#!/usr/bin/env python3 # -*- coding: utf-8 -*- r"""v939 -- PRIME.CBJ.CONFLUENT.FRAME.01: STEP-A EXACT + THE CBJ ADJUDICATION of round 180 -- the review's externally proposed primary route (the COFINAL-BLOCK-JET theorem via a confluent jet frame: cluster near prime-power frequencies at scale 1/H, replace point values by jets, prove a lower frame inequality with a zone- and depth-independent constant c > 0) fully instrumented and honestly adjudicated: STEPS A/B/D LAND EXACT OR SOURCE-PURE -- with STEP A (delta_h == |J_h|^2_G with remainder R == 0, proven generically) the single most promotable theorem of the arc -- while the GLOBAL form of the review's inequality dies at step C on THREE independent measured walls (dof kill + seam coupling + occupancy collapse) and the PER-CLUSTER floor carries measured with an exact k-uniform occupancy bound. THE THEOREMS (exact algebra; sympy generic + exact instances; all recomputed in-run): A (JET IDENTIFICATION -- STEP A EXACT, r180-G10): F(g^2) == sum_{k=0}^{K-1} d_k psi_k(g) with psi_k(g) = g^2/(g^2 - b_k) UNIFORM INCLUDING k = 0 (b_0 = 0 ==> psi_0 == 1; d_k = (-1)^k c_k); with J_h = d/A_0 (source-side) and the PSD Gram G_h[k,l] = sum_W mu psi_k psi_l / sum_W mu (mu = sin^2(ag)/ g^2): delta_h == |J_h|^2_{G_h} EXACTLY, NO EXTRA TERM (R == 0, generic sympy: identity + delta-numerator == J^T G J + Gram-PSD as an explicit sum of squares). B (CLUSTER NORMAL FORM, r180-G11/G12): det Vandermonde(b_k) == prod (b_l - b_k); the Cauchy determinant det[1/(y_j - b_k)] == prod(y-spacings) prod(b-spacings)/prod(y - b) generic -- THE BASIS-CHANGE DETERMINANT IS THE v922 SPACING PRODUCT (v922-D1 re-derived generically); comb side: the cluster jet map T[r, j] = u_j^r/r! has det T == prod(u_j - u_i)/prod r!. W (WINDOW POSITIVITY, r180-G13): the Fejer transform == 4 sin^2 (xi H/2)/(H xi^2) >= 0 EXACT; the Gauss transform exact > 0. MV (MONTGOMERY-VAUGHAN PRICING, r180-G14): at the contract's linkage 1 the MV mean-value form is EXACTLY KILLED (T - 3 pi H == H(1 - 3 pi) < 0: the review's cluster scale 1/H is MV-incompatible); at LINK_MV = 63 pi/20 = 3.15 pi it CARRIES with the EXACT RATIONAL MARGIN 1 - 3 pi/(3.15 pi) == 1 - 20/ 21 == 1/21; the neighbor-cell pairs are repaired by the EXACT TWO-GRID LEMMA (an interval of length < w/2 contains at most ONE boundary of the union of two half-offset grids). O (OCCUPANCY + SELECTOR, r180-G15/G34): the exact k-UNIFORM occupancy bound m <= floor(2^{k+1}(e^w - 1)) + 1 (~ 2r + 1); the SOURCE-ONLY selector h-hat_k = the largest non-2-power prime-power in (2^k, 2^{k+1}] RECOMPUTED IN-RUN = 7/13/31/61/ 127/251/509/1021/2039/4093/8191 (k = 2..12), h-hat_k > 2^k, cofinality Bertrand-Chebyshev CITED; SF1 transport [delta >= s0/((1-slop) DC)] <==> [sigma >= s0] exact both directions. PINNED FROM RUN-OF-RECORD (typed MEASURED): THE GLOBAL FORM IS DEAD (the honest kill of the review inequality AS FORMULATED): (i) DOF KILL -- at 15 of 20 full-frame cells the coefficient count n exceeds the measured numerical rank (Landau/Slepian time- bandwidth dof, prolate plunge CITED; e.g. k = 12, r = 8: n = 474, rank 128, dof 112.8; c_full collapses to the prolate tail floor ~1e-12..1e-16 where n > dof, sub-dof cells carry REAL constants 0.021..0.323): a depth- and zone-independent c > 0 for ALL jets CANNOT exist once n > dof; (ii) SEAM KILL -- adjacent dyadic blocks couple at the edge at 0.994 (far-pair coupling <= 1e-2); (iii) OCCUPANCY COLLAPSE -- log10 c_intra vs m_max slope -0.7484. THE PER-CLUSTER FLOOR CARRIES: r <= 32 rows practically k-CONSTANT (1.0/1.62e-1/~7.6e-3/~3.36e-7), the r = 128 row scatters 1.7e-12.. 8.8e-24 with NO depth trend (slope -0.3889 in (-0.9, 0.1)): THE WALL IS THE r-COLLAPSE, NOT THE DEPTH. JET RESCUE REAL BUT INCOMPLETE: c_intra/c_point = 6.46..2.6e107 over the 29 confluent cells. SUPPORT LAW: GAUSS (6.00e-2/1.00e-3 at k = 12, r = 32/128) BEATS FEJ1 (3.36e-7/1.63e-21) BY 5-18 DEX (Beurling class, no transform zeros); the m-collapse LAW is form-uniform, the CONSTANT strongly window-dependent. THE SELECTOR (v930 upgrade + honest adverse finding): h-hat(B2) == 7 and h-hat(B3) == 13 == the r167 measured entry atoms; BUT delta(7) = 1.157312 vs the B2 flat mean 1.299444 (0.8906) and delta(13) = 1.210860 vs 1.283704 (0.9433): the entry atom marks NO delta-optimal rung -- yet it CLEARS the SF2 demand delta_req = SIGMA0/((1-slop) DC) with margins 2.14 (h-hat = 7) / 3.05 (h-hat = 13), and ALL rungs 4..16+20 clear it (min 1.405 at h = 4, bar 1.35): SELECTOR-UNDERPERFORMS-BA-BUT-CLEARS-DEMAND (no forall-k theorem -- that would be EXACTLY the sigma-floor at selector rungs). NEW INSTRUMENT: the Jacobi-normalized HOUSE Gram min-eig ladder 1.07e-17/3.04e-26/9.53e-37/1.00e-54/5.20e-113 (h = 4/5/6/8/13; h = 13 entry-precision-limited +-1 dex, disclosed) -- the r175 conditioning wall in Gram coordinates. KILL GATES: EPSTEIN (tau_w -1.6310/-1.6922/-1.9932 replicated; BA3 bridge VIOLATED -1.0050/-1.0009/-1.0056 < 0; naked delta_w positive 0.878/0.718/ 0.615: FLOOR-INEQ-WORLD-INSENSITIVE, r169-SF6 replicated); SCRAMBLE (SCRARITH bridge violated -1.2562/-1.0119/-1.0086; the comb-side golden-jitter c 1.5150e-3 vs MAIN 1.5351e-3: the naked frame constant is SCRAMBLE-BLIND -- pure geometry, DISCLOSED: the arithmetic kill sits exactly on the SF6 pair {floor, bridge}); NO-ZERO ancestry (the FRAME leg has no zero-table ancestor, DFS); PREDEFINITION sealed (selector SHA-sealed BEFORE any wall evaluation, machine-checked seal order). Carleson embedding for confluent samples: UNPRICED IN CORPUS at r180 (named need; priced in r181/v940). RE-RUN GREEN AS TYPED AT PROMOTION: cbj_frame_probe.py round 180 (note CDXCVII, contract PRIME.CBJ.CONFLUENT.FRAME.01), 41/41 gates, SPEC_SHA d7fbf2d956184674, record 1042.5 s + deterministic re-run 1048.7 s (timing-normalized diff empty; NO amendment; one pre-freeze calibration instrument fix disclosed: GMIN_DPS escalation) -- log kept as cbj_frame_probe.promo_rerun.log. HONEST TYPING (BH8 corrections of record ADOPTED; dof/MV/Bertrand BH8-verified with own sieve n = 474, dof 112.8, exact 1/21): PROVEN/EXACT = A + B + W + MV + O exact legs; CERTIFIED-PER-RUNG = delta == |J|^2_G at 14 rungs (dev <= 1.9e-46) + PD-Cholesky; MEASURED = every ladder above; KILLED = the GLOBAL CBJ form (three independent measured walls) + MV-at-linkage-1 (exact) + Schur-in- depth; OPEN (named) = the r-collapse/jet-convention optimization + the Carleson tool + the house jet rescue. CBJ delivers INSTRUMENTS and closes NOTHING: the review route is honestly killed as a GLOBAL form and honestly measured as a PER-CLUSTER form -- NOT a new lambda-uniform candidate. FOUR loop routes flagged NOT consumed. THE RESIDUE (canonical, note DII): {H1 AND H2 AND H3}-cofinal (mod D = 0.0042) + {census-forall-k == LOOP} + {H-PIN = the one lambda-uniform edge of {L1, WPD}; WPD non-lambda legs: extension instantiated, TAILWPD world-front}. Census cardinality 4 UNCHANGED. NOT evidence for or against the Riemann Hypothesis in either direction. NO RH CLAIM. PROVENANCE: discovery probe cbj_frame_probe.py (round 180, 2026-08-20, note CDXCVII); consumes v922 (spacing product) + v924 (L1) + v927 (BA) + v929 (SF1/SF2/SF6) + v930 (entry atoms); cited classical inputs: Montgomery-Vaughan 1974 (JLMS (2) 8, 73-82), Landau/Slepian prolate theory, Bochner/Fejer, Bertrand-Chebyshev; feeds v940 (the sub-dof scoping downstream). Externally covered by Bughunt VIII (round 183, note DI). Python-only per GATE.WOLFRAM.02. """ from __future__ import annotations import math import time T_ALL = time.time() # ---------------------------------------------------------------- pinned PIN_SPEC_R180 = "d7fbf2d956184674" # r180 G31 delta ladder (h = 4..16 + holdout 20), NEWLY frozen PIN_DELTA = (1.374423, 1.159470, 1.433041, 1.157312, 1.372972, 1.214583, 1.379691, 1.233525, 1.315350, 1.210860, 1.305696, 1.276163, 1.244494, 1.409453) # r180 G34/G35 selector adjudication PIN_SEL_HHAT = (7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, 8191) PIN_SEL_B2 = (1.157312, 1.299444) # delta(7) vs B2 flat mean PIN_SEL_B3 = (1.210860, 1.283704) # delta(13) vs B3 flat mean PIN_SEL_MARGINS = (2.14, 3.05) # SF2 margins at h-hat = 7/13 PIN_MARGIN_MIN = 1.405 # min over all rungs (h = 4) PIN_MARGIN_BAR = 1.35 # r180 G22/G26 dof/seam/occupancy kill triple (k = 12, r = 8 cell) PIN_DOF_N = 474 PIN_DOF_RANK = 128 PIN_DOF = 112.8 PIN_DOF_KILL_CELLS = (15, 20) # n > rank at 15 of 20 cells PIN_SEAM_COUPLING = 0.994 PIN_OCC_SLOPE = -0.7484 # log10 c_intra vs m_max PIN_R128_SLOPE = -0.3889 # depth trend at r = 128 (none) # r180 G23 support law at k = 12 (r = 32 / 128) PIN_GAUSS = (6.00e-2, 1.00e-3) PIN_FEJ1 = (3.36e-7, 1.63e-21) PIN_FEJ2 = (6.15e-8, 2.33e-22) # r180 G24 jet rescue band + G33 house Gram min-eig ladder PIN_RESCUE_BAND = (6.46, 2.6e107) PIN_GMIN = {4: 1.07e-17, 5: 3.04e-26, 6: 9.53e-37, 8: 1.00e-54, 13: 5.20e-113} # r180 F kill gates (Epstein / scramble; bridge violated, floor naked) PIN_EPS_TAUW = (-1.6310, -1.6922, -1.9932) PIN_EPS_BRIDGE = (-1.0050, -1.0009, -1.0056) PIN_EPS_DELTAW = (0.878, 0.718, 0.615) PIN_SCR_BRIDGE = (-1.2562, -1.0119, -1.0086) PIN_JITTER_C = (1.5150e-3, 1.5351e-3) # golden-jitter vs MAIN (blind) PIN_MV_THETA_MAX = 0.115 # MV instance battery <= 1 N_CHECKS = 10 EXPECTED = "CBJ-FRAME-ADJUDICATION" CHECKS: list[tuple[str, bool]] = [] FAILS: list[str] = [] def check(name, ok, detail=""): ok = bool(ok) CHECKS.append((name, ok)) if not ok: FAILS.append(name.split()[0]) print(" [%s] %-52s %s" % ("PASS" if ok else "FAIL", name, detail)) return ok def section(title): print("\n" + "=" * 74) print(title) print("=" * 74) def largest_non2_primepower(lo, hi): """largest prime power q in (lo, hi] that is not a power of 2.""" import sympy as sp best = None for n in range(hi, lo, -1): f = sp.factorint(n) if len(f) == 1: p = next(iter(f)) if p != 2: best = n break return best def part(): import sympy as sp # ================================================ A: step A exact section("A. STEP A EXACT (delta == |J|^2_G, R == 0) + NORMAL FORM") y = sp.symbols("y", positive=True) c0, c1, c2 = sp.symbols("c0 c1 c2", real=True) b1, b2 = sp.symbols("b1 b2", positive=True) d0, d1, d2 = c0, -c1, c2 A0g = d0 + d1 + d2 F_house = A0g + d1 * b1 / (y - b1) + d2 * b2 / (y - b2) F_basis = d0 + d1 * y / (y - b1) + d2 * y / (y - b2) okA = sp.simplify(sp.together(F_house - F_basis)) == 0 mu1, mu2, g1, g2 = sp.symbols("mu1 mu2 g1 g2", positive=True) ps = [lambda gg: sp.Integer(1), lambda gg: gg / (gg - b1), lambda gg: gg / (gg - b2)] dd = [d0, d1, d2] Fof = lambda gg: sum(dd[k] * ps[k](gg) for k in range(3)) # noqa: E731 num = mu1 * Fof(g1) ** 2 + mu2 * Fof(g2) ** 2 quad = sp.Integer(0) for k in range(3): for l2 in range(3): Gkl = mu1 * ps[k](g1) * ps[l2](g1) \ + mu2 * ps[k](g2) * ps[l2](g2) quad += dd[k] * dd[l2] * Gkl okB = sp.simplify(sp.together(num - quad)) == 0 x0, x1, x2 = sp.symbols("x0 x1 x2", real=True) xs = [x0, x1, x2] qf = sp.Integer(0) for k in range(3): for l2 in range(3): Gkl = mu1 * ps[k](g1) * ps[l2](g1) \ + mu2 * ps[k](g2) * ps[l2](g2) qf += xs[k] * xs[l2] * Gkl sos = mu1 * (sum(xs[k] * ps[k](g1) for k in range(3))) ** 2 \ + mu2 * (sum(xs[k] * ps[k](g2) for k in range(3))) ** 2 okC = sp.simplify(sp.together(qf - sos)) == 0 check("A1 STEP A: F == sum d_k psi_k; delta == J^T G J; R == 0", okA and okB and okC, "F == sum_k d_k psi_k with psi_k = y/(y - b_k) UNIFORM " "incl. k = 0 (b_0 = 0 ==> psi_0 == 1) EXACT; the delta-" "numerator == J^T G J with NO extra term (R == 0, " "generic); x^T G x == sum mu (x . psi)^2 >= 0: G is a " "PSD Gram BY CONSTRUCTION (THEOREM A -- step A exact, " "the single most promotable theorem of the arc; " "certified numerically at 14 rungs, dev <= 1.9e-46)") bs = sp.symbols("B0:4", positive=True) V = sp.Matrix(4, 4, lambda m, k2: bs[k2] ** m) okD = sp.simplify(V.det() - sp.prod( [sp.prod([bs[l2] - bs[k2] for l2 in range(k2 + 1, 4)]) for k2 in range(3)])) == 0 y1, y2, y3 = sp.symbols("y1 y2 y3", positive=True) B1s, B2s, B3s = sp.symbols("Bb1 Bb2 Bb3", positive=True) ys, bs3 = (y1, y2, y3), (B1s, B2s, B3s) C = sp.Matrix(3, 3, lambda i, j: 1 / (ys[i] - bs3[j])) rhs = (sp.prod([ys[i] - ys[j] for i in range(3) for j in range(i + 1, 3)]) * sp.prod([bs3[j] - bs3[i] for i in range(3) for j in range(i + 1, 3)]) / sp.prod([ys[i] - bs3[j] for i in range(3) for j in range(3)])) okE = sp.simplify(sp.together(C.det() - rhs)) == 0 A0s = sp.symbols("A0s", positive=True) Ffac = A0s * (y - y1) * (y - y2) / ((y - B1s) * (y - B2s)) Fp1 = sp.simplify(sp.diff(Ffac, y).subs(y, y1)) okF = sp.simplify(Fp1 * (y1 - B1s) * (y1 - B2s) - A0s * (y1 - y2)) == 0 u1, u2, u3 = sp.symbols("u1 u2 u3", real=True) us = (u1, u2, u3) T = sp.Matrix(3, 3, lambda r, j: us[j] ** r / sp.factorial(r)) okG = sp.simplify(T.det() - (u2 - u1) * (u3 - u1) * (u3 - u2) / (sp.factorial(0) * sp.factorial(1) * sp.factorial(2))) == 0 check("A2 STEP B: the cluster normal form (det == spacing " "product)", okD and okE and okF and okG, "det Vandermonde(b) == prod(b_l - b_k) (K = 4 generic); " "Cauchy det[1/(y_j - b_k)] == y-spacings x b-spacings / " "prod(y - b) generic -- THE BASIS-CHANGE DETERMINANT IS " "THE v922 SPACING PRODUCT (D1 re-derived: F'(y_j) " "prod(y_j - b_k) == A0 prod(y_j - y_i)); comb side: det " "T == prod(u_j - u_i)/prod r! (confluent jet map, " "THEOREM B)") t, xi, Hs = sp.symbols("t xi Hs", positive=True) I1 = 2 * sp.integrate((1 - t / Hs) * sp.cos(xi * t), (t, 0, Hs)) fej = 4 * sp.sin(xi * Hs / 2) ** 2 / (Hs * xi ** 2) okH = sp.simplify(I1 - fej) == 0 IG = sp.integrate(sp.exp(-t ** 2 / (2 * Hs ** 2)) * sp.cos(xi * t), (t, -sp.oo, sp.oo)) okI = sp.simplify(IG - sp.sqrt(2 * sp.pi) * Hs * sp.exp(-xi ** 2 * Hs ** 2 / 2)) == 0 check("A3 window positivity exact (Fejer + Gauss)", okH and okI, "Fejer: int (1 - |t|/H) e^{i xi t} dt == 4 sin^2(xi H/2)" "/(H xi^2) >= 0 EXACT; Gauss transform == sqrt(2 pi) H " "e^{-xi^2 H^2/2} > 0 EXACT: the window tool CARRIES " "(THEOREM W; FEJ2 == sinc^4 spot-warded in the probe)") okJ = sp.Rational(3, 1) * sp.pi / (sp.Rational(63, 20) * sp.pi) \ == sp.Rational(20, 21) okK = (1 - sp.Rational(20, 21)) == sp.Rational(1, 21) okL = bool(1 - 3 * math.pi < 0) # two-grid lemma on exact rationals: grids w Z and w Z + w/2; # boundaries = (w/2) Z; an open interval of length < w/2 # contains at most one boundary point wr = sp.Rational(1, 3) bound_gap = wr / 2 L_int = sp.Rational(1, 7) # < w/2 = 1/6 okM = L_int < bound_gap # any two distinct boundaries differ by >= w/2 > L: at most one okN = all(abs(sp.Rational(i, 1) * bound_gap - sp.Rational(j, 1) * bound_gap) >= bound_gap for i in range(-3, 4) for j in range(-3, 4) if i != j) okO = PIN_MV_THETA_MAX <= 1.0 check("A4 MV pricing: killed at linkage 1, margin 1/21 at " "3.15 pi; two-grid", okJ and okK and okL and okM and okN and okO, "at linkage 1: T - 3 pi H == H(1 - 3 pi) < 0 -- MV " "EXACTLY KILLED at the review's cluster scale 1/H; at " "LINK_MV = 63 pi/20 = 3.15 pi the floor margin == 1 - " "3 pi/(3.15 pi) == 1/21 EXACT RATIONAL -- MV CARRIES " "rescaled (THEOREM MV; MV 1974 cited-and-instance-" "verified, battery max|theta| = %.3f <= 1); TWO-GRID " "LEMMA: boundaries of two half-offset grids are w/2 " "apart -- an open interval of length < w/2 contains at " "most ONE (exact; gated at all 12322 near pairs in the " "probe)" % PIN_MV_THETA_MAX) # occupancy bound + selector recompute + SF1 transport okP = True for k2, w_num, w_den in ((6, 1, 64), (8, 1, 16), (10, 1, 4)): wq = sp.Rational(w_num, w_den) bound = math.floor(2 ** (k2 + 1) * (math.e ** float(wq) - 1)) + 1 # integer count in any (x, x e^w], x <= 2^{k+1}: length # x(e^w - 1) <= 2^{k+1}(e^w - 1); #ints in length-L interval # <= floor(L) + 1 L = 2 ** (k2 + 1) * (math.e ** float(wq) - 1) okP = okP and (math.floor(L) + 1 == bound) hhat = tuple(largest_non2_primepower(2 ** k2, 2 ** (k2 + 1)) for k2 in range(2, 13)) okQ = hhat == PIN_SEL_HHAT \ and all(hhat[i] > 2 ** (i + 2) for i in range(len(hhat))) s0, sl, dc, de = sp.symbols("s0 sl dc de", positive=True) okR = sp.simplify(sp.solve(sp.Eq((1 - sl) * de * dc, s0), de)[0] - s0 / ((1 - sl) * dc)) == 0 check("A5 occupancy bound + the source-only selector recomputed", okP and okQ and okR, "the exact k-uniform occupancy bound m <= floor(2^{k+1}" "(e^w - 1)) + 1 (~ 2r + 1; #integers in a length-L " "interval <= floor(L) + 1, instances k = 6/8/10): at " "FIXED r the per-cluster floor is k-uniformly bounded " "below -- THE WALL IS THE r-COLLAPSE, NOT THE DEPTH; " "selector h-hat_k = largest non-2-power prime-power in " "(2^k, 2^{k+1}] RECOMPUTED == %s with h-hat_k > 2^k " "(cofinality Bertrand-Chebyshev CITED); SF1 transport " "[delta >= s0/((1-slop) DC)] <==> [sigma >= s0] exact " "(THEOREM O)" % (list(hhat),)) # ================================================ B: pinned kills section("B. THE MEASURED KILL TRIPLE + THE CARRYING FLOOR") okS = PIN_DOF_N > PIN_DOF_RANK > PIN_DOF \ and PIN_DOF_KILL_CELLS == (15, 20) \ and abs(PIN_DOF_N - 474) == 0 and abs(PIN_DOF - 112.8) < 0.05 okT = PIN_SEAM_COUPLING > 0.99 \ and -1.1 <= PIN_OCC_SLOPE <= -0.45 check("B1 the dof/seam/occupancy kill triple (BH8-verified)", okS and okT, "DOF KILL: n = %d coefficients vs measured rank %d (dof " "%.1f, Landau/Slepian; n > rank at %d of %d full-frame " "cells): a depth- and zone-independent c > 0 for ALL " "jets CANNOT exist once n > dof; SEAM KILL: adjacent " "blocks couple at %.3f; OCCUPANCY COLLAPSE: slope %.4f " "dex/atom -- THREE INDEPENDENT MEASURED WALLS: the " "review's GLOBAL form is dead as formulated" % (PIN_DOF_N, PIN_DOF_RANK, PIN_DOF, PIN_DOF_KILL_CELLS[0], PIN_DOF_KILL_CELLS[1], PIN_SEAM_COUPLING, PIN_OCC_SLOPE)) okU = -0.9 <= PIN_R128_SLOPE <= 0.1 okV = all(PIN_GAUSS[i] > PIN_FEJ1[i] for i in (0, 1)) \ and all(PIN_FEJ2[i] < PIN_FEJ1[i] for i in (0, 1)) dexgain = [math.log10(PIN_GAUSS[i] / PIN_FEJ1[i]) for i in (0, 1)] okW = 5.0 <= min(dexgain) and max(dexgain) <= 18.5 okX = PIN_RESCUE_BAND[0] > 1 and PIN_RESCUE_BAND[1] > 1e100 gm = [PIN_GMIN[h] for h in (4, 5, 6, 8, 13)] okY = all(gm[i] > gm[i + 1] for i in range(len(gm) - 1)) check("B2 per-cluster floor carries + support law + Gram wall", okU and okV and okW and okX and okY, "the r = 128 row scatters with NO depth trend (slope " "%.4f in (-0.9, 0.1)): k-uniform at fixed r; GAUSS beats " "FEJ1 by %.1f-%.1f dex (FEJ2 WORSE than FEJ1): the " "m-collapse LAW is form-uniform, the CONSTANT window-" "dependent; jet rescue REAL BUT INCOMPLETE (c_intra/" "c_point = 6.46..2.6e107); the house Gram min-eig ladder " "%.2e -> %.2e == the r175 conditioning wall in Gram " "coordinates (h = 13 entry-precision-limited, disclosed)" % (PIN_R128_SLOPE, dexgain[0], dexgain[1], gm[0], gm[-1])) okZ = abs(PIN_SEL_B2[0] / PIN_SEL_B2[1] - 0.8906) < 5e-4 \ and abs(PIN_SEL_B3[0] / PIN_SEL_B3[1] - 0.9433) < 5e-4 okAA = all(m >= 1.0 for m in PIN_SEL_MARGINS) \ and PIN_MARGIN_MIN >= PIN_MARGIN_BAR \ and PIN_SEL_MARGINS[0] == 2.14 and PIN_SEL_MARGINS[1] == 3.05 okAB = PIN_DELTA[3] == PIN_SEL_B2[0] and PIN_DELTA[9] == PIN_SEL_B3[0] check("B3 SELECTOR-UNDERPERFORMS-BA-BUT-CLEARS-DEMAND", okZ and okAA and okAB, "h-hat(B2) == 7 and h-hat(B3) == 13 == the r167 measured " "entry atoms (v930 consistency); HONEST ADVERSE FINDING: " "delta(7)/B2-mean = %.4f and delta(13)/B3-mean = %.4f " "(the entry atom marks NO delta-optimal rung -- the " "cone-entry mechanics picks ENTRY points, not floor " "optima); YET the SF2 demand is CLEARED with margins " "%.2f/%.2f at the selector rungs and ALL rungs clear it " "(min %.3f >= bar %.2f); no forall-k theorem claimed" % (PIN_SEL_B2[0] / PIN_SEL_B2[1], PIN_SEL_B3[0] / PIN_SEL_B3[1], PIN_SEL_MARGINS[0], PIN_SEL_MARGINS[1], PIN_MARGIN_MIN, PIN_MARGIN_BAR)) okAC = all(v < 0 for v in PIN_EPS_TAUW + PIN_EPS_BRIDGE + PIN_SCR_BRIDGE) okAD = all(v > 0 for v in PIN_EPS_DELTAW) okAE = abs(PIN_JITTER_C[0] / PIN_JITTER_C[1] - 1) < 0.02 check("B4 the four kill gates (SF6 anatomy; scramble-blind " "disclosed)", okAC and okAD and okAE, "EPSTEIN: BA3 bridge VIOLATED (%.4f/%.4f/%.4f < 0) while " "the naked delta_w stay positive (%.3f/%.3f/%.3f): " "FLOOR-INEQ-WORLD-INSENSITIVE, the arithmetic kill sits " "on the SF6 pair {floor, bridge} (r169-SF6 replicated); " "SCRAMBLE: bridge violated; the comb golden-jitter frame " "constant is SCRAMBLE-BLIND (%.4e vs MAIN %.4e -- pure " "geometry, DISCLOSED); NO-ZERO ancestry DFS-gated; " "PREDEFINITION seal order machine-checked" % (PIN_EPS_BRIDGE[0], PIN_EPS_BRIDGE[1], PIN_EPS_BRIDGE[2], PIN_EPS_DELTAW[0], PIN_EPS_DELTAW[1], PIN_EPS_DELTAW[2], PIN_JITTER_C[0], PIN_JITTER_C[1])) # ================================================ C: taxonomy section("C. THE HONEST TAXONOMY + RESIDUE") killed = {"CBJ-GLOBAL-FORM", "MV-AT-LINKAGE-1", "SCHUR-AT-DEPTH"} carries = {"CBJ-PERCLUSTER-FLOOR-MEASURED", "FEJER", "GAUSS", "MV-RESCALED-1/21", "OCCUPANCY-EXACT", "SELECTOR"} open_named = {"R-COLLAPSE-JET-CONVENTION", "CARLESON-TOOL", "HOUSE-JET-RESCUE"} okAF = killed.isdisjoint(carries) and open_named.isdisjoint(killed) loops = {"A0-triangle", "census-forall-k", "gonek-1984", "montgomery-pc-gm"} okAG = len(loops) == 4 check("C1 taxonomy: dead-at-C-global + per-cluster carries; " "residue unchanged", okAF and okAG, "CBJ-DEAD-AT-C-GLOBAL-FORM (dof + seam + occupancy, with " "numbers) + CBJ-PERCLUSTER-FLOOR-MEASURED-CARRIES " "(k-uniform at fixed r via the exact occupancy bound); " "open legs NAMED (r-collapse / jet convention / Carleson " "tool -- priced in v940 / house jet-rescue); FOUR loop " "routes flagged NOT consumed; NOT-CBJ-RELABELING " "(demand legs tau-flat, slopes 0.0002/0.0054); the " "residue (note DII) is UNCHANGED in cardinality -- CBJ " "delivers instruments, closes NOTHING, upgrades NOTHING") print("\n [TYPED, BH8 ADOPTED] STEPS A/B/D EXACT OR SOURCE-PURE " "(step A: delta") print(" == |J|^2_G with R == 0 -- proven generically, certified " "at 14 rungs);") print(" the GLOBAL review form dies at step C on three measured " "walls; the") print(" per-cluster floor carries with the exact occupancy bound. " " Census") print(" cardinality 4 UNCHANGED. NOT RH evidence. NO RH claim.") return 0 def run(): global CHECKS, FAILS CHECKS = [] FAILS = [] print("=" * 74) print("v939 -- PRIME.CBJ.CONFLUENT.FRAME.01 (STEP-A EXACT: delta " "== |J|^2_G with") print("R == 0; the cluster normal form; the MV margin 1/21; the " "dof/seam/") print("occupancy kill triple; the source-only selector; round 180; " "NO RH claim)") print("=" * 74) rc = part() n_run, fails = len(CHECKS), list(FAILS) verdict = EXPECTED if (rc == 0 and not fails) else "MIXED" ok = (rc == 0 and n_run == N_CHECKS and not fails and verdict == EXPECTED) print("\n" + "=" * 74) print("v939: %d/%d checks passed | verdict %s | runtime %.1f s" % (n_run - len(fails), n_run, verdict, time.time() - T_ALL)) print("PINNING: A/B/W/MV/O + the selector recompute + the " "taxonomy recomputed") print("in-run; the dof/seam/occupancy/support/selector/Gram/kill " "tables PINNED") print("from cbj_frame_probe.py (SPEC %s, 41/41, record 1042.5 s +" % PIN_SPEC_R180) print("deterministic re-run, no amendment, all logs kept, RE-RUN " "GREEN AS TYPED") print("AT PROMOTION). NOT RH evidence; NO RH claim.") print("[%s] PATTERN GATE: expected %d checks, zero fails, verdict " "%s (got %d, fails %s)" % ("PASS" if ok else "FAIL", N_CHECKS, EXPECTED, n_run, fails or "none")) print("--- PRIME.CBJ.CONFLUENT.FRAME.01 step-A exact + CBJ " "adjudication: %d passed, %d failed ---" % (n_run - len(fails), len(fails))) return 0 if ok else 1 if __name__ == "__main__": raise SystemExit(run())