma_min 0.998 per link), the roughness is import-truncation noise: the whitened remnant directions rotate erratically rung-to-rung and mask any cell signal in M. * (d) THE DECOUPLED PAIR DOES NOT TRACK WEIL: err_d = 0.24.. 0.78 across the ladder, med5(GATE_BLOCK) = 0.388 (bar 0.05), trend flat (b = -0.003/X). Cutting the imported band out of the bulk moves the battery Weil-state evaluation by ~40%: the polar-whitened boundary directions carry large GNS state weight -- same root cause as (b). (The bulk trace formula itself is exact: Gauss/Weil state identity 2.3e-12.) * CONTROLS ALL FIRE: CS Wheeler breakdown 9/9 rungs (kbad 16 at 888); CE 31/31 (kbad 27 at 400); CB GOE bulk med5 rho_b^goe = 12.97 >> 0.25 (generic bulk does not deliver); CW random boundary med5 rho_b^cw = 132.5 AND 992-contrast 1.19 < 3 (random band neither delivers nor responds). * CONSEQUENCE FOR THE Z1 PROGRAMME (stated plainly): the sharpened Z1 object survives as a FRAME and dies as an IMPORT. What stands: the finite boundary triple exists and is exactly Herglotz; half its boundary spectrum already sits on the qf block at the right scale; bulk Gauss/Weil trace identity exact; all of it arithmetic-specific under controls. What the failure teaches, typed: the Gram near-kernel packets live on the FULL M-cell window (cell-mass exactly 1/2 in the half-window, every rung), so any K = M/2 GNS import truncates them and the polar whitening turns the truncation loss into quasi-generic boundary noise that kills delivery (b), masks the cell structure (c), and overweights the boundary in the state (d). The next Z1 module must couple the frames WITHOUT whitening: either (1) the mu-weighted triple -- use the raw import U = L^T B[:K] (no polar) and compare against the P-conjugated Gram block, i.e. renormalize the reference by the MEASURED import distortion (source-native, declarable); or (2) pose the triple on the full M-cell frame directly (Toeplitz bulk + Gram band, where the Gram route already owns the Feshbach block) and demand instead an INTERTWINING with J_K's spectral data -- the delivery gate becomes a commutation statement rather than an entrywise match. A full-depth GNS frame (K = M) is stated to be OUT OF REACH by deepening (needs lags to 2M, X = 27.75 at the first entry, e^27.75 atoms). NOT claimed: anything beyond X = 20.3125, eps-uniformity, continuum self-adjointness, spectral reality, RH. Run: experiments/tfpt-discovery/.venv/bin/python \ experiments/tfpt-discovery/z1_boundary_triple_probe.py Original variable-edge M-function probe docstring (verbatim): SHARPENED-Z1 module 3 -- the variable-edge M-function with the fixed import: mu-weighted boundary triple (Candidate A) / full-frame intertwining (Candidate B), entry-pole isolation, Herglotz compactness, and the moment-functional cluster leg that measures whether PRIME.KMS.INDUCTIVE_STATE.02 and PRIME.Z1.OPERATOR.01 are the same remaining object on this surface. z1_variable_edge_mfunction_probe. Exploration only (tfpt-experiment firewall): NOT wired into run_all.py, no ledger row, no paper edit, no website edit, NO RH CLAIM, no spectral-reality claim beyond measurement, and this probe writes no files. AST-firewalled; everything below is source-native (unified window measure and its Gram/GNS frames only). BINDING STOP RULE (user): NO fixed-d variants anywhere -- every object in this module carries the variable dimension d(X) of the frozen threshold rule; the only 6-mode expression is the drainage ANCHOR reproduction (a source Ward, not an analysis object; declared). INPUT STATE (frozen findings, none re-adjudicated here): * z1_boundary_triple_probe (Z1-TRIPLE-PARTIAL, gate a only): the finite triple (A = 2 - J_K, imported Gram band) is EXACTLY Herglotz on all 104 rungs incl. the typed transitions -- the frame survives. The import dies: the Gram near-kernel packets are delocalized (cell-mass exactly 0.500 in the half-window on every gate rung), so the K = M/2 truncation + polar WHITENING turned the truncation loss into quasi-generic boundary noise (sigma_min(U) = 2.4e-4 blown up to O(1)): delivery med5 rho_b = 5.88 (split spectrum: half the directions AT the qf scale 0.0101..0.0106 vs 0.0100, two hot directions 5x..16x eps), broadband S-roughness 25%/rung masking any cell signal, Weil-state overweight ~40%. Candidate-vs-generic stayed real: 5.9 vs 13.0 (GOE bulk) vs 132.5 (random boundary). Full-depth GNS (K = M) is OUT OF REACH by deepening (lags to 2M = X 27.75, e^27.75 atoms). * qf_edge_separation_probe (1e9): typed entries at M = 888/992/ 1108/1276; anchors as in the parent (counts, gaps incl. 7/8 gap(1240) = 0.0039, lambda_min(1176) = 3.882e-6, drainage levels). qf_cell_cocycle_probe: band rule d(M) = #{lam <= 1e-4}, Kato/polar chain, [J R | N] embedding at entries -- reused verbatim (the variable spectral section P_X = 1_{(-inf,E_X]} with E_X = THR_NULL absorbing one mode at every typed entry; transitions are typed events, not failures). * qf_representation_census_probe: the rung-stable contact (cos 0.997) of ONE near-null direction with the ram-odd negative wavepacket -- the prediction behind the rank-one residue gate. * v718: pole-band threshold GAMMA1 = 14.10 -- the deployed dictionary constant behind the entry-pole cut E_CUT below. COMPUTE BUDGET (declared): same 512-GB/32-core machine and 1e9 comb as the parent (measured 118.3 s there); cap 1800 s. CONSTRUCTION (all frozen before the first run; A/B pattern with at most one adjudication switch, both candidates frozen NOW): SHARED SPINE (parent verbatim): 1e9 comb -> lags p -> Toeplitz T; ladder LAD = 888..1300 step 4; per rung the Gram band (d(X) lowest, threshold rule), sign-fixed, chained transported frame R (polar links, [J R | N] at entries), transported cell basis B = V_d R; bulk J_{K=M/2} by Wheeler, A = 2 I - J_K; GNS map L (cheb Gram Cholesky); RAW import U = L^T B[:K] -- NO polar step, NOTHING whitened. Measured distortion P_X = U^T U (its eigenvalues = the squared mu-norms of the imported band directions; reported). CANDIDATE A (PRIMARY -- the mu-weighted triple): the boundary M-function in the mu-weighted inner product, H_X(z) = U^T (A_X - z)^{-1} U (Herglotz by construction, no normalization anywhere). DELIVERY REFERENCE renormalized by the measured distortion (algebra forced by U = Q P^{1/2}: if the whitened pair delivered, then H = P^{1/2} H_gram P^{1/2}): Fref_X(z) = P^{1/2} H_gram_X(z) P^{1/2}, H_gram_X(z) = R^T diag(1/(lam_i(X) - z))_{i<=d} R (the exact source band resolvent; Ward against the parent Feshbach block: F~ H_gram = I to machine precision). rho_A(X) = ||H_X(Z_REF) - Fref_X(Z_REF)||_F / ||Fref_X(Z_REF)||_F. CANDIDATE B (FALLBACK -- full M-cell frame, intertwining): on the full cell frame the M-function IS the Gram object (delivery to Feshbach exact by construction), so the content is the commutation statement of the import map with the declared threshold dictionary at the resolvent level: rho_B(X) = ||(A + eps)^{-1} U - U (Lam_d + eps)^{-1}||_F / ||U (Lam_d + eps)^{-1}||_F, eps = -Z_REF. SWITCH TRIGGER (frozen): B is adjudicated iff med5 of rho_A over GATE_BLOCK > B_MATCH; the delivery leg then uses rho_B against the SAME bars. Decision trail printed. ENTRY-POLE ISOLATION (Candidate-A object; exact finite decomposition, no fits): with A v_n = a_n v_n and w_n = U^T v_n, H_X(z) = sum_n w_n w_n^T / (a_n - z) exactly (Ward against the banded solve). The ENTRY-BAND poles are those with a_n <= E_CUT = 2 - 2 cos(D * GAMMA1) = 4 sin^2(D * 14.10 / 2) = 0.0483 (the deployed pole-band dictionary; source-native constant). Pole matrix Pi_X = sum_{a_n <= E_CUT} w_n w_n^T (PSD by construction), regular part M~_X(z) = sum_{a_n > E_CUT} w_n w_n^T/(a_n - z). ENTRY RESIDUES: at each typed entry e (d -> d+1), R_e = Pi(e) - pad(Pi(prev rung)) on the transported coordinates (old frame = first d, new direction = last, by the [J R | N] convention); within-run Pi increments reported as drift baseline. MOMENT FUNCTIONALS (the INDUCTIVE_STATE.02 avatar, declared): battery band coordinates c_f = B[:NPAD]^T f (source-native projection); mu_k(f, X) = c_f^T [sum_{a_n > E_CUT} w_n w_n^T a_n^k] c_f for k = 0, 1, 2 -- the moment functionals of the regular boundary spectral measure against the frozen battery (14 functions x 3 moments = 42 tracks). GATES (frozen; no fits anywhere): (P1) ENTRY POLES RANK-ONE PSD: for every typed entry e: min eig R_e >= -PSD_TOL_REL * ||R_e||_2 AND rank ratio s_1(R_e)/sum_i s_i(R_e) >= RANK1_BAR = 0.75 (the 0.997 contact predicts ~0.99; bar generous, value reported). (P2) ENTRY MASS SUMMABLE (the KILL leg): c_mass(X) = sum_{e <= X} ||R_e||_F / tr P_X <= MASS_BAR = 1.0 on every rung AND ||R_last||_F <= ENTRY_GROWTH_BAR = 10 x ||R_first||_F. KILL (DEAD-grade, 'nicht summierbare Eintrittsmasse') iff c_mass(top) > 1.0. Mass fraction phi(X) = tr Pi/tr P reported along the ladder. (B1) LOCAL UNIFORM BOUNDEDNESS (compactness leg 1): on the frozen grid ZGRID = {Re in (-0.5,-0.25,0,0.25,0.5)} x {Im in (1e-3,1e-2,1e-1,1)}, C(X) = max over the GATED sub-grid (Im >= 1e-2) of ||M~_X(z)||_2; PASS iff med5(LAST5)/med5(FIRST5) of C <= CBND_RATIO = 2.0. The Im = 1e-3 row is REPORTED, not gated (declared: at K <= 650 the regular-pole spacing ~6e-3 makes that row a pole-distance roulette, not a compactness statistic). (B2) EQUICONTINUITY PROXY (compactness leg 2): same statistic on the exact derivative ||M~'_X(z)||_2 = ||sum w w^T/(a-z)^2||_2 (the Cauchy-estimate object); PASS iff med5(LAST5)/med5(FIRST5) <= CDER_RATIO = 2.0. B1 AND B2 = the normal-family (Montel/Helly) evidence at finite level -- the Herglotz-compactness form of the contract; typed as measurement, never as a limit claim. (CL) MOMENT-FUNCTIONAL CLUSTER: for each of the 42 tracks the tail oscillation osc = (max - min)/max(median |.|, 1e-30) over LAST10; PASS iff median over tracks <= CL_BAR = 0.2. (DEL) DELIVERY RE-TEST: rho (A, or B after trigger) med5 over GATE_BLOCK = 1256..1272 <= B_MATCH = 0.25 (parent bar); structural fail iff BOTH candidates > B_DEAD = 10. (CR) CELL-RESPONSE RE-TEST (reported + typed; NOT CARRIES-blocking per the frozen enum): cocycle rel-max increments of H_X(Z_REF)/tr P_X along the ladder (transported corner at entries), contrast rho(e) >= C_RESP = 3.0 at E_TEST with uniqueness <= 1. GUARDS (parent verbatim + new Wards; run invalid on failure): G0.1 AST firewall; G0.2 SHA-freeze of battery + ladders + bars + anchors BEFORE comb data; G0.3 reach + runtime cap 1800 s; G1.1 deep-table overlap; G1.2 kappa envelope; G1.3 parent comb; G1.4 prefix Ward; G1.5a-d source anchors (counts/gaps/lmin/ drainage/transition set == E_TEST); G1.6 Wheeler + Cholesky + Gauss recon; G1.7 GNS frame Ward at 888; G1.8 Gram PD; G1.9 coupling + transport Wards; G1.10 pole-decomposition Ward (H from eigenpairs == banded solve at rungs 888/1272, <= 1e-9) + Feshbach inversion Ward (F~ H_gram = I <= 1e-8) + residue completeness (sum_n w_n w_n^T == P, <= 1e-10 rel); G1.11 Herglotz guard on H at both complex parent points (structural, min eig Im H >= -1e-8); G1.12 import floor sigma_min(U) >= 1e-8 (collapse = typed structural fail as in parent). CONTROLS (mandatory, must fire; frozen fire rules): CS scramble (seed 7) and CE Epstein (cap 640): Wheeler breakdown as in both parents. CB GOE bulk (seed 11, z = -1e-1): FIRE iff med5 rho_A^goe over GATE_BLOCK > B_MATCH (generic bulk does not deliver the renormalized block); the GOE entry-pole structure (mass, rank ratios at the typed entries) is REPORTED -- 'no arithmetic entry events' is typed from it, not gated (parent CB honesty note carries over: the boundary path is shared by construction). CW random boundary (seed 20260805, 6-dim, d = 6 run + 992): FIRE iff med5 rho_A^cw > B_MATCH AND 992-contrast < C_RESP. VERDICT ENUM (frozen; decision order as listed): 0. any guard fails or a control fails to fire -> Z1-VAREDGE-INVALID, exit 1, no structural statement. 1. Z1-VAREDGE-DEAD = P2 kill (entry mass not summable) OR B1 fails (boundedness of the regularized family broken) OR both candidates > B_DEAD on delivery: the operator route is typed at its honest end on this surface. 2. Z1-VAREDGE-CARRIES = DEL and P1 and P2 and B1 and B2 and CL all pass: the sharpened Z1 object exists at finite level in the variable-edge form; the proof-grade contract must then say: the variable-edge boundary triple of the window chain has a normal Herglotz family with summable rank-one entry poles at the arithmetic thresholds, whose weak-* cluster states (INDUCTIVE_STATE.02) are exactly the Herglotz limits of the Z1 M-function (OPERATOR.01) -- one compactness theorem, two contract names. 3. Z1-VAREDGE-PARTIAL = anything else; legs named. UNIFICATION REPORT (5) (report only, no gate): the measured evidence whether the weak-* cluster demand of PRIME.KMS.INDUCTIVE_STATE.02 and the Z1 operator demand of PRIME.Z1.OPERATOR.01 are the same remaining object here: B1+B2 (normal family) + CL (moment clustering) measured on the SAME spectral measure -- if both hold, the two contracts share their missing theorem (Helly selection for the boundary measure chain); recommended contract text printed either way. STOP-LIST (binding): NO fixed-d variants; no zeros/prime tables; no bare A^{-1}; no PD-margin or 1/eps in gates; no fits in gates; NO RH claim. This probe writes no files. RESULTS (2026-08-05; single preregistered execution, no reruns, 117.6 s; GUARDS+CONTROLS 23/23 -- the run is VALID; LEGS 3/6: DEL FAIL, P1 FAIL (PSD half only), P2 PASS, B1 PASS, B2 PASS, CL FAIL; CR (reported) FAIL; adjudicated candidate B after the frozen trigger; verdict Z1-VAREDGE-PARTIAL -- no kill fired: c_mass 0.032 << 1, boundedness holds, both candidates at 0.92, far from dead-grade 10): * A/B DECISION TRAIL: rho_A med5 = 0.9243 > 0.25 -> frozen switch -> Candidate B adjudicated: rho_B med5 = 0.9246 -- the two candidates are numerically the SAME failure (rung profiles differ by < 0.012 everywhere). Both say: in the mu-weighted metric the imported band does NOT reproduce the P-renormalized Gram resolvent -- H_raw is ~92% SMALLER than Fref. Anatomy (measured): the entry-band mass fraction is phi = tr Pi / tr P = 0.016 -- only ~1.6% of the imported mu-mass sits below E_CUT = 0.0483; the raw import spreads 98% of its weight into the bulk region, while Fref ~ P^{1/2} (1/(lam+eps)) P^{1/2} demands the top mu-direction (sigma_1^2 = 1.08e-2, two decades above the rest -- the contact direction) to sit AT the threshold. DISCLOSURE (typed, load-bearing for reading the controls): in this raw form the delivery statistic LOSES its discriminating power -- candidate 0.92 vs GOE bulk 0.93 vs random boundary 0.99 (parent whitened separation was 5.9 vs 13.0 vs 132.5). The control fire rules (rho > 0.25) are satisfied and the run is valid, but a delivery number of this form carries no arithmetic signature either way; the delivery leg is honestly typed UNRESOLVED-BY-THIS-METRIC, not merely failed. * ENTRY-POLE TABLE (the genuinely new positive): typed entries vs isolated poles, raw mu-weighted metric -- M= 992: lam_gram 9.944e-5, n_pole 34, ||R_e||_F 5.45e-5, rank-ratio 0.796, min eig -9.4e-6; M=1108: lam_gram 9.946e-5, n_pole 38, ||R_e||_F 7.93e-5, rank-ratio 0.869, min eig -9.1e-6; M=1276: lam_gram 9.975e-5, n_pole 44, ||R_e||_F 5.48e-5, rank-ratio 0.804, min eig -1.1e-5. The RANK-ONE HALF of P1 PASSES at every entry (0.80/0.87/ 0.80 >= 0.75) -- the 0.997-contact prediction is CONFIRMED in the raw metric: each arithmetic entry adds one dominant residue direction. The PSD half fails at -20% of ||R_e||_2: the increment Pi(e) - Pi(prev) also carries a mass REBALANCING of the old directions (within-run drift median 5.3e-6, max 6.4e-5 -- same scale), so exact PSD-ness of a 4-rung increment against a moving bulk (K grows by 2) was too strong a clause; typed: entries = predominantly rank-one additions plus O(20%) non-PSD drift. * (P2) ENTRY MASS SUMMABLE -- THE KILL CRITERION IS FAR AWAY: c_mass profile 5.8e-3 -> 1.6e-2 -> 1.7e-2 (top), max 3.2e-2 vs bar 1.0; entry-mass growth ||R_last||/||R_first|| = 1.01 (the three entry masses are CONSTANT to 1%: 5.4e-5 / 7.9e-5 / 5.5e-5). 'Nicht summierbare Eintrittsmasse' does NOT occur on this surface. * (B1)+(B2) HERGLOTZ COMPACTNESS CARRIES: on the frozen compacts (Im z >= 1e-2) the regularized family is bounded with ratio 0.936 (grid-sup ||M~|| med5 9.27e-2 -> 8.67e-2: it FALLS) and equicontinuous with derivative ratio 0.807 (2.63 -> 2.12); even the reported 1e-3 roulette row is flat (9.5e-2 -> 8.8e-2). The variable-edge M-function family is a normal family on the reachable surface -- the Herglotz-compactness form of the contract is MEASURED TO HOLD, including through all three typed transitions. * (CL) MOMENT FUNCTIONALS DO NOT SETTLE: median tail oscillation 22.1 (max 73.9) over the 42 battery-moment tracks -- the weak-* avatar swings by an order of magnitude over LAST10. Same root cause as (CR): the raw H-path is broadband-rough (within-run median rel increment 0.196/rung, entry contrasts 1.5..2.4 vs bar 3.0, 24 comparable increments) -- the half-window import noise rotates the residue weights rung to rung. * CONTROLS: CS 9/9 and CE 31/31 Wheeler breakdowns; CB 0.93 > 0.25 and CW 0.99 > 0.25 with 992-contrast 2.30 < 3 -- all fire per the frozen rules, with the discrimination disclosure above. * UNIFICATION EVIDENCE (the module's real yield, stated plainly): the two contract demands SPLIT EXACTLY along the measured line. The CLUSTER-EXISTENCE half -- what compactness gives -- is CARRIED: bounded mass (P2), bounded + equicontinuous regularized family (B1+B2) mean every subsequence of the variable-edge boundary chain has weak-* / locally-uniform cluster points (Helly/Montel at finite level). The SELECTION half -- WHICH cluster point, i.e. actual settling of the state -- is NOT carried (CL osc 22), and its obstruction is the SAME measured object that fails DEL and CR: the K = M/2 import noise. So PRIME.KMS.INDUCTIVE_STATE.02 and PRIME.Z1.OPERATOR.01 are measured to share their compactness theorem, and to share their remaining obstruction. RECOMMENDED CONTRACT TEXT for the next promotion round (report only, nothing filed here): 'Merge the compactness halves of INDUCTIVE_STATE.02 and OPERATOR.01 into one target Z1-COMPACTNESS: the variable-edge boundary triple of the window chain has a normal Herglotz family with bounded, ~rank-one, summable entry poles at the arithmetic thresholds (measured at X <= 20.3125: mass ratio 0.032, boundedness ratio 0.936, equicontinuity ratio 0.807, rank ratios 0.80..0.87). The residual deltas are ONE object viewed twice: state SELECTION (INDUCTIVE_STATE.02: the moment tracks must settle) == import-faithful boundary map (OPERATOR.01: a coupling of the Gram band to the bulk that does not pass through the lossy K = M/2 half-window frame). Any future module must attack that shared delta, not the two contracts separately.' NOT claimed: any statement beyond X = 20.3125, limit existence, eps-uniformity, continuum self-adjointness, spectral reality, RH. Run: experiments/tfpt-discovery/.venv/bin/python \ experiments/tfpt-discovery/z1_variable_edge_mfunction_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__)) _HERE_DISC = os.path.abspath(os.path.join(_HERE, "..", "experiments", "tfpt-discovery")) sys.path.insert(0, _HERE) sys.path.insert(0, _HERE_DISC) import v563_paper2_readouts as core # noqa: E402 import v696_z1_jacobi as jac # noqa: E402 (Wheeler, locked) 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 T_START = time.time() # ------------------------------------------------ frozen specification D = srp.DGRID # 1/64, dyadic float-exact ATOM_MAX_DEEP = 100000000 # deep comb cap (drainage cap) M_CAP_DEEP = int(math.floor(math.log(ATOM_MAX_DEEP) / D)) # 1178 M_TOP = 1176 # deepest rung (X = 18.375) M_PAR = 824 # parent cap (prefix Ward) M_PRE = 644 # census baseline rung LAD = list(range(648, 1177, 4)) # 133 rungs, K = 324..588 LAST5 = list(range(1160, 1177, 4)) PARENT5 = list(range(956, 973, 4)) # drainage blocks verbatim MID5 = list(range(1056, 1073, 4)) TOP5 = list(range(1160, 1177, 4)) HALF2 = list(range(1072, 1177, 4)) M_WARD = 648 # GNS frame Ward rung TAU_EDGE = 14.10 # v718 GAMMA1 pole-band bound X_EDGE = 2.0 * math.cos(TAU_EDGE * D) SRC_ENTRY_M = (888, 992, 1108, 1276) # frozen source record SRC_DX = (1.625, 1.8125, 2.625) SRC_R1 = SRC_DX[1] / SRC_DX[0] # 1.11538 SRC_R2 = SRC_DX[2] / SRC_DX[1] # 1.44828 RATIO_BAR = 0.25 # Z1-A cadence ratio bar DIP_BAR = 0.25 # Z1-B dip vs ladder median W_ENTRY_X = 1.0 # Z1-B entry co-location window CONTACT_BAR = 0.95 # Z1-C principal cosine bar CONTACT_RUNGS = 4 # of the LAST5 SRC_CONTACT = 0.997 # source contact (report) SRC_G78MIN = 0.0039 # source crossing min (report) P_SLOPE = 0.05 # Z1-D drainage P bars verbatim P_FLOOR = 1.0e-3 P_SPREAD = 0.15 N_MED = 5 NPAD = 128 R_BAT = (1.0, 2.0) QF_FLOOR = 1.0e-12 THR_NULL = 1.0e-4 # source near-null threshold BAR_GAUSS = 1.0e-8 # G1.6 moment reconstruction WARD_FRAME = 1.0e-3 # G1.7 frame consistency Ward WARD_RO = 1.0e-12 # G1.10 ro-comb Ward ANCH_CONTACT = 0.97 # G1.10 source contact anchor COMB_DEV_BAR = 1.0e-12 # G1.3 PREFIX_WARD = 1.0e-12 # G1.4 REPRO_COUNTS = {884: 5, 888: 6, 988: 6, 992: 7, 1104: 7, 1108: 8} REPRO_G78_1176 = 0.0613 REPRO_TOLG = 2.0e-4 REPRO_LMIN1176 = 3.882e-6 REPRO_LTOL = 2.0e-8 DRAIN_LEVELS = { # source settled levels (frozen) "R2:box[0,R]": 0.3583, "R2:box[R/2,R]": 0.3370, "R2:hat(R/2,R/2)": 0.3127, "R2:hat(3R/4,R/4)": 0.2590, "R2:box[R/4,3R/4]": 0.2249, "R1:box[R/2,R]": 0.0793, "R1:box[0,R]": 0.0741, "R2:box[0,R/2]": 0.0741, "R1:hat(R/4,R/4)": 0.0082} REPRO_QTOL = 2.0e-3 BOUND_TOL = 1.0e-9 RUNTIME_CAP = 1200.0 CG_SEEDS = (11, 12, 13) # GOE structural control seeds SEED_CS = 7 # scramble seed (verbatim) CTRL_LAD_CS = list(range(888, 1177, 32)) # 10 rungs EP_NCAP = 34000 EP_MMAX = 640 CTRL_LAD_CE = list(range(400, 641, 8)) # 31 rungs BANNED = ("zetazero", "nzeros", "isprime", "primerange", "nextprime", "prevprime", "primepi", "sympy") CHECKS = [] # guards + controls: all must pass, else invalid run GATES = [] # signature gates: feed the verdict only 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(): """Battery bytes + ladders + bars + anchors, SHA-256 frozen BEFORE any comb data is built in this probe.""" bats = {} hsh = hashlib.sha256() hsh.update(("z1-edge-signature spec: candidate = v718 gns_nodes " "machinery at dyadic D=%.10f, K=M/2, deep comb cap " "%d, M_TOP=%d, LAD=%s, M_PRE=%d; frame map = " "cholesky of cos-Gram (p_|j-k|+p_{j+k})/2, coords " "L^T f; edge band tau < %g (v718 GAMMA1, declared); " "Z1-A: last-3 gaps widening AND ratios vs (%f, %f) " "within %g; Z1-B: boundary-pair gap dip <= %g x " "ladder median within |X-Xentry| <= %g; Z1-C: 5-dim " "ro-negative frame (hand comb u=(2k+1)ln2, mu=2ln2 " "2^{-(2k+1)/2}) contact >= %g on >= %d of LAST5=%s; " "Z1-D: drainage P bars |b|<=%g floor %g spread %g " "on PARENT5=%s MID5=%s TOP5=%s HALF2=%s, 14/14; " "guards: gauss recon <= %g at 648/888/1176, frame " "ward <= %g at %d, ro ward <= %g, contact anchor >= " "%g at 972, counts %s, g78(1176)=%g+-%g, lmin=%g+-" "%g, drain levels %s +- %g, comb<=%g prefix<=%g " "runtime<=%g; controls: CG = 3 GOE truncation " "families (A+A^T)[:K,:K]/sqrt(2K) seeds %s + free " "Chebyshev Jacobi, fire iff 0/4 pass Z1-A; CS " "scramble seed %d rungs %s, CE Epstein cap %d M %d " "rungs %s, fire = wheeler breakdown OR no Z1-A " "match; verdict order: invalid -> MATCH(ABCD) -> " "PARTIAL(any) -> ABSENT" % (D, ATOM_MAX_DEEP, M_TOP, LAD, M_PRE, TAU_EDGE, SRC_R1, SRC_R2, RATIO_BAR, DIP_BAR, W_ENTRY_X, CONTACT_BAR, CONTACT_RUNGS, LAST5, P_SLOPE, P_FLOOR, P_SPREAD, PARENT5, MID5, TOP5, HALF2, BAR_GAUSS, WARD_FRAME, M_WARD, WARD_RO, ANCH_CONTACT, sorted(REPRO_COUNTS.items()), REPRO_G78_1176, REPRO_TOLG, REPRO_LMIN1176, REPRO_LTOL, sorted(DRAIN_LEVELS.items()), REPRO_QTOL, COMB_DEV_BAR, PREFIX_WARD, RUNTIME_CAP, CG_SEEDS, SEED_CS, CTRL_LAD_CS, EP_NCAP, EP_MMAX, CTRL_LAD_CE)).encode()) for R in R_BAT: bats[R] = hbp.battery(R) for nm, v in bats[R]: hsh.update(nm.encode()) hsh.update(v.tobytes()) return bats, hsh.hexdigest() def battery_matrix(bats): cols, names = [], [] for R in R_BAT: nR = int(round(R / D)) for nm, v in bats[R]: f = np.zeros(NPAD) f[:nR] = v cols.append(f) names.append("R%g:%s" % (R, nm)) return np.stack(cols, axis=1), names # ------------------------------------------------ towers (verbatim) def build_parent_tower(): alpha = 0.5 * M_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 atoms to e^%.4f" % (dev_m, ka, 2.0 * alpha)) c = srp.continuum_lags(M_PAR) for cnl in ("ro", "re", "sp", "in"): c = c + srp.atom_channel_lags(alpha, M_PAR, masks[cnl]) return sla.toeplitz(c[:M_PAR]), masks, alpha 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 over " "[%.0f, %d] <= KAPPA_REF + %.0e = %.6f" % (kappa, core.KAPPA_X0, ATOM_MAX_DEEP, core.TOL_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 * D ka = int(np.searchsorted(u_deep, 2.0 * alpha + 1.0e-14, side="right")) c_cont = srp.continuum_lags(M_TOP) c_at, _dd = core.atom_lags_at(alpha, M_TOP, u_deep[:ka], mu_deep[:ka]) p = c_cont + c_at T = sla.toeplitz(p[:M_TOP]) dev = float(np.max(np.abs(T[:M_PAR, :M_PAR] - T_par))) check("G1.4 prefix Ward: deep tower leading %d x %d block == " "parent tower, max abs dev %.1e <= %.0e" % (M_PAR, M_PAR, dev, PREFIX_WARD), dev <= PREFIX_WARD) print(" deep census: ka = %d atoms to e^%.4f" % (ka, 2.0 * alpha)) return p, T, c_cont, alpha, ka def build_ro_comb(alpha_top, masks, alpha_par): """Hand-built ramified-odd comb (powers 2^{2k+1}), zeta-free; Ward against the srp ro channel at parent reach.""" ns, k = [], 0 while (2 * k + 1) * math.log(2.0) <= 2.0 * alpha_top + 1e-14: ns.append(2 ** (2 * k + 1)) k += 1 ns = np.array(ns, float) u_ro = np.log(ns) mu_ro = 2.0 * math.log(2.0) / np.sqrt(ns) c_ro, _dd = core.atom_lags_at(alpha_top, M_TOP, u_ro, mu_ro) keep = u_ro <= 2.0 * alpha_par + 1e-14 c_hand, _dd = core.atom_lags_at(alpha_par, M_PAR, u_ro[keep], mu_ro[keep]) c_srp = srp.atom_channel_lags(alpha_par, M_PAR, masks["ro"]) dev = float(np.max(np.abs(c_hand - c_srp))) check("G1.10a ro-comb Ward: hand ramified-odd lags == srp ro " "channel lags at parent reach (%d atoms), max abs dev " "%.1e <= %.0e" % (int(np.sum(keep)), dev, WARD_RO), dev <= WARD_RO) return c_ro # ------------------------------------------------ source-side anchors def source_anchors(T, c_ro, F, names): anchor_rungs = sorted(set(list(REPRO_COUNTS) + [972, 1176] + TOP5)) spec = {} for M in anchor_rungs: lam, V = np.linalg.eigh(T[:M, :M]) spec[M] = (lam, V) ok_cnt = True det = [] for M, want in sorted(REPRO_COUNTS.items()): got = int(np.sum(spec[M][0] <= THR_NULL)) det.append("%d:%d" % (M, got)) ok_cnt = ok_cnt and (got == want) check("G1.5a source entry anchors: near-null counts (thr %g) " "%s == frozen %s" % (THR_NULL, "/".join(det), sorted(REPRO_COUNTS.items())), ok_cnt) lam76 = spec[1176][0] g78 = float((lam76[7] - lam76[6]) / lam76[7]) check("G1.5b source gap/PD anchors: 7/8 gap(1176) = %.4f vs " "frozen %.4f (tol %.0e); lambda_min(1176) = %.4e vs " "frozen %.4e (tol %.0e)" % (g78, REPRO_G78_1176, REPRO_TOLG, lam76[0], REPRO_LMIN1176, REPRO_LTOL), abs(g78 - REPRO_G78_1176) <= REPRO_TOLG and abs(lam76[0] - REPRO_LMIN1176) <= REPRO_LTOL) qs = [] for M in TOP5: V6 = spec[M][1][:, :6] qs.append(np.sum((V6[:NPAD, :].T @ F) ** 2, axis=0)) med = np.median(np.stack(qs), axis=0) dev_worst = max(abs(float(med[j]) - DRAIN_LEVELS[nm]) for j, nm in enumerate(names) if nm in DRAIN_LEVELS) check("G1.5c source drainage-level anchors: med%d(TOP5) " "reproduces the nine frozen levels, worst dev %.1e <= " "%.0e" % (N_MED, dev_worst, REPRO_QTOL), dev_worst <= REPRO_QTOL) lam72, V72 = spec[972] n72 = int(np.sum(lam72 <= THR_NULL)) lam_ro, v_ro = np.linalg.eigh(sla.toeplitz(c_ro[:972])) sv = np.linalg.svd(V72[:, :n72].T @ v_ro[:, :5], compute_uv=False) cosc = float(sv[0]) check("G1.10b source contact anchor at M = 972: near-null " "count %d (== 6), max principal cosine near-kernel vs " "5-dim ram-odd negative frame = %.4f >= %g (census band " "0.992..0.999)" % (n72, cosc, ANCH_CONTACT), n72 == 6 and cosc >= ANCH_CONTACT) return {M: spec[M][0] for M in anchor_rungs} # ------------------------------------------------ candidate machinery def cheb_gram(p, K): """Cos-basis Gram G[j,k] = (p_|j-k| + p_{j+k})/2 (even folding of the Toeplitz Gram under x = 2 cos theta).""" idx = np.arange(K) return 0.5 * (p[np.abs(idx[:, None] - idx[None, :])] + p[idx[:, None] + idx[None, :]]) def cand_rung(p, M, Fp, c_ro, want_recon=False): """One candidate rung: J_{K=M/2} of the unified measure; edge census, boundary gap, contact cosine, battery couplings.""" K = M // 2 aM, gM, kbad = jac.wheeler(p[:M], K) if kbad is not None: return dict(M=M, K=K, kbad=int(kbad)) bJ = aM.copy() aJ = np.sqrt(gM[1:K]) ev = sla.eigh_tridiagonal(bJ, aJ, eigvals_only=True) tau = np.sort(np.arccos(np.clip(ev / 2.0, -1.0, 1.0)) / D) n_edge = int(np.sum(ev > X_EDGE)) g_bd = np.nan if 1 <= n_edge < K: g_bd = float((tau[n_edge] - tau[n_edge - 1]) / tau[n_edge]) _evE, UE = sla.eigh_tridiagonal(bJ, aJ, select="v", select_range=(X_EDGE, 4.0)) G = cheb_gram(p, K) try: L = sla.cholesky(G, lower=True, check_finite=False) except np.linalg.LinAlgError: return dict(M=M, K=K, kbad=None, chol=False) Fk = np.zeros((K, Fp.shape[1])) Fk[:NPAD, :] = Fp C = L.T @ Fk q = (np.sum((UE.T @ C) ** 2, axis=0) / np.maximum(np.sum(C ** 2, axis=0), QF_FLOOR)) lam_ro, v_ro = sla.eigh(sla.toeplitz(c_ro[:K]), subset_by_index=[0, 4]) Qu, _r = np.linalg.qr(L.T @ v_ro) sv = np.linalg.svd(UE.T @ Qu, compute_uv=False) cosc = float(sv[0]) if sv.size else 0.0 recon = None if want_recon: rec = jac.gauss_reconstruct(aM, gM, p[0], min(2 * K, M)) recon = float(np.max(np.abs(rec - p[:len(rec)])) / np.max(np.abs(p[:len(rec)]))) return dict(M=M, K=K, kbad=None, chol=True, n_edge=n_edge, g_bd=g_bd, q=q, cos=cosc, recon=recon, lam_ro=float(lam_ro[0]), L=L if M == M_WARD else None, aM=aM if M == M_WARD else None, gM=gM if M == M_WARD else None) def frame_ward(p, blk): """G1.7: L^{-1} A_x L^{-T} == Wheeler tridiagonal at M_WARD.""" K = blk["K"] L, aM, gM = blk["L"], blk["aM"], blk["gM"] Gx = cheb_gram(p, K + 1) A = np.zeros((K, K)) A[:, 0] = 2.0 * Gx[:K, 1] for k in range(1, K): A[:, k] = Gx[:K, k + 1] + Gx[:K, k - 1] A = 0.5 * (A + A.T) Y = sla.solve_triangular(L, A, lower=True, check_finite=False) J = sla.solve_triangular(L, Y.T, lower=True, check_finite=False).T J = 0.5 * (J + J.T) Jw = np.diag(aM) + np.diag(np.sqrt(gM[1:K]), 1) \ + np.diag(np.sqrt(gM[1:K]), -1) dev = float(np.max(np.abs(J - Jw))) check("G1.7 GNS frame Ward at M = %d (K = %d): max |L^-1 A_x " "L^-T - J_wheeler| = %.1e <= %.0e (frame consistency)" % (M_WARD, K, dev, WARD_FRAME), dev <= WARD_FRAME) lg = math.log(float(p[0])) + float(np.sum(np.log(gM[1:K]))) lc = 2.0 * math.log(2.0 * float(L[K - 1, K - 1])) print(" norm-chain report (never gated): log ||pi_%d||^2 " "wheeler %.6f vs cholesky %.6f (dev %.1e)" % (K - 1, lg, lc, abs(lg - lc))) # ------------------------------------------------ census + cadence def entry_census(xs, counts, n_base): """Entry level n -> first x with count >= n (n > baseline).""" entries = [] cmax = max(counts) for n in range(n_base + 1, cmax + 1): for x, c in zip(xs, counts): if c >= n: entries.append((n, x)) break return entries def cadence_match(entries, label): """Frozen Z1-A statistic: last-3 gaps widening AND ratios match the source ratios within RATIO_BAR (fit-free).""" xs = [x for (_n, x) in entries] gaps = [b - a for a, b in zip(xs, xs[1:])] if len(gaps) < 3: return False, ("%s: insufficient entries (%d gaps < 3)" % (label, len(gaps))), gaps g1, g2, g3 = gaps[-3:] widening = (g1 > 0.0) and (g1 < g2 < g3) r1 = g2 / g1 if g1 > 0 else float("inf") r2 = g3 / g2 if g2 > 0 else float("inf") d1 = abs(r1 / SRC_R1 - 1.0) d2 = abs(r2 / SRC_R2 - 1.0) ok = widening and d1 <= RATIO_BAR and d2 <= RATIO_BAR det = ("%s: last-3 gaps %.4f/%.4f/%.4f, ratios %.3f/%.3f vs " "source %.3f/%.3f (devs %.3f/%.3f, bar %g), widening=%s" % (label, g1, g2, g3, r1, r2, SRC_R1, SRC_R2, d1, d2, RATIO_BAR, widening)) return ok, det, gaps # ------------------------------------------------ controls def control_cg(): print("\n-- CG structural control (3 GOE truncation families + " "free Chebyshev Jacobi, identical census)") K_top = M_TOP // 2 n_match = 0 for seed in CG_SEEDS: rng = np.random.default_rng(seed) A = rng.standard_normal((K_top, K_top)) H = A + A.T counts = [] for M in LAD: K = M // 2 evs = np.linalg.eigvalsh(H[:K, :K] / math.sqrt(2.0 * K)) counts.append(int(np.sum(evs > X_EDGE))) entries = entry_census([M * D for M in LAD], counts, counts[0]) ok, det, _g = cadence_match(entries, "GOE seed %d" % seed) print(" " + det) n_match += int(ok) counts = [] for M in LAD: K = M // 2 j = np.arange(1, K + 1) x = 2.0 * np.cos(j * math.pi / (K + 1)) counts.append(int(np.sum(x > X_EDGE))) entries = entry_census([M * D for M in LAD], counts, counts[0]) okf, detf, _g = cadence_match(entries, "free Jacobi") print(" " + detf) n_match += int(okf) return check("CG structural control fires: 0/4 generic " "families pass the Z1-A cadence bars (%d matched)" % n_match, n_match == 0) def control_measure(pc, lad, label): """CS/CE fire rule: wheeler breakdown OR census completes without passing Z1-A.""" kbads, counts, xs = [], [], [] for M in lad: K = M // 2 aM, gM, kbad = jac.wheeler(pc[:M], K) if kbad is not None: kbads.append((M, int(kbad))) continue ev = sla.eigh_tridiagonal(aM, np.sqrt(gM[1:K]), eigvals_only=True) counts.append(int(np.sum(ev > X_EDGE))) xs.append(M * D) if kbads: return check("%s control fires: candidate construction " "breaks (Wheeler breakdown on %d/%d rungs, " "first kbad = %d at M = %d)" % (label, len(kbads), len(lad), kbads[0][1], kbads[0][0]), True) entries = entry_census(xs, counts, counts[0]) ok, det, _g = cadence_match(entries, label) print(" " + det) return check("%s control fires: construction survives and the " "census does NOT pass the Z1-A bars" % label, not ok) # ------------------------------------------------ run def run(): print("=" * 78) print("SHARPENED-Z1 kickoff -- edge-signature gate: the N2 " "GNS/Jacobi family vs the source moving-edge record " "(X <= %.4f)" % (M_TOP * D)) print("=" * 78) hits = ast_firewall() check("G0.1 AST firewall (construction path zeta-free; edge " "census line is a declared constant)", not hits, str(hits)) bats, spec_sha = freeze_spec() check("G0.2 battery + ladders + bars + anchors SHA-256-frozen " "BEFORE any comb data is built here", True, "SHA256 %s..." % spec_sha[:16]) check("G0.3 reach census: M_TOP = %d <= floor(64 ln %d) = %d; " "sieve cover exp(X_top) + 2 = %d <= %d; runtime cap " "%.0f s predeclared" % (M_TOP, ATOM_MAX_DEEP, M_CAP_DEEP, int(math.exp(M_TOP * D)) + 2, ATOM_MAX_DEEP, RUNTIME_CAP), M_TOP <= M_CAP_DEEP and int(math.exp(M_TOP * D)) + 2 <= ATOM_MAX_DEEP) # ---- combs + towers strictly after the freeze u_deep, mu_deep = build_deep_comb() T_par, masks, alpha_par = build_parent_tower() p, T, c_cont, alpha_top, ka = build_deep_tower(u_deep, mu_deep, T_par) c_ro = build_ro_comb(alpha_top, masks, alpha_par) F, names = battery_matrix(bats) # ---- source-side anchors (same glued object, Gram frame) print("\n-- source anchors (Gram frame; guards, not gates)") source_anchors(T, c_ro, F, names) # ---- candidate ladder print("\n-- candidate ladder: J_{K=M/2} on LAD = %d..%d step 4 " "(%d rungs), edge line tau < %.2f (x > %.6f)" % (LAD[0], LAD[-1], len(LAD), TAU_EDGE, X_EDGE)) blks = {} recs = {} for M in [M_PRE] + LAD: blk = cand_rung(p, M, F, c_ro, want_recon=(M in (648, 888, 1176))) blks[M] = blk if blk.get("recon") is not None: recs[M] = blk["recon"] bad = [(M, b["kbad"]) for M, b in blks.items() if b.get("kbad") is not None] check("G1.6 Wheeler validity: kbad None on every rung (%d " "rungs) AND Gauss moment reconstruction rel dev %s <= " "%.0e" % (len(LAD) + 1, "/".join("%.1e" % recs[M] for M in sorted(recs)), BAR_GAUSS), not bad and all(v <= BAR_GAUSS for v in recs.values()), str(bad[:3]) if bad else "") if bad: print("\nVERDICT: Z1-GATE-INVALID (candidate construction " "broke)") return 1 nochol = [M for M, b in blks.items() if not b.get("chol", False)] check("G1.8 Cholesky PD of the cos-Gram on every rung", not nochol, str(nochol[:3])) if nochol: print("\nVERDICT: Z1-GATE-INVALID (Gram not PD)") return 1 frame_ward(p, blks[M_WARD]) # ---- Z1-A cadence print("\n-- Z1-A: edge census + entry cadence (source record: " "entries M = %s, DX = %s)" % (list(SRC_ENTRY_M), list(SRC_DX))) counts = [blks[M]["n_edge"] for M in LAD] print(" edge count profile (every 8th rung): %s" % "/".join("%d:%d" % (M, blks[M]["n_edge"]) for M in LAD[::8])) entries = entry_census([M * D for M in LAD], counts, blks[M_PRE]["n_edge"]) print(" entry table (baseline count %d at M = %d):" % (blks[M_PRE]["n_edge"], M_PRE)) for n, x in entries: print(" level %2d: entry X = %.4f (M = %d)" % (n, x, int(round(x / D)))) a_ok, a_det, gaps = cadence_match(entries, "candidate") if gaps: print(" inter-entry gaps DX = %s (mean %.4f); source DX = " "%s" % ("/".join("%.4f" % g for g in gaps), float(np.mean(gaps)), list(SRC_DX))) print(" predicted next entry (REPORTED only): X ~ %.2f" % (entries[-1][1] + float(np.mean(gaps)))) a_ok = gate("Z1-A MOVING-EDGE CADENCE: %s" % a_det, a_ok) # ---- Z1-B crossing print("\n-- Z1-B: boundary-pair gap profile (source analog: " "7/8 min gap %.4f at M = 1240)" % SRC_G78MIN) gprof = {M: blks[M]["g_bd"] for M in LAD if np.isfinite(blks[M]["g_bd"])} med_g = float(np.median(list(gprof.values()))) m_min = min(gprof, key=gprof.get) print(" gap profile (every 16th rung): %s" % " ".join("M=%d:%.4f" % (M, gprof[M]) for M in LAD[::16] if M in gprof)) print(" ladder median %.4f; global min %.4f at M = %d " "(%.3f x median)" % (med_g, gprof[m_min], m_min, gprof[m_min] / med_g)) dips = [] for n, xe in entries: near = [gprof[M] for M in gprof if abs(M * D - xe) <= W_ENTRY_X] if near: dips.append((n, xe, min(near))) for n, xe, gmin in dips: print(" entry level %d (X = %.4f): min gap within +-%g X " "= %.4f (%.3f x median)" % (n, xe, W_ENTRY_X, gmin, gmin / med_g)) b_ok = gate("Z1-B AVOIDED CROSSING: min entry-adjacent gap = " "%.4f, bar <= %.4f (%g x ladder median %.4f)" % (min((d[2] for d in dips), default=float("inf")), DIP_BAR * med_g, DIP_BAR, med_g), bool(dips) and min(d[2] for d in dips) <= DIP_BAR * med_g) # ---- Z1-C contact print("\n-- Z1-C: ram-odd contact direction (source: cos %.3f " "rung-stable; chance floor ~ sqrt(n_edge/K) ~ %.2f)" % (SRC_CONTACT, math.sqrt(blks[LAD[-1]]["n_edge"] / float(blks[LAD[-1]]["K"])))) cos_all = [blks[M]["cos"] for M in LAD] print(" contact profile on LAST5: %s; ladder median %.4f, max " "%.4f" % (" ".join("M=%d:%.4f" % (M, blks[M]["cos"]) for M in LAST5), float(np.median(cos_all)), max(cos_all))) n_hit = sum(1 for M in LAST5 if blks[M]["cos"] >= CONTACT_BAR) c_ok = gate("Z1-C RAM-ODD CONTACT: cos >= %g on %d/%d of " "LAST5 (need >= %d)" % (CONTACT_BAR, n_hit, len(LAST5), CONTACT_RUNGS), n_hit >= CONTACT_RUNGS) # ---- Z1-D settled couplings print("\n-- Z1-D: settled coupling levels (drainage P bars " "verbatim; mu-normalized -- level identity with the " "source NOT gated)") qmap = {M: blks[M]["q"] for M in LAD} med_par = np.median(np.stack([qmap[M] for M in PARENT5]), axis=0) med_mid = np.median(np.stack([qmap[M] for M in MID5]), axis=0) med_top = np.median(np.stack([qmap[M] for M in TOP5]), axis=0) q_t5 = np.stack([qmap[M] for M in TOP5]) spread = (q_t5.max(axis=0) - q_t5.min(axis=0)) \ / np.maximum(q_t5.max(axis=0), QF_FLOOR) xs_h = np.array([M * D for M in HALF2]) q_h = np.stack([qmap[M] for M in HALF2]) print(" %-18s %-8s %-8s %-8s %6s %7s %6s %8s" % ("function", "parent", "mid", "top", "b/X", "spread", "type", "src-lvl")) n_p = 0 for j, nm in enumerate(names): rows = [dict(XmR=float(x), mx=float(v)) for x, v in zip(xs_h, q_h[:, j])] b, _res = hbp.fit_rate(rows) ty = "P" if (abs(b) <= P_SLOPE and med_top[j] >= P_FLOOR and spread[j] <= P_SPREAD) else "U" n_p += int(ty == "P") src = ("%.4f" % DRAIN_LEVELS[nm]) if nm in DRAIN_LEVELS \ else "--" print(" %-18s %.4f %.4f %.4f %+5.3f %5.3f %s %8s" % (nm, med_par[j], med_mid[j], med_top[j], b, spread[j], ty, src)) d_ok = gate("Z1-D SETTLED COUPLINGS: %d/14 functions type P " "(|b| <= %g, level >= %g, spread <= %g)" % (n_p, P_SLOPE, P_FLOOR, P_SPREAD), n_p == 14) qall = np.stack([qmap[M] for M in LAD]) check("G1.9 boundedness: every q_f in [%.1e, %.4f] inside " "[-1e-12, 1 + %.0e]; max contact cos %.4f <= 1 + 1e-12" % (float(np.min(qall)), float(np.max(qall)), BOUND_TOL, max(cos_all)), float(np.min(qall)) >= -1.0e-12 and float(np.max(qall)) <= 1.0 + BOUND_TOL and max(cos_all) <= 1.0 + 1.0e-12) # ---- controls cg_ok = control_cg() print("\n-- CS position-scramble control (deep comb, masses " "kept, seed %d)" % SEED_CS) rng = np.random.default_rng(SEED_CS) pos = np.sort(rng.uniform(0.5, 2.0 * alpha_top, ka)) cat_s, _dd = core.atom_lags_at(alpha_top, M_TOP, pos, mu_deep[:ka]) control_measure(c_cont + cat_s, CTRL_LAD_CS, "CS scramble") print("\n-- CE Epstein control (x^2 + 5y^2, cap M = %d)" % EP_MMAX) 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] catE, _dd = core.atom_lags_at(0.5 * EP_MMAX * D, EP_MMAX, np.log(supp.astype(float)), 2.0 * lamE[supp] / np.sqrt(supp.astype(float))) control_measure(srp.continuum_lags(EP_MMAX) + catE, CTRL_LAD_CE, "CE Epstein") _ = cg_ok # ---- runtime guard dt = time.time() - T_START check("G0.4 runtime %.1f s <= predeclared cap %.0f s" % (dt, RUNTIME_CAP), dt <= RUNTIME_CAP) # ---- verdict (preregistered decision order) guards_ok = all(ok for (n, ok) in CHECKS if not n.startswith(("CG", "CS", "CE"))) controls_ok = all(ok for (n, ok) in CHECKS if n.startswith(("CG", "CS", "CE"))) sigs = dict(A=a_ok, B=b_ok, C=c_ok, D=d_ok) n_sig = sum(sigs.values()) if not (guards_ok and controls_ok): verdict = "Z1-GATE-INVALID" elif n_sig == 4: verdict = "Z1-SIGNATURE-MATCH" elif n_sig >= 1: verdict = "Z1-SIGNATURE-PARTIAL" else: verdict = "Z1-SIGNATURE-ABSENT" n_chk = sum(1 for (_n, ok) in CHECKS if ok) print("\nVERDICT: %s" % verdict) print("GATES %d/4 (A=%s B=%s C=%s D=%s), GUARDS+CONTROLS " "%d/%d, runtime %.1f s" % (n_sig, *["P" if sigs[k] else "F" for k in "ABCD"], n_chk, len(CHECKS), time.time() - T_START)) if verdict == "Z1-SIGNATURE-MATCH": print("CONSEQUENCE (stated plainly): the N2 truncation " "family carries the measured threshold structure " "natively in its self-adjoint operator frame -- the " "next Z1 module is the Weyl-M-function / boundary-" "triple construction on the candidate's edge band, " "with the entry rungs above as its cell boundaries. " "NO RH claim.") elif verdict == "Z1-SIGNATURE-PARTIAL": print("CONSEQUENCE (stated plainly): the candidate family " "carries ONLY the signature(s) %s of the measured " "handover constraints; the failing signature(s) %s " "name the structure a Z1 boundary triple cannot get " "from J_K as-is and must add explicitly. NO RH " "claim." % ([k for k in "ABCD" if sigs[k]], [k for k in "ABCD" if not sigs[k]])) else: print("CONSEQUENCE (stated plainly): the candidate family " "lacks the measured threshold structure entirely -- " "the handover constraint list rules out the plain " "GNS/Jacobi family as the Z1 bulk operator; any " "future candidate must carry the Gram near-kernel " "band as genuine spectral structure (moving edge " "with widening cadence, edge collision, ram-odd " "contact). NO RH claim.") return 0 if (guards_ok and controls_ok) else 1 _run_part1 = run def _run_part2(): # PART 2 -- z1_boundary_triple_probe.py (verbatim; module-level names # local to this function scope; sibling imports remapped as declared) 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__)) _HERE_DISC = os.path.abspath(os.path.join(_HERE, "..", "experiments", "tfpt-discovery")) sys.path.insert(0, _HERE) sys.path.insert(0, _HERE_DISC) import v563_paper2_readouts as core # noqa: E402 import v696_z1_jacobi as jac # noqa: E402 (Wheeler, locked) 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 (sign_fix) T_START = time.time() # ------------------------------------------------ frozen specification D = srp.DGRID # 1/64, dyadic float-exact ATOM_MAX_DEEP = 1000000000 # deep comb cap (1e9, declared) M_CAP_DEEP = int(math.floor(math.log(ATOM_MAX_DEEP) / D)) # 1326 M_TOP = 1300 # deepest rung (X = 20.3125) M_PAR = 824 # parent cap (prefix Ward) LAD = list(range(888, 1301, 4)) # 104 rungs, X = 13.875..20.3125 E_TEST = (992, 1108, 1276) # frozen entry/transition rungs GATE_BLOCK = list(range(1256, 1273, 4)) # last 5 of the d=8 run TOP5W = list(range(1160, 1177, 4)) # drainage-anchor rungs HALF2 = LAD[len(LAD) // 2:] # second-half trend block M_WARD = 888 # GNS frame Ward rung WARD_H_RUNGS = (888, 1272) # dense-H Ward rungs WARD_D_RUNGS = (888, 1108, 1300) # Gauss/Weil + recon Ward rungs THR_NULL = 1.0e-4 # band rule threshold (cocycle) H_IM = 1.0e-2 ZSET = (-1.0e-1, -1.0e-2, -1.0e-3, complex(0.0, H_IM), complex(-1.0e-3, H_IM)) Z_REF = -1.0e-2 # delivery reference cell ZC = ZSET[3:] # Herglotz points Z_CB = -1.0e-1 # GOE-bulk control cell HERG_FLOOR = 1.0e-8 # gate (a) HERG_DEAD = 1.0e-6 # DEAD-grade violation B_MATCH = 0.25 # gate (b) med5 bar B_DEAD = 10.0 # gate (b) structural-fail bar C_RESP = 3.0 # gate (c) contrast bar C_UNIQ = 1 # gate (c) uniqueness allowance D_LEVEL = 0.05 # gate (d) med5 level bar D_SLOPE_MIN = -0.01 # gate (d) trend floor (b >= ) N_MED = 5 NPAD = 128 # battery support in cells R_BAT = (1.0, 2.0) QF_FLOOR = 1.0e-12 IMPORT_FLOOR = 1.0e-8 # import collapse floor SVD_FLOOR = 1.0e-8 # K4 transport kill floor WARD_ORTH = 1.0e-10 # R orthogonality COUP_WARD = 1.0e-8 # coupling |E_c| Ward WARD_FRAME = 1.0e-3 # GNS frame Ward WARD_SOLVE = 1.0e-9 # banded-solve residual WARD_SH = 1.0e-8 # S H = I Ward WARD_HDENSE = 1.0e-9 # dense-H Ward WARD_GAUSSW = 1.0e-8 # Gauss/Weil state identity BAR_GAUSS = 1.0e-8 # moment reconstruction PD_TOL = 1.0e-9 COMB_DEV_BAR = 1.0e-12 PREFIX_WARD = 1.0e-12 RUNTIME_CAP = 1800.0 REPRO_COUNTS = {884: 5, 888: 6, 988: 6, 992: 7, 1104: 7, 1108: 8, 1272: 8, 1276: 9} REPRO_GAPS = {("67", 1096): 0.1008, ("67", 1176): 0.1397, ("78", 1176): 0.0613, ("78", 1240): 0.0039} REPRO_TOLG = 2.0e-4 REPRO_LMIN1176 = 3.882e-6 REPRO_LTOL = 2.0e-8 DRAIN_LEVELS = { "R2:box[0,R]": 0.3583, "R2:box[R/2,R]": 0.3370, "R2:hat(R/2,R/2)": 0.3127, "R2:hat(3R/4,R/4)": 0.2590, "R2:box[R/4,3R/4]": 0.2249, "R1:box[R/2,R]": 0.0793, "R1:box[0,R]": 0.0741, "R2:box[0,R/2]": 0.0741, "R1:hat(R/4,R/4)": 0.0082} REPRO_QTOL = 2.0e-3 SEED_CS = 7 SEED_CB = 11 SEED_CW = 20260805 CTRL_LAD_CS = list(range(888, 1301, 48)) EP_NCAP = 34000 EP_MMAX = 640 CTRL_LAD_CE = list(range(400, 641, 8)) CW_LAD = list(range(888, 989, 4)) # d = 6 run for CW 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(): bats = {} hsh = hashlib.sha256() hsh.update(("z1-boundary-triple spec: bulk A = 2I - J_{K=M/2} " "(v718 machinery, dyadic D=%.10f), deep cap %d " "(512-GB machine declared), M_TOP=%d, LAD=%s; band " "rule d(M)=#{lam<=%g} cocycle verbatim, transitions " "R'=[JR|N]; import U=L^T B[:K], polar, floor %g; " "M-function H=Q^T(A-z)^-1 Q, S=H^-1, ZSET=%s, " "Z_REF=%g; gates: (a) Herglotz >= -%g (dead %g); " "(b) rho_b med5 over %s <= %g (dead > %g); (c) " "rel-increment contrast rho(e) >= %g on E_TEST=%s, " "uniqueness <= %d, cocycle normalizer verbatim; " "(d) err_d med5 <= %g AND fit_rate b >= %g over " "HALF2, battery autocorr g_f, Gauss/Weil ward %g; " "wards: solve %g, SH %g, denseH %g at %s, frame %g " "at %d, coup %g, orth %g, svd %g, recon %g at %s; " "anchors: counts %s, gaps %s tol %g, lmin1176 %g " "tol %g, drain %s tol %g; guards comb %g prefix %g " "pd %g runtime %g; controls: CS seed %d rungs %s, " "CE cap %d M %d rungs %s, CB GOE seed %d z=%g fire " "rho_b>%g (declared deviation: response reported " "not gated), CW seed %d rungs %s fire rho_b>%g AND " "contrast<%g; verdict: invalid -> DEAD(a>%g or " "b>%g or import collapse) -> CARRIES(abcd) -> " "PARTIAL" % (D, ATOM_MAX_DEEP, M_TOP, LAD, THR_NULL, IMPORT_FLOOR, ZSET, Z_REF, HERG_FLOOR, HERG_DEAD, GATE_BLOCK, B_MATCH, B_DEAD, C_RESP, E_TEST, C_UNIQ, D_LEVEL, D_SLOPE_MIN, WARD_GAUSSW, WARD_SOLVE, WARD_SH, WARD_HDENSE, WARD_H_RUNGS, WARD_FRAME, M_WARD, COUP_WARD, WARD_ORTH, SVD_FLOOR, BAR_GAUSS, WARD_D_RUNGS, sorted(REPRO_COUNTS.items()), sorted(REPRO_GAPS.items()), REPRO_TOLG, REPRO_LMIN1176, REPRO_LTOL, sorted(DRAIN_LEVELS.items()), REPRO_QTOL, COMB_DEV_BAR, PREFIX_WARD, PD_TOL, RUNTIME_CAP, SEED_CS, CTRL_LAD_CS, EP_NCAP, EP_MMAX, CTRL_LAD_CE, SEED_CB, Z_CB, B_MATCH, SEED_CW, CW_LAD, B_MATCH, C_RESP, HERG_DEAD, B_DEAD) ).encode()) for R in R_BAT: bats[R] = hbp.battery(R) for nm, v in bats[R]: hsh.update(nm.encode()) hsh.update(v.tobytes()) return bats, hsh.hexdigest() def battery_matrix(bats): cols, names = [], [] for R in R_BAT: nR = int(round(R / D)) for nm, v in bats[R]: f = np.zeros(NPAD) f[:nR] = v cols.append(f) names.append("R%g:%s" % (R, nm)) return np.stack(cols, axis=1), names # ------------------------------------------------ towers (verbatim) def build_parent_tower(): alpha = 0.5 * M_PAR * D ka, masks, dev_m = srp.channel_masks(alpha) check("G1.3 parent tower comb consistency (rel dev <= %.0e)" % COMB_DEV_BAR, dev_m <= COMB_DEV_BAR, "rel dev %.1e, ka=%d" % (dev_m, ka)) c = srp.continuum_lags(M_PAR) for cnl in ("ro", "re", "sp", "in"): c = c + srp.atom_channel_lags(alpha, M_PAR, masks[cnl]) return sla.toeplitz(c[:M_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: 1e9 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 over " "[%.0f, %d] <= %.6f" % (kappa, core.KAPPA_X0, ATOM_MAX_DEEP, 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 * D ka = int(np.searchsorted(u_deep, 2.0 * alpha + 1.0e-14, side="right")) c_cont = srp.continuum_lags(M_TOP) c_at, _dd = core.atom_lags_at(alpha, M_TOP, u_deep[:ka], mu_deep[:ka]) p = c_cont + c_at T = sla.toeplitz(p[:M_TOP]) dev = float(np.max(np.abs(T[:M_PAR, :M_PAR] - T_par))) check("G1.4 prefix Ward: deep tower leading %d block == parent " "tower, max abs dev %.1e <= %.0e" % (M_PAR, dev, PREFIX_WARD), dev <= PREFIX_WARD) print(" deep census: ka = %d atoms to e^%.4f" % (ka, 2 * alpha)) return p, T, c_cont, alpha, ka # ------------------------------------------------ candidate frame def cheb_gram(p, K): idx = np.arange(K) return 0.5 * (p[np.abs(idx[:, None] - idx[None, :])] + p[idx[:, None] + idx[None, :]]) def frame_ward(p, K, L, aM, gM): Gx = cheb_gram(p, K + 1) A = np.zeros((K, K)) A[:, 0] = 2.0 * Gx[:K, 1] for k in range(1, K): A[:, k] = Gx[:K, k + 1] + Gx[:K, k - 1] A = 0.5 * (A + A.T) Y = sla.solve_triangular(L, A, lower=True, check_finite=False) J = sla.solve_triangular(L, Y.T, lower=True, check_finite=False).T J = 0.5 * (J + J.T) Jw = np.diag(aM) + np.diag(np.sqrt(gM[1:K]), 1) \ + np.diag(np.sqrt(gM[1:K]), -1) dev = float(np.max(np.abs(J - Jw))) check("G1.7 GNS frame Ward at M = %d (K = %d): dev %.1e <= " "%.0e" % (M_WARD, K, dev, WARD_FRAME), dev <= WARD_FRAME) def tri_solve(bJ, aJ, z, Bmat): """(A - z) Y = Bmat with A = 2 - J tridiagonal, via banded LU.""" K = len(bJ) cplx = isinstance(z, complex) dt = complex if cplx else float ab = np.zeros((3, K), dtype=dt) ab[0, 1:] = -aJ ab[1, :] = (2.0 - z) - bJ ab[2, :-1] = -aJ return sla.solve_banded((1, 1), ab, Bmat.astype(dt)) def cheb_eval(a_all, x): """g_f(x) = a_0 + 2 sum_d a_d T_d(x/2) for all battery rows.""" y = x / 2.0 t_prev = np.ones_like(x) t_cur = y.copy() acc = np.outer(a_all[:, 0], t_prev) for dd in range(1, a_all.shape[1]): acc += 2.0 * np.outer(a_all[:, dd], t_cur) t_prev, t_cur = t_cur, x * t_cur - t_prev return acc # ------------------------------------------------ per-rung machinery def gram_rung(T, M, want_q6=False, Fb=None): lam, V = np.linalg.eigh(T[:M, :M]) d = int(np.sum(lam <= THR_NULL)) Vd = qsb.sign_fix(V[:, :d]) Ec = V[:, d:].T @ (T[:M, :M] @ Vd) out = dict(M=M, lam=lam[:16].copy(), lam_min=float(lam[0]), d=d, Vd=Vd, coup=float(np.max(np.abs(Ec))), lam_rest=lam[d:], Ec=Ec) if want_q6 and Fb is not None: out["q6"] = np.sum((V[:NPAD, :6].T @ Fb) ** 2, axis=0) return out def f_tilde(gr, R, z): """Transported Gram effective block (Feshbach machinery verbatim): R^T [Lambda_d - z - C_d(z)] R.""" d = gr["d"] lam_d = gr["lam"][:d] C = gr["Ec"].T @ (gr["Ec"] / (gr["lam_rest"][:, None] - z)) core_blk = np.diag(lam_d).astype(complex) \ - z * np.eye(d) - C out = R.T @ core_blk @ R return out.real if not isinstance(z, complex) else out def transport_update(prev, gr, R_prev): """Cocycle transition convention verbatim.""" Ma, Mb = prev["M"], gr["M"] da, db = prev["d"], gr["d"] S_ov = gr["Vd"][:Ma, :].T @ prev["Vd"] # (db x da) Uu, s, Vt = np.linalg.svd(S_ov, full_matrices=False) smin = float(s[-1]) if db == da: R = (Uu @ Vt) @ R_prev kind = "link" elif db > da: Jiso = Uu @ Vt # (db x da) isometry JR = Jiso @ R_prev Qf, _ = np.linalg.qr(JR, mode="complete") N = Qf[:, da:] for j in range(N.shape[1]): i0 = int(np.argmax(np.abs(N[:, j]))) if N[i0, j] < 0: N[:, j] = -N[:, j] R = np.hstack([JR, N]) kind = "entry" else: R = np.eye(db) kind = "MODE-EXIT" orth = float(np.max(np.abs(R.T @ R - np.eye(db)))) return R, smin, orth, kind # ------------------------------------------------ run def run(): print("=" * 78) print("SHARPENED-Z1 module 2 -- boundary triple: J_K bulk + " "Gram near-kernel boundary (1e9 comb, X <= %.4f)" % (M_TOP * D)) print("=" * 78) hits = ast_firewall() check("G0.1 AST firewall", not hits, str(hits)) bats, spec_sha = freeze_spec() check("G0.2 battery + ladders + bars + anchors SHA-256-frozen " "BEFORE any comb data is built", 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, M_CAP_DEEP, int(math.exp(M_TOP * D)) + 2, ATOM_MAX_DEEP, RUNTIME_CAP), M_TOP <= M_CAP_DEEP and int(math.exp(M_TOP * D)) + 2 <= ATOM_MAX_DEEP) # ---- combs + towers strictly after the freeze u_deep, mu_deep = build_deep_comb() T_par = build_parent_tower() p, T, c_cont, alpha_top, ka = build_deep_tower(u_deep, mu_deep, T_par) Fb, names = battery_matrix(bats) a_all = np.stack([np.correlate(Fb[:, j], Fb[:, j], "full") [NPAD - 1:] for j in range(Fb.shape[1])]) w_f = a_all[:, 0] * p[0] + 2.0 * (a_all[:, 1:] @ p[1:NPAD]) # ---- CW boundary (frozen random band) rng_cw = np.random.default_rng(SEED_CW) B_cw0 = np.linalg.qr(rng_cw.standard_normal((888, 6)))[0] # ---- CB bulk (frozen GOE draw at top K) rng_cb = np.random.default_rng(SEED_CB) A_cb = rng_cb.standard_normal((M_TOP // 2, M_TOP // 2)) A_cb = A_cb + A_cb.T # ---- main ladder (single pass) lam884 = np.linalg.eigvalsh(T[:884, :884]) counts = {884: int(np.sum(lam884 <= THR_NULL))} gaps = {} q6_med = [] rungs = [] prev_gr, R = None, None trans_events = [] smin_min, orth_max, coup_max, pd_min = np.inf, 0.0, 0.0, np.inf herg_min, antih_max = np.inf, -np.inf ward_solve = ward_sh = 0.0 ward_hd = ward_gw = ward_rec = 0.0 import_smin_min = np.inf kbads = [] for M in LAD: K = M // 2 gr = gram_rung(T, M, want_q6=(M in TOP5W), Fb=Fb) counts[M] = gr["d"] pd_min = min(pd_min, gr["lam_min"]) coup_max = max(coup_max, gr["coup"]) if M in (1096, 1176, 1240): lam = gr["lam"] gaps[("67", M)] = float((lam[6] - lam[5]) / lam[6]) gaps[("78", M)] = float((lam[7] - lam[6]) / lam[7]) if M == 1176: lmin1176 = gr["lam_min"] if M in TOP5W: q6_med.append(gr["q6"]) # transport if prev_gr is None: R = np.eye(gr["d"]) kind = "start" else: R, smin, orth, kind = transport_update(prev_gr, gr, R) smin_min = min(smin_min, smin) orth_max = max(orth_max, orth) if kind == "entry": trans_events.append( (M, prev_gr["d"], gr["d"], float(gr["lam"][gr["d"] - 1]))) prev_gr = gr # bulk aM, gM, kbad = jac.wheeler(p[:M], K) if kbad is not None: kbads.append((M, int(kbad))) continue bJ = aM.copy() aJ = np.sqrt(gM[1:K]) Gc = cheb_gram(p, K) try: L = sla.cholesky(Gc, lower=True, check_finite=False) except np.linalg.LinAlgError: kbads.append((M, -1)) continue if M == M_WARD: frame_ward(p, K, L, aM, gM) if M in WARD_D_RUNGS: rec = jac.gauss_reconstruct(aM, gM, p[0], min(2 * K, M)) ward_rec = max(ward_rec, float( np.max(np.abs(rec - p[:len(rec)])) / np.max(np.abs(p[:len(rec)])))) # import B = gr["Vd"] @ R U = L.T @ B[:K] Uu, s_imp, Vt = np.linalg.svd(U, full_matrices=False) Qh = Uu @ Vt import_smin_min = min(import_smin_min, float(s_imp[-1])) cellmass = float(np.sum(B[:K] ** 2) / np.sum(B ** 2)) # M-function on ZSET Hs, Ss, Fts, rhos = {}, {}, {}, {} for z in ZSET: Y = tri_solve(bJ, aJ, z, Qh) res = float(np.max(np.abs( ((2.0 - z) * Y - (np.diag(bJ) @ Y + np.concatenate( [aJ[:, None] * Y[1:], np.zeros((1, Y.shape[1]), Y.dtype)]) + np.concatenate( [np.zeros((1, Y.shape[1]), Y.dtype), aJ[:, None] * Y[:-1]]))) - Qh))) ward_solve = max(ward_solve, res) H = Qh.T @ Y H = 0.5 * (H + (H.T if not isinstance(z, complex) else H.T)) S = np.linalg.inv(H) ward_sh = max(ward_sh, float(np.max(np.abs( S @ H - np.eye(gr["d"]))))) Ft = f_tilde(gr, R, z) Hs[z], Ss[z], Fts[z] = H, S, Ft rhos[z] = float(np.linalg.norm(S - Ft) / max(np.linalg.norm(Ft), QF_FLOOR)) for z in ZC: ImH = (Hs[z] - Hs[z].conj().T) / 2.0j herg_min = min(herg_min, float(np.min( np.linalg.eigvalsh(ImH)))) ImS = (Ss[z] - Ss[z].conj().T) / 2.0j antih_max = max(antih_max, float(np.max( np.linalg.eigvalsh(ImS)))) if M in WARD_H_RUNGS: xj, Uj = sla.eigh_tridiagonal(bJ, aJ) z0 = ZC[0] QU = Uj.T @ Qh H2 = QU.T @ (QU / (2.0 - z0 - xj)[:, None]) ward_hd = max(ward_hd, float(np.max(np.abs( H2 - Hs[z0])) / np.max(np.abs(H2)))) # trace leg Jf = np.diag(bJ) + np.diag(aJ, 1) + np.diag(aJ, -1) Pq = Qh @ Qh.T Pc = np.eye(K) - Pq JD = Pq @ Jf @ Pq + Pc @ Jf @ Pc xD, UD = np.linalg.eigh(0.5 * (JD + JD.T)) wD = p[0] * UD[0, :] ** 2 om_D = cheb_eval(a_all, xD) @ wD errd = float(np.sum(np.abs(om_D - w_f)) / np.sum(np.abs(w_f))) if M in WARD_D_RUNGS: xg, Ug = sla.eigh_tridiagonal(bJ, aJ) wg = p[0] * Ug[0, :] ** 2 om = cheb_eval(a_all, xg) @ wg ward_gw = max(ward_gw, float(np.max( np.abs(om - w_f) / np.abs(w_f)))) # CB (GOE bulk, same boundary) Hk = A_cb[:K, :K] / math.sqrt(2.0 * K) Ycb = np.linalg.solve((2.0 - Z_CB) * np.eye(K) - Hk, Qh) Scb = np.linalg.inv(Qh.T @ Ycb) rho_cb = float(np.linalg.norm(Scb - Fts[Z_CB]) / np.linalg.norm(Fts[Z_CB])) # CW (random boundary, true bulk) on the d = 6 run + 992 S_cw = rho_cw = None if M in CW_LAD or M == 992: Bcw = np.zeros((M, 6)) Bcw[:888, :] = B_cw0 Ucw = L.T @ Bcw[:K] Uu2, s2, Vt2 = np.linalg.svd(Ucw, full_matrices=False) Qcw = Uu2 @ Vt2 Ycw = tri_solve(bJ, aJ, Z_REF, Qcw) S_cw = np.linalg.inv(Qcw.T @ Ycw) Ft6 = Fts[Z_REF][:6, :6] if gr["d"] > 6 \ else Fts[Z_REF] rho_cw = float(np.linalg.norm(S_cw - Ft6) / np.linalg.norm(Ft6)) rungs.append(dict(M=M, K=K, d=gr["d"], kind=kind, S_ref=Ss[Z_REF].real.copy(), rho=dict(rhos), errd=errd, rho_cb=rho_cb, S_cw=S_cw, rho_cw=rho_cw, s_imp=s_imp.copy(), cellmass=cellmass, eigS=np.sort(np.linalg.eigvalsh( 0.5 * (Ss[Z_REF].real + Ss[Z_REF].real.T))), eigF=np.sort(np.linalg.eigvalsh( 0.5 * (Fts[Z_REF].real + Fts[Z_REF].real.T))))) # ---- construction guards check("G1.6 Wheeler + Cholesky valid on every rung (%d) AND " "Gauss reconstruction %.1e <= %.0e" % (len(LAD), ward_rec, BAR_GAUSS), not kbads and ward_rec <= BAR_GAUSS, str(kbads[:3])) if kbads: print("\nVERDICT: Z1-TRIPLE-INVALID (construction broke)") return 1 check("G1.8 measured Gram PD: lambda_min = %.3e > -%.0e" % (pd_min, PD_TOL), pd_min > -PD_TOL) check("G1.9 coupling Ward max |E_c| = %.1e <= %.0e; transport " "sigma_min = %.6f >= %.0e; orthogonality %.1e <= %.0e" % (coup_max, COUP_WARD, smin_min, SVD_FLOOR, orth_max, WARD_ORTH), coup_max <= COUP_WARD and smin_min >= SVD_FLOOR and orth_max <= WARD_ORTH) check("G1.10 resolvent/Schur Wards: banded residual %.1e <= " "%.0e; S H - I %.1e <= %.0e; dense-H %.1e <= %.0e" % (ward_solve, WARD_SOLVE, ward_sh, WARD_SH, ward_hd, WARD_HDENSE), ward_solve <= WARD_SOLVE and ward_sh <= WARD_SH and ward_hd <= WARD_HDENSE) check("G1.11 Gauss/Weil state identity: max rel dev %.1e <= " "%.0e at rungs %s" % (ward_gw, WARD_GAUSSW, WARD_D_RUNGS), ward_gw <= WARD_GAUSSW) check("G1.12 import health: min sigma_min(U) = %.3e >= %.0e " "(no import collapse)" % (import_smin_min, IMPORT_FLOOR), import_smin_min >= IMPORT_FLOOR) # ---- anchors ok_cnt = all(counts.get(M) == want for M, want in REPRO_COUNTS.items()) check("G1.5a source entry anchors: counts %s == frozen" % {M: counts.get(M) for M in sorted(REPRO_COUNTS)}, ok_cnt) ok_gap = all(abs(gaps[k] - v) <= REPRO_TOLG for k, v in REPRO_GAPS.items() if k in gaps) check("G1.5b gap anchors: %s vs frozen %s (tol %.0e); " "lambda_min(1176) = %.4e (tol %.0e)" % ({k: round(gaps[k], 4) for k in sorted(gaps)}, sorted(REPRO_GAPS.items()), REPRO_TOLG, lmin1176, REPRO_LTOL), ok_gap and abs(lmin1176 - REPRO_LMIN1176) <= REPRO_LTOL) med_q6 = np.median(np.stack(q6_med), axis=0) dev_q = max(abs(float(med_q6[j]) - DRAIN_LEVELS[nm]) for j, nm in enumerate(names) if nm in DRAIN_LEVELS) check("G1.5c drainage-level anchors: worst dev %.1e <= %.0e" % (dev_q, REPRO_QTOL), dev_q <= REPRO_QTOL) trans_rungs = tuple(t[0] for t in trans_events) check("G1.5d measured transition set %s == frozen E_TEST %s " "(entering eigenvalues %s)" % (trans_rungs, E_TEST, ["%.4e" % t[3] for t in trans_events]), trans_rungs == E_TEST) # ---- gate (a) Herglotz a_ok = gate("(a) HERGLOTZ: min eig Im H = %+.3e >= -%.0e over " "all rungs x both complex z (anti-Herglotz Ward " "max eig Im S = %+.3e)" % (herg_min, HERG_FLOOR, antih_max), herg_min >= -HERG_FLOOR) a_dead = herg_min < -HERG_DEAD # ---- gate (b) delivery print("\n-- (b) qf-block delivery: rho_b(X) = ||S - F~||_F / " "||F~||_F at Z_REF = %g (both in transported reference " "coordinates)" % Z_REF) rmap = {r["M"]: r for r in rungs} print(" rho_b profile (every 8th rung): %s" % " ".join("M=%d:%.3f" % (r["M"], r["rho"][Z_REF]) for r in rungs[::8])) zt = rungs[-1] print(" z-profile at top rung M = %d (d = %d): %s" % (zt["M"], zt["d"], " ".join("z=%s:%.4f" % (z, zt["rho"][z]) for z in ZSET))) gb = rmap[GATE_BLOCK[-1]] print(" eig S(Z_REF) top gate rung M = %d: %s" % (gb["M"], "/".join("%.4f" % v for v in gb["eigS"]))) print(" eig F~(Z_REF) same rung: %s" % "/".join("%.4f" % v for v in gb["eigF"])) print(" import health on GATE_BLOCK: sigma_min(U) %s; " "cell-mass %s" % ("/".join("%.3f" % rmap[M]["s_imp"][-1] for M in GATE_BLOCK), "/".join("%.3f" % rmap[M]["cellmass"] for M in GATE_BLOCK))) b_med = float(np.median([rmap[M]["rho"][Z_REF] for M in GATE_BLOCK])) tail9 = [r for r in rungs if r["d"] == 9] if tail9: print(" d = 9 frontier tail (reported, unadjudicated): " "rho_b = %s" % "/".join("%.3f" % r["rho"][Z_REF] for r in tail9)) b_ok = gate("(b) QF-BLOCK DELIVERY: med%d over %s of rho_b = " "%.4f <= %g (structural-fail bar %g)" % (N_MED, GATE_BLOCK, b_med, B_MATCH, B_DEAD), b_med <= B_MATCH) b_dead = (b_med > B_DEAD) or (import_smin_min < IMPORT_FLOOR) # ---- gate (c) cell response print("\n-- (c) cell structure: relative S(Z_REF) increments " "(cocycle normalizer), contrast at E_TEST = %s" % (E_TEST,)) rels_in, rels_e = [], {} for ra, rb in zip(rungs, rungs[1:]): Sa, Sb = ra["S_ref"], rb["S_ref"] if rb["kind"] == "entry": d0 = Sa.shape[0] dlt = float(np.max(np.abs(Sb[:d0, :d0] - Sa))) nrm = max(np.max(np.abs(Sa)), np.max(np.abs(Sb[:d0, :d0]))) rels_e[rb["M"]] = dlt / max(nrm, QF_FLOOR) elif Sa.shape == Sb.shape: dlt = float(np.max(np.abs(Sb - Sa))) nrm = max(np.max(np.abs(Sa)), np.max(np.abs(Sb))) rels_in.append((rb["M"], dlt / max(nrm, QF_FLOOR))) med_in = float(np.median([v for _m, v in rels_in])) rhos_e = {e: rels_e[e] / med_in for e in rels_e} top5 = sorted(rels_in, key=lambda t: -t[1])[:5] print(" within-run increments: median rel = %.4e over %d; " "top-5: %s" % (med_in, len(rels_in), " ".join("M=%d:%.3e" % t for t in top5))) print(" entry increments: %s" % " ".join("M=%d: rel %.3e (rho %.2f)" % (e, rels_e[e], rhos_e[e]) for e in sorted(rels_e))) min_rho = min(rhos_e.values()) if rhos_e else 0.0 min_rel_e = min(rels_e.values()) if rels_e else np.inf n_over = sum(1 for _m, v in rels_in if v >= min_rel_e) c_ok = gate("(c) CELL RESPONSE: min entry contrast rho = %.2f " ">= %g AND non-transition increments reaching it " "= %d <= %d" % (min_rho, C_RESP, n_over, C_UNIQ), min_rho >= C_RESP and n_over <= C_UNIQ) # ---- gate (d) trace precursor print("\n-- (d) trace-formula precursor: decoupled pair vs " "deployed Weil evaluation (battery-summed)") errs = [(r["M"] * D, r["errd"]) for r in rungs] print(" err_d profile (every 8th rung): %s" % " ".join("M=%d:%.2e" % (r["M"], r["errd"]) for r in rungs[::8])) d_med = float(np.median([rmap[M]["errd"] for M in GATE_BLOCK])) rows = [dict(XmR=x, mx=v) for x, v in errs if int(round(x / D)) in [r["M"] for r in rungs] and x >= HALF2[0] * D] b_tr, _res = hbp.fit_rate(rows) d_ok = gate("(d) TRACE PRECURSOR: med%d(GATE_BLOCK) err_d = " "%.3e <= %g AND second-half trend b = %+.3f/X >= " "%g (b > 0 = falling)" % (N_MED, d_med, D_LEVEL, b_tr, D_SLOPE_MIN), d_med <= D_LEVEL and b_tr >= D_SLOPE_MIN) # ---- controls print("\n-- controls") kb_cs = [] rng = np.random.default_rng(SEED_CS) pos = np.sort(rng.uniform(0.5, 2.0 * alpha_top, ka)) cat_s, _dd = core.atom_lags_at(alpha_top, M_TOP, pos, mu_deep[:ka]) pcs = c_cont + cat_s for M in CTRL_LAD_CS: _a, _g, kb = jac.wheeler(pcs[:M], M // 2) if kb is not None: kb_cs.append((M, int(kb))) check("CS scramble control fires: Wheeler breakdown on %d/%d " "rungs (first kbad %s)" % (len(kb_cs), len(CTRL_LAD_CS), kb_cs[0] if kb_cs else "--"), len(kb_cs) == len(CTRL_LAD_CS)) 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] catE, _dd = core.atom_lags_at(0.5 * EP_MMAX * D, EP_MMAX, np.log(supp.astype(float)), 2.0 * lamE[supp] / np.sqrt(supp.astype(float))) pce = srp.continuum_lags(EP_MMAX) + catE kb_ce = [] for M in CTRL_LAD_CE: _a, _g, kb = jac.wheeler(pce[:M], M // 2) if kb is not None: kb_ce.append((M, int(kb))) check("CE Epstein control fires: Wheeler breakdown on %d/%d " "rungs (first kbad %s)" % (len(kb_ce), len(CTRL_LAD_CE), kb_ce[0] if kb_ce else "--"), len(kb_ce) == len(CTRL_LAD_CE)) cb_med = float(np.median([rmap[M]["rho_cb"] for M in GATE_BLOCK])) check("CB GOE-bulk control fires: med%d rho_b^goe = %.2f > %g " "at z = %g (generic bulk does not deliver)" % (N_MED, cb_med, B_MATCH, Z_CB), cb_med > B_MATCH) cw_rungs = [r for r in rungs if r["M"] in CW_LAD and r["rho_cw"] is not None] cw_last5 = [r["rho_cw"] for r in cw_rungs[-5:]] cw_med = float(np.median(cw_last5)) cw_pairs = [(ra, rb) for ra, rb in zip(cw_rungs, cw_rungs[1:])] cw_rels = [] for ra, rb in cw_pairs: dlt = float(np.max(np.abs(rb["S_cw"] - ra["S_cw"]))) nrm = max(np.max(np.abs(ra["S_cw"])), np.max(np.abs(rb["S_cw"]))) cw_rels.append(dlt / max(nrm, QF_FLOOR)) r992 = rmap.get(992) r988 = rmap.get(988) dlt992 = float(np.max(np.abs(r992["S_cw"] - r988["S_cw"]))) nrm992 = max(np.max(np.abs(r992["S_cw"])), np.max(np.abs(r988["S_cw"]))) cw_contrast = (dlt992 / max(nrm992, QF_FLOOR)) \ / max(float(np.median(cw_rels)), QF_FLOOR) check("CW wrong-boundary control fires: med%d rho_b^cw = %.2f " "> %g AND contrast at 992 = %.2f < %g" % (N_MED, cw_med, B_MATCH, cw_contrast, C_RESP), cw_med > B_MATCH and cw_contrast < C_RESP) dt = time.time() - T_START check("G0.4 runtime %.1f s <= predeclared 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", "CB", "CW"))) controls_ok = all(ok for (n, ok) in CHECKS if n.startswith(("CS", "CE", "CB", "CW"))) sigs = dict(a=a_ok, b=b_ok, c=c_ok, d=d_ok) if not (guards_ok and controls_ok): verdict = "Z1-TRIPLE-INVALID" elif a_dead or b_dead: verdict = "Z1-TRIPLE-DEAD" elif all(sigs.values()): verdict = "Z1-TRIPLE-CARRIES" else: verdict = "Z1-TRIPLE-PARTIAL" n_chk = sum(1 for (_n, ok) in CHECKS if ok) print("\nVERDICT: %s" % verdict) print("GATES %d/4 (a=%s b=%s c=%s d=%s), GUARDS+CONTROLS " "%d/%d, runtime %.1f s" % (sum(sigs.values()), *["P" if sigs[k] else "F" for k in "abcd"], n_chk, len(CHECKS), time.time() - T_START)) if verdict == "Z1-TRIPLE-CARRIES": print("CONSEQUENCE (stated plainly): the sharpened Z1 " "object exists at finite level -- Herglotz triple, " "qf-block delivery, cell structure, Weil tracking. " "A proof-grade Z1 still needs the continuum triple " "with self-adjointness, the z -> 0 Nevanlinna " "boundary limit, and the relative trace formula at " "theorem level. NO RH claim.") elif verdict == "Z1-TRIPLE-DEAD": print("CONSEQUENCE (stated plainly): the sharpened Z1 form " "is wrong as constructed (Herglotz or delivery " "fails structurally); the failure anatomy above " "types what must change. NO RH claim.") else: print("CONSEQUENCE (stated plainly): the triple carries " "the legs %s and misses %s; the failing legs name " "the structure the next module must add. NO RH " "claim." % ([k for k in "abcd" if sigs[k]], [k for k in "abcd" if not sigs[k]])) return 0 if (guards_ok and controls_ok) else 1 return run(), list(CHECKS), list(GATES) def _run_part3(): # PART 3 -- z1_variable_edge_mfunction_probe.py (verbatim; module- # level names local to this function scope; imports remapped) 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__)) _HERE_DISC = os.path.abspath(os.path.join(_HERE, "..", "experiments", "tfpt-discovery")) sys.path.insert(0, _HERE) sys.path.insert(0, _HERE_DISC) import v563_paper2_readouts as core # noqa: E402 import v696_z1_jacobi as jac # 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 T_START = time.time() # ------------------------------------------------ frozen specification D = srp.DGRID ATOM_MAX_DEEP = 1000000000 M_CAP_DEEP = int(math.floor(math.log(ATOM_MAX_DEEP) / D)) M_TOP = 1300 M_PAR = 824 LAD = list(range(888, 1301, 4)) E_TEST = (992, 1108, 1276) GATE_BLOCK = list(range(1256, 1273, 4)) TOP5W = list(range(1160, 1177, 4)) FIRST5 = LAD[:5] LAST5 = LAD[-5:] LAST10 = LAD[-10:] M_WARD = 888 WARD_H_RUNGS = (888, 1272) THR_NULL = 1.0e-4 GAMMA1 = 14.10 # v718 pole-band threshold E_CUT = 2.0 - 2.0 * math.cos(D * GAMMA1) H_IM = 1.0e-2 ZSET = (-1.0e-1, -1.0e-2, -1.0e-3, complex(0.0, H_IM), complex(-1.0e-3, H_IM)) Z_REF = -1.0e-2 ZC = ZSET[3:] Z_CB = -1.0e-1 RE_GRID = (-0.5, -0.25, 0.0, 0.25, 0.5) IM_GRID = (1.0e-3, 1.0e-2, 1.0e-1, 1.0) IM_GATE_MIN = 1.0e-2 # gated sub-grid rows B_MATCH = 0.25 B_DEAD = 10.0 RANK1_BAR = 0.75 PSD_TOL_REL = 1.0e-6 MASS_BAR = 1.0 ENTRY_GROWTH_BAR = 10.0 CBND_RATIO = 2.0 CDER_RATIO = 2.0 CL_BAR = 0.2 C_RESP = 3.0 C_UNIQ = 1 N_MED = 5 NPAD = 128 R_BAT = (1.0, 2.0) QF_FLOOR = 1.0e-12 MOM_KS = (0, 1, 2) IMPORT_FLOOR = 1.0e-8 SVD_FLOOR = 1.0e-8 WARD_ORTH = 1.0e-10 COUP_WARD = 1.0e-8 WARD_FRAME = 1.0e-3 WARD_POLE = 1.0e-9 WARD_FESH = 1.0e-8 WARD_COMPL = 1.0e-10 HERG_FLOOR = 1.0e-8 BAR_GAUSS = 1.0e-8 PD_TOL = 1.0e-9 COMB_DEV_BAR = 1.0e-12 PREFIX_WARD = 1.0e-12 RUNTIME_CAP = 1800.0 REPRO_COUNTS = {884: 5, 888: 6, 988: 6, 992: 7, 1104: 7, 1108: 8, 1272: 8, 1276: 9} REPRO_GAPS = {("67", 1096): 0.1008, ("67", 1176): 0.1397, ("78", 1176): 0.0613, ("78", 1240): 0.0039} REPRO_TOLG = 2.0e-4 REPRO_LMIN1176 = 3.882e-6 REPRO_LTOL = 2.0e-8 DRAIN_LEVELS = { "R2:box[0,R]": 0.3583, "R2:box[R/2,R]": 0.3370, "R2:hat(R/2,R/2)": 0.3127, "R2:hat(3R/4,R/4)": 0.2590, "R2:box[R/4,3R/4]": 0.2249, "R1:box[R/2,R]": 0.0793, "R1:box[0,R]": 0.0741, "R2:box[0,R/2]": 0.0741, "R1:hat(R/4,R/4)": 0.0082} REPRO_QTOL = 2.0e-3 SEED_CS = 7 SEED_CB = 11 SEED_CW = 20260805 CTRL_LAD_CS = list(range(888, 1301, 48)) EP_NCAP = 34000 EP_MMAX = 640 CTRL_LAD_CE = list(range(400, 641, 8)) CW_LAD = list(range(888, 989, 4)) 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(): bats = {} hsh = hashlib.sha256() hsh.update(("z1-variable-edge spec: shared spine parent-verbatim " "(D=%.10f cap %d M_TOP %d LAD %s band %g cocycle " "transport, RAW import U=L^T B[:K], no polar); " "CAND A: H=U^T(A-z)^-1 U vs Fref=P^1/2 Hgram P^1/2, " "rho_A at Z_REF=%g; CAND B: resolvent intertwining " "rho_B eps=%g; trigger: B iff med%d rho_A over %s > " "%g; poles: E_CUT=%.6f (GAMMA1=%g), Pi=sum_{a<=cut} " "ww^T, R_e = Pi(e)-pad(Pi(prev)) at E_TEST=%s; " "gates: P1 psd %g rank1 %g; P2 mass %g growth %g " "KILL c_mass(top)>%g; B1 grid %s x %s gate Im>=%g " "ratio %g; B2 deriv ratio %g; CL last10 osc med <= " "%g over 14f x k=%s; DEL bar %g dead %g; CR resp %g " "uniq %d (reported); anchors counts %s gaps %s tol " "%g lmin %g tol %g drain %s tol %g; wards pole %g " "fesh %g compl %g herg %g frame %g coup %g orth %g " "svd %g gauss %g import %g pd %g comb %g prefix %g " "runtime %g; controls CS %d %s CE %d %d %s CB %d " "z=%g fire>%g CW %d %s fire>%g and<%g; verdict " "order: invalid -> DEAD(P2kill or B1fail or both>" "%g) -> CARRIES(DEL P1 P2 B1 B2 CL) -> PARTIAL" % (D, ATOM_MAX_DEEP, M_TOP, LAD, THR_NULL, Z_REF, -Z_REF, N_MED, GATE_BLOCK, B_MATCH, E_CUT, GAMMA1, E_TEST, PSD_TOL_REL, RANK1_BAR, MASS_BAR, ENTRY_GROWTH_BAR, MASS_BAR, RE_GRID, IM_GRID, IM_GATE_MIN, CBND_RATIO, CDER_RATIO, CL_BAR, MOM_KS, B_MATCH, B_DEAD, C_RESP, C_UNIQ, sorted(REPRO_COUNTS.items()), sorted(REPRO_GAPS.items()), REPRO_TOLG, REPRO_LMIN1176, REPRO_LTOL, sorted(DRAIN_LEVELS.items()), REPRO_QTOL, WARD_POLE, WARD_FESH, WARD_COMPL, HERG_FLOOR, WARD_FRAME, COUP_WARD, WARD_ORTH, SVD_FLOOR, BAR_GAUSS, IMPORT_FLOOR, PD_TOL, COMB_DEV_BAR, PREFIX_WARD, RUNTIME_CAP, SEED_CS, CTRL_LAD_CS, EP_NCAP, EP_MMAX, CTRL_LAD_CE, SEED_CB, Z_CB, B_MATCH, SEED_CW, CW_LAD, B_MATCH, C_RESP, B_DEAD)).encode()) for R in R_BAT: bats[R] = hbp.battery(R) for nm, v in bats[R]: hsh.update(nm.encode()) hsh.update(v.tobytes()) return bats, hsh.hexdigest() def battery_matrix(bats): cols, names = [], [] for R in R_BAT: nR = int(round(R / D)) for nm, v in bats[R]: f = np.zeros(NPAD) f[:nR] = v cols.append(f) names.append("R%g:%s" % (R, nm)) return np.stack(cols, axis=1), names # ------------------------------------------------ towers (verbatim) def build_parent_tower(): alpha = 0.5 * M_PAR * D ka, masks, dev_m = srp.channel_masks(alpha) check("G1.3 parent tower comb consistency (rel dev <= %.0e)" % COMB_DEV_BAR, dev_m <= COMB_DEV_BAR, "rel dev %.1e, ka=%d" % (dev_m, ka)) c = srp.continuum_lags(M_PAR) for cnl in ("ro", "re", "sp", "in"): c = c + srp.atom_channel_lags(alpha, M_PAR, masks[cnl]) return sla.toeplitz(c[:M_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 EXACT on [0, %d]" % 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 * D ka = int(np.searchsorted(u_deep, 2.0 * alpha + 1.0e-14, side="right")) c_cont = srp.continuum_lags(M_TOP) c_at, _dd = core.atom_lags_at(alpha, M_TOP, u_deep[:ka], mu_deep[:ka]) p = c_cont + c_at T = sla.toeplitz(p[:M_TOP]) dev = float(np.max(np.abs(T[:M_PAR, :M_PAR] - T_par))) check("G1.4 prefix Ward: dev %.1e <= %.0e" % (dev, PREFIX_WARD), dev <= PREFIX_WARD) print(" deep census: ka = %d atoms to e^%.4f" % (ka, 2 * alpha)) return p, T, c_cont, alpha, ka def cheb_gram(p, K): idx = np.arange(K) return 0.5 * (p[np.abs(idx[:, None] - idx[None, :])] + p[idx[:, None] + idx[None, :]]) def frame_ward(p, K, L, aM, gM): Gx = cheb_gram(p, K + 1) A = np.zeros((K, K)) A[:, 0] = 2.0 * Gx[:K, 1] for k in range(1, K): A[:, k] = Gx[:K, k + 1] + Gx[:K, k - 1] A = 0.5 * (A + A.T) Y = sla.solve_triangular(L, A, lower=True, check_finite=False) J = sla.solve_triangular(L, Y.T, lower=True, check_finite=False).T J = 0.5 * (J + J.T) Jw = np.diag(aM) + np.diag(np.sqrt(gM[1:K]), 1) \ + np.diag(np.sqrt(gM[1:K]), -1) dev = float(np.max(np.abs(J - Jw))) check("G1.7 GNS frame Ward at M = %d: dev %.1e <= %.0e" % (M_WARD, dev, WARD_FRAME), dev <= WARD_FRAME) def tri_solve(bJ, aJ, z, Bmat): K = len(bJ) dt = complex if isinstance(z, complex) else float ab = np.zeros((3, K), dtype=dt) ab[0, 1:] = -aJ ab[1, :] = (2.0 - z) - bJ ab[2, :-1] = -aJ return sla.solve_banded((1, 1), ab, Bmat.astype(dt)) def gram_rung(T, M, Fb): lam, V = np.linalg.eigh(T[:M, :M]) d = int(np.sum(lam <= THR_NULL)) Vd = qsb.sign_fix(V[:, :d]) Ec = V[:, d:].T @ (T[:M, :M] @ Vd) out = dict(M=M, lam=lam[:16].copy(), lam_min=float(lam[0]), d=d, Vd=Vd, coup=float(np.max(np.abs(Ec))), lam_rest=lam[d:], Ec=Ec) if M in TOP5W: out["q6"] = np.sum((V[:NPAD, :6].T @ Fb) ** 2, axis=0) return out def transport_update(prev, gr, R_prev): Ma = prev["M"] da, db = prev["d"], gr["d"] S_ov = gr["Vd"][:Ma, :].T @ prev["Vd"] Uu, s, Vt = np.linalg.svd(S_ov, full_matrices=False) smin = float(s[-1]) if db == da: R = (Uu @ Vt) @ R_prev kind = "link" elif db > da: Jiso = Uu @ Vt JR = Jiso @ R_prev Qf, _ = np.linalg.qr(JR, mode="complete") N = Qf[:, da:] for j in range(N.shape[1]): i0 = int(np.argmax(np.abs(N[:, j]))) if N[i0, j] < 0: N[:, j] = -N[:, j] R = np.hstack([JR, N]) kind = "entry" else: R = np.eye(db) kind = "MODE-EXIT" orth = float(np.max(np.abs(R.T @ R - np.eye(db)))) return R, smin, orth, kind def h_gram(gr, R, z): d = gr["d"] return R.T @ np.diag(1.0 / (gr["lam"][:d] - z)) @ R def f_feshbach(gr, R, z): d = gr["d"] C = gr["Ec"].T @ (gr["Ec"] / (gr["lam_rest"][:, None] - z)) return R.T @ (np.diag(gr["lam"][:d]) - z * np.eye(d) - C) @ R def psqrt(P): w, Vp = np.linalg.eigh(P) w = np.maximum(w, 0.0) return (Vp * np.sqrt(w)) @ Vp.T def specnorm(Mz): return float(np.linalg.norm(Mz, 2)) def run(): print("=" * 78) print("SHARPENED-Z1 module 3 -- variable-edge M-function, " "mu-weighted import (A) / intertwining (B), entry poles, " "Herglotz compactness, moment clusters") print("=" * 78) hits = ast_firewall() check("G0.1 AST firewall", not hits, str(hits)) bats, spec_sha = freeze_spec() check("G0.2 spec SHA-256-frozen BEFORE any comb data", True, "SHA256 %s..." % spec_sha[:16]) check("G0.3 reach: M_TOP %d <= %d, cover %d <= %d, E_CUT = " "%.6f" % (M_TOP, M_CAP_DEEP, int(math.exp(M_TOP * D)) + 2, ATOM_MAX_DEEP, E_CUT), M_TOP <= M_CAP_DEEP and int(math.exp(M_TOP * D)) + 2 <= ATOM_MAX_DEEP) u_deep, mu_deep = build_deep_comb() T_par = build_parent_tower() p, T, c_cont, alpha_top, ka = build_deep_tower(u_deep, mu_deep, T_par) Fb, names = battery_matrix(bats) rng_cw = np.random.default_rng(SEED_CW) B_cw0 = np.linalg.qr(rng_cw.standard_normal((888, 6)))[0] rng_cb = np.random.default_rng(SEED_CB) A_cb = rng_cb.standard_normal((M_TOP // 2, M_TOP // 2)) A_cb = A_cb + A_cb.T lam884 = np.linalg.eigvalsh(T[:884, :884]) counts = {884: int(np.sum(lam884 <= THR_NULL))} gaps = {} lmin1176 = None q6_med = [] rungs = [] prev_gr, R = None, None trans_events = [] smin_min, orth_max, coup_max, pd_min = np.inf, 0.0, 0.0, np.inf herg_min = np.inf ward_pole = ward_fesh = ward_compl = ward_rec = 0.0 import_smin_min = np.inf kbads = [] Pi_prev = None for M in LAD: K = M // 2 gr = gram_rung(T, M, Fb) counts[M] = gr["d"] pd_min = min(pd_min, gr["lam_min"]) coup_max = max(coup_max, gr["coup"]) if M in (1096, 1176, 1240): lam = gr["lam"] gaps[("67", M)] = float((lam[6] - lam[5]) / lam[6]) gaps[("78", M)] = float((lam[7] - lam[6]) / lam[7]) if M == 1176: lmin1176 = gr["lam_min"] if "q6" in gr: q6_med.append(gr["q6"]) if prev_gr is None: R = np.eye(gr["d"]) kind = "start" else: R, smin, orth, kind = transport_update(prev_gr, gr, R) smin_min = min(smin_min, smin) orth_max = max(orth_max, orth) if kind == "entry": trans_events.append((M, prev_gr["d"], gr["d"], float(gr["lam"][gr["d"] - 1]))) prev_gr = gr aM, gM, kbad = jac.wheeler(p[:M], K) if kbad is not None: kbads.append((M, int(kbad))) continue bJ = aM.copy() aJ = np.sqrt(gM[1:K]) Gc = cheb_gram(p, K) try: L = sla.cholesky(Gc, lower=True, check_finite=False) except np.linalg.LinAlgError: kbads.append((M, -1)) continue if M == M_WARD: frame_ward(p, K, L, aM, gM) if M in WARD_H_RUNGS: rec = jac.gauss_reconstruct(aM, gM, p[0], min(2 * K, M)) ward_rec = max(ward_rec, float( np.max(np.abs(rec - p[:len(rec)])) / np.max(np.abs(p[:len(rec)])))) # raw import (no whitening anywhere) B = gr["Vd"] @ R U = L.T @ B[:K] s_imp = np.linalg.svd(U, compute_uv=False) import_smin_min = min(import_smin_min, float(s_imp[-1])) P = U.T @ U Ph = psqrt(P) trP = float(np.trace(P)) # exact pole decomposition of the bulk pair xj, Vj = sla.eigh_tridiagonal(bJ, aJ) a_n = 2.0 - xj # A-eigenvalues W = U.T @ Vj # d x K residue vectors idx_pole = a_n <= E_CUT n_pole = int(np.sum(idx_pole)) Pi = W[:, idx_pole] @ W[:, idx_pole].T Wreg = W[:, ~idx_pole] areg = a_n[~idx_pole] ward_compl = max(ward_compl, float( np.max(np.abs(W @ W.T - P)) / max(np.max(np.abs(P)), QF_FLOOR))) def h_raw(z): return (W / (a_n - z)[None, :]) @ W.conj().T \ if isinstance(z, complex) else \ (W / (a_n - z)[None, :]) @ W.T # candidate A delivery + wards Hs = {z: h_raw(z) for z in ZSET} if M in WARD_H_RUNGS: Y = tri_solve(bJ, aJ, Z_REF, U) Hsolve = U.T @ Y ward_pole = max(ward_pole, float( np.max(np.abs(Hsolve - Hs[Z_REF])) / np.max(np.abs(Hsolve)))) Hg = h_gram(gr, R, Z_REF) Ff = f_feshbach(gr, R, Z_REF) ward_fesh = max(ward_fesh, float( np.max(np.abs(Ff @ Hg - np.eye(gr["d"]))))) for z in ZC: ImH = (Hs[z] - Hs[z].conj().T) / 2.0j herg_min = min(herg_min, float(np.min( np.linalg.eigvalsh(ImH)))) Fref = Ph @ h_gram(gr, R, Z_REF) @ Ph rho_a = float(np.linalg.norm(Hs[Z_REF].real - Fref) / max(np.linalg.norm(Fref), QF_FLOOR)) # candidate B (resolvent intertwining, frozen fallback) eps = -Z_REF lamd = gr["lam"][:gr["d"]] Yb = tri_solve(bJ, aJ, Z_REF, U) # (A+eps)^-1 U UB = U / (lamd + eps)[None, :] rho_b = float(np.linalg.norm(Yb - UB) / max(np.linalg.norm(UB), QF_FLOOR)) # entry residues R_e = None if kind == "entry": d0 = Pi_prev.shape[0] pad = np.zeros_like(Pi) pad[:d0, :d0] = Pi_prev R_e = Pi - pad dPi_run = None if kind == "link" and Pi_prev is not None \ and Pi_prev.shape == Pi.shape: dPi_run = float(np.linalg.norm(Pi - Pi_prev)) Pi_prev = Pi.copy() # compactness grid + moments on the regular part Cgrid, Cgrid_lo, Dgrid = 0.0, 0.0, 0.0 for re_z in RE_GRID: for im_z in IM_GRID: z = complex(re_z, im_z) Mt = (Wreg / (areg - z)[None, :]) @ Wreg.conj().T Mtp = (Wreg / (areg - z)[None, :] ** 2) \ @ Wreg.conj().T nz = specnorm(Mt) if im_z >= IM_GATE_MIN: Cgrid = max(Cgrid, nz) Dgrid = max(Dgrid, specnorm(Mtp)) else: Cgrid_lo = max(Cgrid_lo, nz) cf = B[:NPAD].T @ Fb # d x 14 moms = {} for kmom in MOM_KS: Om = (Wreg * (areg ** kmom)[None, :]) @ Wreg.T moms[kmom] = np.einsum("df,de,ef->f", cf, Om, cf) # controls per rung Hk = A_cb[:K, :K] / math.sqrt(2.0 * K) Ycb = np.linalg.solve((2.0 - Z_CB) * np.eye(K) - Hk, U) Fref_cb = Ph @ h_gram(gr, R, Z_CB) @ Ph rho_cb = float(np.linalg.norm(U.T @ Ycb - Fref_cb) / max(np.linalg.norm(Fref_cb), QF_FLOOR)) H_cw = rho_cw = None if M in CW_LAD or M == 992: Bcw = np.zeros((M, 6)) Bcw[:888, :] = B_cw0 Ucw = L.T @ Bcw[:K] Pcw = Ucw.T @ Ucw Ycw = tri_solve(bJ, aJ, Z_REF, Ucw) H_cw = Ucw.T @ Ycw Hg6 = h_gram(gr, R, Z_REF)[:6, :6] if gr["d"] > 6 \ else h_gram(gr, R, Z_REF) Pcwh = psqrt(Pcw) Fref_cw = Pcwh @ Hg6 @ Pcwh rho_cw = float(np.linalg.norm(H_cw - Fref_cw) / max(np.linalg.norm(Fref_cw), QF_FLOOR)) rungs.append(dict( M=M, K=K, d=gr["d"], kind=kind, trP=trP, trPi=float(np.trace(Pi)), n_pole=n_pole, s_imp=s_imp.copy(), rho_a=rho_a, rho_b=rho_b, R_e=R_e, dPi_run=dPi_run, Cgrid=Cgrid, Cgrid_lo=Cgrid_lo, Dgrid=Dgrid, moms=moms, Href=Hs[Z_REF].real.copy(), rho_cb=rho_cb, H_cw=H_cw, rho_cw=rho_cw, lam_entry=float(gr["lam"][gr["d"] - 1]))) # ---- guards check("G1.6 Wheeler + Cholesky valid on all %d rungs AND Gauss " "recon %.1e <= %.0e" % (len(LAD), ward_rec, BAR_GAUSS), not kbads and ward_rec <= BAR_GAUSS, str(kbads[:3])) if kbads: print("\nVERDICT: Z1-VAREDGE-INVALID (construction broke)") return 1 check("G1.8 Gram PD lambda_min = %.3e > -%.0e" % (pd_min, PD_TOL), pd_min > -PD_TOL) check("G1.9 coupling %.1e <= %.0e; transport sigma_min %.4f >= " "%.0e; orth %.1e <= %.0e" % (coup_max, COUP_WARD, smin_min, SVD_FLOOR, orth_max, WARD_ORTH), coup_max <= COUP_WARD and smin_min >= SVD_FLOOR and orth_max <= WARD_ORTH) check("G1.10 pole-decomposition Ward %.1e <= %.0e; Feshbach " "inversion Ward %.1e <= %.0e; residue completeness %.1e " "<= %.0e" % (ward_pole, WARD_POLE, ward_fesh, WARD_FESH, ward_compl, WARD_COMPL), ward_pole <= WARD_POLE and ward_fesh <= WARD_FESH and ward_compl <= WARD_COMPL) check("G1.11 Herglotz guard: min eig Im H = %+.3e >= -%.0e" % (herg_min, HERG_FLOOR), herg_min >= -HERG_FLOOR) check("G1.12 import floor: min sigma_min(U) = %.3e >= %.0e" % (import_smin_min, IMPORT_FLOOR), import_smin_min >= IMPORT_FLOOR) ok_cnt = all(counts.get(M) == want for M, want in REPRO_COUNTS.items()) check("G1.5a entry anchors %s == frozen" % {M: counts.get(M) for M in sorted(REPRO_COUNTS)}, ok_cnt) ok_gap = all(abs(gaps[k] - v) <= REPRO_TOLG for k, v in REPRO_GAPS.items() if k in gaps) check("G1.5b gap anchors ok; lambda_min(1176) = %.4e" % lmin1176, ok_gap and abs(lmin1176 - REPRO_LMIN1176) <= REPRO_LTOL) med_q6 = np.median(np.stack(q6_med), axis=0) dev_q = max(abs(float(med_q6[j]) - DRAIN_LEVELS[nm]) for j, nm in enumerate(names) if nm in DRAIN_LEVELS) check("G1.5c drainage anchors (anchor-only, declared): worst " "dev %.1e <= %.0e" % (dev_q, REPRO_QTOL), dev_q <= REPRO_QTOL) trans_rungs = tuple(t[0] for t in trans_events) check("G1.5d transitions %s == E_TEST %s (entering %s)" % (trans_rungs, E_TEST, ["%.4e" % t[3] for t in trans_events]), trans_rungs == E_TEST) rmap = {r["M"]: r for r in rungs} # ---- A/B decision trail + delivery gate print("\n-- delivery re-test (A primary, B on trigger)") a_med = float(np.median([rmap[M]["rho_a"] for M in GATE_BLOCK])) b_med = float(np.median([rmap[M]["rho_b"] for M in GATE_BLOCK])) print(" rho_A profile (every 8th): %s" % " ".join("M=%d:%.3f" % (r["M"], r["rho_a"]) for r in rungs[::8])) print(" rho_B profile (every 8th): %s" % " ".join("M=%d:%.3f" % (r["M"], r["rho_b"]) for r in rungs[::8])) print(" P spectrum at top gate rung M = %d (squared mu-norms " "of the raw band import): %s" % (GATE_BLOCK[-1], "/".join("%.2e" % (s ** 2) for s in rmap[GATE_BLOCK[-1]]["s_imp"]))) if a_med <= B_MATCH: which, del_med = "A", a_med print(" TRIGGER: rho_A med%d = %.4f <= %g -> Candidate A " "adjudicated (B reported only)" % (N_MED, a_med, B_MATCH)) else: which, del_med = "B", b_med print(" TRIGGER: rho_A med%d = %.4f > %g -> switch, " "Candidate B adjudicated" % (N_MED, a_med, B_MATCH)) del_ok = gate("(DEL) delivery via Candidate %s: med%d = %.4f " "<= %g (A = %.4f, B = %.4f; dead-grade both > %g)" % (which, N_MED, del_med, B_MATCH, a_med, b_med, B_DEAD), del_med <= B_MATCH) del_dead = (a_med > B_DEAD) and (b_med > B_DEAD) # ---- entry-pole gates print("\n-- entry-pole isolation (E_CUT = %.4f, GAMMA1 = %g)" % (E_CUT, GAMMA1)) entry_rows = [] for e in E_TEST: r = rmap[e] Re = r["R_e"] sv = np.linalg.svd(Re, compute_uv=False) mineig = float(np.min(np.linalg.eigvalsh( 0.5 * (Re + Re.T)))) rk = float(sv[0] / max(np.sum(sv), QF_FLOOR)) entry_rows.append((e, r["lam_entry"], r["n_pole"], float(np.linalg.norm(Re)), rk, mineig)) print(" entry M=%d: lam_gram=%.4e, n_pole(bulk<=cut)=%d, " "||R_e||_F=%.3e, rank-ratio=%.3f, min eig=%+.2e" % entry_rows[-1]) drift = [r["dPi_run"] for r in rungs if r["dPi_run"] is not None] print(" within-run ||dPi|| drift: median %.3e, max %.3e" % (float(np.median(drift)), float(np.max(drift)))) p1_ok = gate("(P1) entry residues PSD + rank-one: min rank-" "ratio %.3f >= %g AND worst min-eig ratio %+.2e " ">= -%g" % (min(t[4] for t in entry_rows), RANK1_BAR, min(t[5] / max(np.linalg.norm(rmap[t[0]]["R_e"], 2), QF_FLOOR) for t in entry_rows), PSD_TOL_REL), all(t[4] >= RANK1_BAR for t in entry_rows) and all(t[5] >= -PSD_TOL_REL * np.linalg.norm(rmap[t[0]]["R_e"], 2) for t in entry_rows)) cum = 0.0 c_mass_prof = [] for r in rungs: if r["R_e"] is not None: cum += float(np.linalg.norm(r["R_e"])) c_mass_prof.append((r["M"], cum / max(r["trP"], QF_FLOOR))) c_mass_max = max(v for _m, v in c_mass_prof) c_mass_top = c_mass_prof[-1][1] growth = entry_rows[-1][3] / max(entry_rows[0][3], QF_FLOOR) phi_prof = [(r["M"], r["trPi"] / max(r["trP"], QF_FLOOR)) for r in rungs] print(" entry-mass fraction phi = tr Pi / tr P: first %.3f, " "top %.3f; c_mass profile: 992:%.3e 1108:%.3e 1276:%.3e " "top:%.3e" % (phi_prof[0][1], phi_prof[-1][1], dict(c_mass_prof)[992], dict(c_mass_prof)[1108], dict(c_mass_prof)[1276], c_mass_top)) p2_ok = gate("(P2) entry mass summable: max c_mass = %.3e <= " "%g AND growth ||R_last||/||R_first|| = %.2f <= %g" % (c_mass_max, MASS_BAR, growth, ENTRY_GROWTH_BAR), c_mass_max <= MASS_BAR and growth <= ENTRY_GROWTH_BAR) p2_kill = c_mass_top > MASS_BAR # ---- compactness gates print("\n-- Herglotz compactness (regularized family M~ on the " "frozen grid; Im = 1e-3 row reported only)") Cf = float(np.median([rmap[M]["Cgrid"] for M in FIRST5])) Cl = float(np.median([rmap[M]["Cgrid"] for M in LAST5])) Df = float(np.median([rmap[M]["Dgrid"] for M in FIRST5])) Dl = float(np.median([rmap[M]["Dgrid"] for M in LAST5])) Clo_f = float(np.median([rmap[M]["Cgrid_lo"] for M in FIRST5])) Clo_l = float(np.median([rmap[M]["Cgrid_lo"] for M in LAST5])) print(" grid-sup ||M~||: med5 FIRST5 %.4e -> LAST5 %.4e " "(1e-3 row: %.3e -> %.3e, reported)" % (Cf, Cl, Clo_f, Clo_l)) print(" grid-sup ||M~'||: med5 FIRST5 %.4e -> LAST5 %.4e" % (Df, Dl)) b1_ok = gate("(B1) local uniform boundedness: ratio %.3f <= %g" % (Cl / max(Cf, QF_FLOOR), CBND_RATIO), Cl / max(Cf, QF_FLOOR) <= CBND_RATIO) b2_ok = gate("(B2) equicontinuity proxy: derivative ratio %.3f " "<= %g" % (Dl / max(Df, QF_FLOOR), CDER_RATIO), Dl / max(Df, QF_FLOOR) <= CDER_RATIO) # ---- moment-functional cluster print("\n-- moment functionals (INDUCTIVE_STATE.02 avatar): " "42 tracks, tail LAST10 oscillation") oscs = [] for kmom in MOM_KS: for jf in range(Fb.shape[1]): tail = np.array([rmap[M]["moms"][kmom][jf] for M in LAST10]) osc = float((tail.max() - tail.min()) / max(np.median(np.abs(tail)), 1.0e-30)) oscs.append(osc) osc_med = float(np.median(oscs)) osc_max = float(np.max(oscs)) print(" osc distribution: median %.4f, max %.4f " "(k x f = %d tracks)" % (osc_med, osc_max, len(oscs))) cl_ok = gate("(CL) moment functionals cluster: median tail " "osc = %.4f <= %g" % (osc_med, CL_BAR), osc_med <= CL_BAR) # ---- cell-response re-test (reported + typed, not blocking) print("\n-- cell-response re-test on H(Z_REF)/tr P (reported)") rels_in, rels_e = [], {} for ra, rb in zip(rungs, rungs[1:]): Sa = ra["Href"] / max(ra["trP"], QF_FLOOR) Sb = rb["Href"] / max(rb["trP"], QF_FLOOR) if rb["kind"] == "entry": d0 = Sa.shape[0] dlt = float(np.max(np.abs(Sb[:d0, :d0] - Sa))) nrm = max(np.max(np.abs(Sa)), np.max(np.abs(Sb[:d0, :d0]))) rels_e[rb["M"]] = dlt / max(nrm, QF_FLOOR) elif Sa.shape == Sb.shape: dlt = float(np.max(np.abs(Sb - Sa))) nrm = max(np.max(np.abs(Sa)), np.max(np.abs(Sb))) rels_in.append((rb["M"], dlt / max(nrm, QF_FLOOR))) med_in = float(np.median([v for _m, v in rels_in])) rhos_e = {e: rels_e[e] / max(med_in, QF_FLOOR) for e in rels_e} top5 = sorted(rels_in, key=lambda t: -t[1])[:5] n_over = sum(1 for _m, v in rels_in if v >= min(rels_e.values())) cr_ok = min(rhos_e.values()) >= C_RESP and n_over <= C_UNIQ print(" entry contrasts: %s; within-run median %.3e, top-5 %s" % (" ".join("M=%d:rho=%.2f" % (e, rhos_e[e]) for e in sorted(rhos_e)), med_in, " ".join("M=%d:%.2e" % t for t in top5))) print(" (CR) cell response %s (min rho %.2f vs %g, %d " "comparable) -- reported, not CARRIES-blocking" % ("PASS" if cr_ok else "FAIL", min(rhos_e.values()), C_RESP, n_over)) # ---- controls print("\n-- controls") kb_cs = [] rng = np.random.default_rng(SEED_CS) pos = np.sort(rng.uniform(0.5, 2.0 * alpha_top, ka)) cat_s, _dd = core.atom_lags_at(alpha_top, M_TOP, pos, mu_deep[:ka]) pcs = c_cont + cat_s for M in CTRL_LAD_CS: _a, _g, kb = jac.wheeler(pcs[:M], M // 2) if kb is not None: kb_cs.append((M, int(kb))) check("CS scramble fires: Wheeler breakdown %d/%d" % (len(kb_cs), len(CTRL_LAD_CS)), len(kb_cs) == len(CTRL_LAD_CS)) 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] catE, _dd = core.atom_lags_at(0.5 * EP_MMAX * D, EP_MMAX, np.log(supp.astype(float)), 2.0 * lamE[supp] / np.sqrt(supp.astype(float))) pce = srp.continuum_lags(EP_MMAX) + catE kb_ce = [] for M in CTRL_LAD_CE: _a, _g, kb = jac.wheeler(pce[:M], M // 2) if kb is not None: kb_ce.append((M, int(kb))) check("CE Epstein fires: Wheeler breakdown %d/%d" % (len(kb_ce), len(CTRL_LAD_CE)), len(kb_ce) == len(CTRL_LAD_CE)) cb_med = float(np.median([rmap[M]["rho_cb"] for M in GATE_BLOCK])) check("CB GOE bulk fires: med%d rho_A^goe = %.2f > %g at z = " "%g" % (N_MED, cb_med, B_MATCH, Z_CB), cb_med > B_MATCH) cw_rungs = [r for r in rungs if r["M"] in CW_LAD and r["rho_cw"] is not None] cw_med = float(np.median([r["rho_cw"] for r in cw_rungs[-5:]])) cw_rels = [] for ra, rb in zip(cw_rungs, cw_rungs[1:]): dlt = float(np.max(np.abs(rb["H_cw"] - ra["H_cw"]))) nrm = max(np.max(np.abs(ra["H_cw"])), np.max(np.abs(rb["H_cw"]))) cw_rels.append(dlt / max(nrm, QF_FLOOR)) r992, r988 = rmap[992], rmap[988] dlt992 = float(np.max(np.abs(r992["H_cw"] - r988["H_cw"]))) nrm992 = max(np.max(np.abs(r992["H_cw"])), np.max(np.abs(r988["H_cw"]))) cw_contrast = (dlt992 / max(nrm992, QF_FLOOR)) \ / max(float(np.median(cw_rels)), QF_FLOOR) check("CW random boundary fires: med%d rho_A^cw = %.2f > %g " "AND 992-contrast %.2f < %g" % (N_MED, cw_med, B_MATCH, cw_contrast, C_RESP), cw_med > B_MATCH and cw_contrast < C_RESP) dt = time.time() - T_START check("G0.4 runtime %.1f s <= %.0f s" % (dt, RUNTIME_CAP), dt <= RUNTIME_CAP) # ---- verdict guards_ok = all(ok for (n, ok) in CHECKS if not n.startswith(("CS", "CE", "CB", "CW"))) controls_ok = all(ok for (n, ok) in CHECKS if n.startswith(("CS", "CE", "CB", "CW"))) legs = dict(DEL=del_ok, P1=p1_ok, P2=p2_ok, B1=b1_ok, B2=b2_ok, CL=cl_ok) if not (guards_ok and controls_ok): verdict = "Z1-VAREDGE-INVALID" elif p2_kill or (not b1_ok) or del_dead: verdict = "Z1-VAREDGE-DEAD" elif all(legs.values()): verdict = "Z1-VAREDGE-CARRIES" else: verdict = "Z1-VAREDGE-PARTIAL" n_chk = sum(1 for (_n, ok) in CHECKS if ok) print("\nVERDICT: %s" % verdict) print("LEGS %d/6 (%s), CR(reported)=%s, candidate %s, " "GUARDS+CONTROLS %d/%d, runtime %.1f s" % (sum(legs.values()), " ".join("%s=%s" % (k, "P" if v else "F") for k, v in legs.items()), "P" if cr_ok else "F", which, n_chk, len(CHECKS), time.time() - T_START)) print("\nUNIFICATION REPORT (report only): normal-family legs " "B1=%s B2=%s, cluster leg CL=%s on the SAME boundary " "spectral measure." % tuple("PASS" if v else "FAIL" for v in (b1_ok, b2_ok, cl_ok))) if b1_ok and b2_ok and cl_ok: print(" MEASURED EVIDENCE FOR UNIFICATION: the weak-* " "cluster demand of PRIME.KMS.INDUCTIVE_STATE.02 and " "the Z1 operator demand of PRIME.Z1.OPERATOR.01 are " "the same remaining object on this surface -- the " "regularized boundary family is bounded and " "equicontinuous on the frozen compacts AND its " "moment functionals cluster: both contracts reduce " "to one Helly/Montel selection theorem for the " "variable-edge boundary measure chain. Recommended " "contract text (promotion round, report only): " "'INDUCTIVE_STATE.02 and OPERATOR.01 merge into " "Z1-COMPACTNESS: prove that the variable-edge " "boundary triple of the window chain has a normal " "Herglotz family with summable rank-one entry poles " "at the arithmetic thresholds; its weak-* cluster " "states ARE its Herglotz limits.'") else: print(" MEASURED EVIDENCE AGAINST/INCOMPLETE: the failing " "leg(s) above name which half of the unification is " "not yet carried on this surface; the contracts stay " "separate until that leg is repaired.") return 0 if (guards_ok and controls_ok) else 1 return run(), list(CHECKS), list(GATES) def run(): """run_all entry point (combined adjudication, frozen): part 1 must show EXACTLY the Z1-A cadence fail (gates 3/4, 20/20 guards+controls, Z1-SIGNATURE-PARTIAL); part 2 EXACTLY the b/c/d import fails with (a) Herglotz green (gates 1/4, 23/23, Z1-TRIPLE-PARTIAL); part 3 EXACTLY the DEL/P1/CL fails with P2/B1/B2 green (legs 3/6, 23/23, Z1-VAREDGE-PARTIAL) -- the measured Z1-COMPACTNESS unification.""" rc1 = _run_part1() chk_fails1 = [n for (n, ok) in CHECKS if not ok] gate_fails1 = [n.split()[0] for (n, ok) in GATES if not ok] part1_ok = (rc1 == 0 and not chk_fails1 and len(CHECKS) == 20 and len(GATES) == 4 and gate_fails1 == ["Z1-A"]) print("\n[%s] PART-1 PATTERN GATE: expected exactly the Z1-A cadence " "fail (B/C/D pass, 20/20 guards+controls) -- failing gates: %s, " "failing guards: %s" % ("PASS" if part1_ok else "FAIL", gate_fails1, chk_fails1 or "none")) rc2, chks2, gates2 = _run_part2() gf2 = sorted(n.split()[0] for (n, ok) in gates2 if not ok) part2_ok = (rc2 == 0 and all(ok for (_n, ok) in chks2) and len(chks2) == 23 and gf2 == ["(b)", "(c)", "(d)"]) print("\n[%s] PART-2 PATTERN GATE: expected exactly the b/c/d import " "fails with (a) Herglotz green (23/23 guards+controls) -- " "failing gates: %s" % ("PASS" if part2_ok else "FAIL", gf2)) rc3, chks3, gates3 = _run_part3() gf3 = sorted(n.split()[0] for (n, ok) in gates3 if not ok) part3_ok = (rc3 == 0 and all(ok for (_n, ok) in chks3) and len(chks3) == 23 and gf3 == ["(CL)", "(DEL)", "(P1)"]) print("\n[%s] PART-3 PATTERN GATE: expected exactly the DEL/P1/CL " "fails with P2/B1/B2 green (23/23 guards+controls) -- failing " "gates: %s" % ("PASS" if part3_ok else "FAIL", gf3)) ok = part1_ok and part2_ok and part3_ok print("\nCOMBINED ADJUDICATION: %s -- Z1-SIGNATURE-PARTIAL / " "Z1-TRIPLE-PARTIAL / Z1-VAREDGE-PARTIAL: the N2 family carries " "contact, collision and coupling natively but not the cadence; " "the finite triple is exactly Herglotz and dies as a whitened " "import (cell-mass exactly 0.500 beyond the half-window); the " "raw variable-edge family is bounded + equicontinuous with " "summable ~rank-one entry poles (c_mass 0.032) while the moment " "tracks do not settle (osc 22.1) -- INDUCTIVE_STATE.02 and " "Z1.OPERATOR.01 share ONE compactness theorem (carried) and ONE " "remaining obstruction (import-faithful boundary coupling). " "NO RH claim, no statement beyond X = 20.3125." % ("PASS" if ok else "FAIL")) return 0 if ok else 1 if __name__ == "__main__": raise SystemExit(run())