#!/usr/bin/env python3 # -*- coding: utf-8 -*- r"""v932 -- PRIME.TOPROOT.THETA.01: THE TOPROOT STATEMENT + THE QUARTIC CERTIFICATE H3 of round 172 -- the last lambda-uniform edge of the jet-mass chain is pinned to ONE named per-rung hypothesis: TOPROOT(p, C) == y_t(h) <= C h^p with the exact SEQ-COFINAL quantifier and three machine-locked equivalent forms, the exact rate dictionary a = p/2 - 1 (proven p = 3, 4, 5), the new THEOREM TR-CAP (proven, typed circular-for-TOPROOT), the A_0-triangle route flagged as the FOURTH loop route, and the per-rung quartic certificate H3 (y_t <= 0.155 T_z^4, one source evaluation, ancestors == {SOURCE}). THE THEOREMS (exact algebra; sympy generic + exact instances; all recomputed in-run): T1 (THE TOPROOT STATEMENT): y_t(h) <= C h^p, quantifier EXISTS (C, p) finite s.t. FOR EVERY dyadic block THERE IS a rung h in the block with y_t(h) <= C h^p (SEQ-cofinal; an ALL-h reading is NOT demanded). THREE LOCKED FORMS: (i) THETA-FORM theta_y = y_t/T_z^4 <= theta_bar <==> TOPROOT(4, theta_bar (2 pi)^4); (ii) CENSUS-FORM (top root in (0.70, 0.95) y_t under H2); (iii) RATE-FORM: TOPROOT(p) ==> the sigma-floor exponent a = p/2 - 1 (the exact dictionary, proven). TR-CAP (NEW THEOREM, proven): |J_{m+1}| <= rho^m for all m >= 1 ==> PHI(z) != 0 for every real z >= 1 + 2 rho (geometric sum + the positivity polynomial (z-1)(z-rho) - rho == rho + 2 rho^2 + (1 + 3 rho) s + s^2 at z = 1 + 2 rho + s): NO census root above (1 + 2 rho) y_t. TYPED CIRCULAR-FOR-TOPROOT: the dictionary is y_t-normalized BY CONSTRUCTION -- the cap bounds census-top/y_t, never y_t itself. Fujiwara is CIRCULAR: the m = 1 term == B_1 + y_t EXACTLY (the Vieta trace) and is the ARGMAX at every rung. VIETA/POWER-SUM PINCH KILLED: every elementary symmetric function of the census carries 1/A_0 (e_2 == b_1 b_2 + (A_4 - A_2 B_1)/ A_0 generic); y_t == B_1/kappa is a REFORMULATION, typed. THE A_0-TRIANGLE ROUTE == THE FOURTH LOOP: y_t <= b_top C_1/|A_0| is exponentially vacuous (overshoot 10^3.4 -> 10^64.6 riding -log10|A_0| with slope 0.97) AND its only A_0-floor consumes {TAUPOS, TLAWCAP} == the pinning-supply loop in A_0-currency (cycle machine-detected in-run, NOT consumed). ADMISSIBILITY (RECOMPUTED IN-RUN from closed forms): eps_closed (56) = sqrt(56) G(T_PT)/G(2 pi 56) = 4.5338e-9; a_max = ln(0.0767/eps)/ln 56 = 4.1348; p_max = 2(1 + a_max) = 10.2695 -- the measured exponent p_all = 4.18 leaves SIX POWERS OF h of margin; by r169-SF4 there is NO finite asymptotic ceiling. THE WITNESS (both directions, exact): deflation A_0'' == A_0, y_t'' = y_t/1000; NEW INFLATION d+ = A_2(W - 1)/(b_2 - b_1): A_0 invariant, y_t'' = W y_t EXACTLY, theta'' = 62.69 > theta_bar: H3 IS REFUTABLE; the perturbation price is EXPONENTIALLY small (|d+|/max|c| = 8.1e-2 at h = 5 -> 10^{-17.6} at h = 13): TOPROOT-NOT-NORM-CONTINUOUS -- no proof via source-norm continuity can exist; any proof must consume the arithmetic sign structure. RE-RUN GREEN AS TYPED AT PROMOTION: toproot_theta_probe.py round 172 (note CDLXXXVIII, contract PRIME.TOPROOT.THETA.01), 33/33 gates, SPEC_SHA cf27df22aa5dffbf, run-of-record 2813 s + deterministic re-run (timing-normalized diff empty, all logs kept incl. one pre-freeze calibration; one disclosed smoke-stage fix, no bar/window/tab moved) -- RE-RUN AT PROMOTION 2933.9 s with identical SPEC_SHA and identical gate count (log kept as toproot_theta_probe.promo_rerun.log). PINNED FROM RUN-OF-RECORD (consistency arithmetic in-run): H3 CERTIFIED at all 25 rungs + the deep holdout h = 30 (K = 128, degree-127 source) with margin theta_bar/theta_y >= 1.99 everywhere; theta_y = 0.0449 -> 0.0779 monotone saturating (growth law p_all = 4.1821 in the r143 window, holdout residual -0.022 dex); rho == |J_2| at EVERY rung (argmax m = 1; 0.107 -> 0.152 inside the r156 quarter-cap window), cap 1 + 2 rho = 1.21 -> 1.30 vs H1's certified c* = 1.10/1.15 (ENVJ-SHARPER); the lock FULLGAP/y_t in (1.0, 8.0) at all 26 rungs (2.23 -> 3.98); witness strings 24.8702 (deflation top) and 62.691 (inflation theta); SIZE-SEPARATOR factors 127/24/302 vs the fake worlds. HONEST TYPING (carried verbatim; BH7-F1 correction of record ADOPTED). PROVEN = T1's three-form locking + TR-CAP + the rate dictionary + the Vieta/e_2 identities + the witness algebra + admissibility; H3 = CERTIFIED-SOURCE-PURE per rung (26/26 + the holdout; ancestors == {SOURCE}); the COFINAL extension is the open edge. THE RESIDUE (BH7-F1): the composed per-block hypothesis is the TRIPLE {H1 AND H2 AND H3}-cofinal, one rung per dyadic block, all three at the same h -- NOT H3 alone (PF is proven only GIVEN H1 + H2 at the same rung; H1/H2/H3 are finite per-rung source checks of the same epistemic type, certified h <= 26/13(24)/30). What remains besides the triple: {census-forall-k == LOOP, flagged} + {L1, WPD}. FOUR loop routes carried flagged NOT consumed (tlaw-window, census-all-k, pinning-supply, A0-floor variant). Census {MEAS, OMEGA-POS} cardinality 4 UNCHANGED. NOT evidence for or against the Riemann Hypothesis in either direction. NO RH CLAIM. PROVENANCE: discovery probe toproot_theta_probe.py (round 172, 2026-08-19/20, note CDLXXXVIII); consumes v931 (PF/H1/H2) + v926 (the theta window, cited); feeds v933 (the H3-cofinal adjudication). Externally covered by Bughunt VII (round 176, note CDXCII: F1 applied here). Python-only per GATE.WOLFRAM.02. """ from __future__ import annotations import math import time T_ALL = time.time() # ---------------------------------------------------------------- pinned PIN_SPEC_R172 = "cf27df22aa5dffbf" T_PT = 3000175332800 # r172 G33/G34 theta ladder + H3 margins (record) PIN_THETA_Y = {4: 0.044901, 5: 0.062691, 8: 0.065250, 13: 0.071983, 28: 0.077144, 30: 0.077858} THETA_BAR = 0.155 PIN_H3_MARGIN_MIN = 1.99 # r172 G35 moments (rho == |J_2|, argmax 1 at every rung) PIN_RHO = {4: 0.106805, 5: 0.125884, 8: 0.139445, 13: 0.147746, 28: 0.151278, 30: 0.151513} PIN_CSTAR = {4: 1.10, 5: 1.15, 8: 1.15} # r172 G43/G44 growth law + admissibility (frozen strings) PIN_P_ALL = 4.1821 PIN_EPS56 = 4.533792e-9 PIN_AMAX = 4.134758 PIN_PMAX = 10.269515 PIN_RATE_C = 0.0767 PIN_HOLD_RESID = 0.022 # dex, h = 30 excluded from fit # r172 G53 witness strings (h = 5) + scaling PIN_WIT_ZTOP_DEFL = 24.870225 PIN_WIT_THETA_INFL = 62.690999 PIN_WIT_DNORM = {"defl": 8.117888e-5, "infl": 8.117888e-2} PIN_WIT_SCALE = {8: -6.726, 13: -17.611} # r172 G50-G52 size separator (min MAIN theta / max world theta_w) PIN_SEP_FACTORS = (127.0, 24.0, 302.0) N_CHECKS = 10 EXPECTED = "TOPROOT-THETA-STATEMENT" 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 has_cycle(edges): color = {} def dfs(u): color[u] = 1 for v in edges.get(u, ()): c = color.get(v, 0) if c == 1: return True if c == 0 and dfs(v): return True color[u] = 2 return False return any(dfs(n) for n in list(edges) if color.get(n, 0) == 0) def reachable(edges, src): seen = {src} stack = [src] while stack: u = stack.pop() for v in edges.get(u, ()): if v not in seen: seen.add(v) stack.append(v) return seen def part(): import sympy as sp # ================================================ A: T1 + TR-CAP section("A. THE TOPROOT STATEMENT + THEOREM TR-CAP (exact)") h, yt, tb = sp.symbols("h yt tb", positive=True) Tz = 2 * sp.pi * h okA = sp.simplify(yt / Tz ** 4 - yt / ((2 * sp.pi) ** 4 * h ** 4)) \ == 0 okB = sp.simplify(tb * (2 * sp.pi) ** 4 * h ** 4 - tb * Tz ** 4) \ == 0 check("A1 T1 statement: theta-form <==> TOPROOT(4) (SEQ " "quantifier)", okA and okB, "theta_y = y_t/T_z^4 <= theta_bar <==> y_t <= theta_bar " "(2 pi)^4 h^4 == TOPROOT(4, theta_bar (2 pi)^4) with T_z " "= 2 pi h (the r131 crossover, definitional); QUANTIFIER " "SEQ-COFINAL: exists (C, p) forall dyadic block exists " "rung -- an ALL-h reading is NOT demanded (r141/r143 " "DENSE-X + r169-SF4 inherited)") z, rho, s = sp.symbols("z rho s", positive=True) okC = sp.simplify((rho / z) / (1 - rho / z) - rho / (z - rho)) == 0 \ and abs(sum((0.1 / 3.0) ** mm for mm in range(1, 60)) - 0.1 / (3.0 - 0.1)) < 1e-15 poly = sp.expand(((z - 1) * (z - rho) - rho) .subs(z, 1 + 2 * rho + s)) pol = sp.Poly(poly, s) okD = all(c.is_positive is True for c in pol.all_coeffs()) okE = sp.simplify(sp.expand(poly) - (rho + 2 * rho ** 2 + (1 + 3 * rho) * s + s ** 2)) == 0 check("A2 THEOREM TR-CAP proven (circular-for-TOPROOT typed)", okC and okD and okE, "|J_{m+1}| <= rho^m ==> PHI(z) != 0 for real z >= 1 + 2 " "rho: geometric closed form sum rho^m z^-m == rho/(z - " "rho) + the positivity polynomial (z-1)(z-rho) - rho == " "rho + 2 rho^2 + (1 + 3 rho)s + s^2 (ALL coefficients " "positive): NO census root above (1 + 2 rho) y_t -- but " "the dictionary is y_t-NORMALIZED: the cap bounds " "census-top/y_t, NEVER y_t itself (CIRCULAR-FOR-TOPROOT; " "carried as a theorem in z-units)") c0, c1, c2 = sp.symbols("c0 c1 c2", real=True) b1 = sp.symbols("b1", positive=True) db = sp.symbols("db", positive=True) b2 = b1 + db A0 = c0 - c1 + c2 A2 = -c1 * b1 + c2 * b2 A4 = -c1 * b1 ** 2 + c2 * b2 ** 2 B1 = b1 + b2 yt_e = -A2 / A0 F = A0 + (-1) * c1 * b1 / (sp.symbols("y") - b1) \ + c2 * b2 / (sp.symbols("y") - b2) y = sp.symbols("y") N = sp.expand(sp.numer(sp.together(F))) cfs = sp.Poly(N, y).all_coeffs() e1 = sp.simplify(-cfs[1] / cfs[0]) e2 = sp.simplify(cfs[2] / cfs[0]) okF = sp.simplify(e1 - (B1 + yt_e)) == 0 okG = sp.simplify(e2 - (b1 * b2 + (A4 - A2 * B1) / A0)) == 0 r1, r2 = sp.symbols("r1 r2", real=True) okH = sp.simplify((r1 ** 2 + r2 ** 2) - ((r1 + r2) ** 2 - 2 * r1 * r2)) == 0 kapv = sp.symbols("kapv", positive=True) okI = sp.simplify(B1 / (B1 / kapv) - kapv) == 0 \ and sp.simplify((B1 / kapv) * kapv - B1) == 0 check("A3 Fujiwara circularity + the Vieta pinch killed", okF and okG and okH and okI, "the Fujiwara m = 1 term == B_1 + y_t EXACTLY (the Vieta " "trace, generic; ARGMAX at every rung in the record): the " "sharpest classical root bound RESTATES the trace, bound " ">= 2(1 + kappa) y_t > y_t; e_2 == b_1 b_2 + (A_4 - A_2 " "B_1)/A_0 generic -- EVERY symmetric function carries " "1/A_0 (no y_t-free pinch in the ring); y_t == B_1/kappa " "is a REFORMULATION (typed, not an advance); Newton p_2 " "== e_1^2 - 2 e_2") # ================================================ B: routes + rates section("B. THE A_0 ROUTE (LOOP) + THE RATE DICTIONARY + " "ADMISSIBILITY") tri_inst = bool(sp.Rational(7, 10) <= 4 * (sp.Rational(1, 3) + sp.Rational(2, 5)) / sp.Rational(1, 2)) tau_s, G_s, tl_s = sp.symbols("tau_s G_s tl_s", positive=True) A0sq = tau_s / (8 * G_s * tl_s) okJ = sp.simplify(8 * A0sq * G_s * tl_s - tau_s) == 0 chain_a0 = { "TAUPOS": ["A0FLOOR"], "TLAWCAP": ["A0FLOOR"], "A0FLOOR": ["TOPROOT"], "TOPROOT": ["RATE"], "RATE": ["JETMASS"], "JETMASS": ["SIGMAFLOOR"], "SIGMAFLOOR": ["DTSTEP_K"], "DTSTEP_K": ["TAUPOS"]} loop_a0 = has_cycle(chain_a0) check("B1 the A_0-triangle route DOUBLY DEAD (vacuous + loop)", tri_inst and okJ and loop_a0, "y_t <= b_top C_1/|A_0| (triangle, exact instance) is " "exponentially VACUOUS (record overshoot 10^3.4 -> " "10^64.6 riding -log10|A_0| slope 0.97: the bound loses " "EXACTLY the cancellation); the only A_0-floor is the " "zero-jet rearrangement A_0^2 == tau/(8 G tlaw_0) which " "consumes {TAUPOS, TLAWCAP}: the cycle TAUPOS/TLAWCAP -> " "A0FLOOR -> TOPROOT -> ... -> DTSTEP_K -> TAUPOS " "DETECTED (THE FOURTH FLAGGED LOOP ROUTE, not consumed)") q = sp.symbols("q", positive=True) Glead = lambda T: (sp.log(T / (2 * sp.pi)) + 1) / (2 * sp.pi * T) # noqa: E731 okK = True for p_e in (3, 4, 5): pe = sp.Integer(p_e) expr = h ** (pe / 2 - 1) * Glead(q * h ** (pe / 2)) \ / Glead(2 * sp.pi * h) okK = okK and sp.simplify(sp.limit(expr, h, sp.oo) - sp.pi * pe / q) == 0 a_s, c_s = sp.symbols("a_s c_s", positive=True) okL = sp.simplify((3 * sp.pi / c_s) * (1 + 2 * a_s / 3) - sp.pi * (2 * a_s + 3) / c_s) == 0 a4 = sp.Integer(4) kc = sp.symbols("kc", positive=True) expr4 = (sp.sqrt(h) * Glead(kc * h ** (sp.Rational(3, 2) + a4)) / Glead(2 * sp.pi * h) * h ** a4) okM = sp.simplify(sp.limit(expr4, h, sp.oo) - 2 * sp.pi * (sp.Rational(3, 2) + a4) / kc) == 0 check("B2 the rate dictionary a == p/2 - 1 (proven p = 3, 4, 5)", okK and okL and okM, "lim h^{p/2-1} G_lead(q h^{p/2})/G_lead(2 pi h) == pi p/q " "at p = 3, 4, 5 (p = 4 replicates the r171 4 pi/q): " "TOPROOT(p) ==> sigma-floor exponent a = p/2 - 1 EXACT; " "census constant (3 pi/c)(1 + 2a/3) == pi(p + 1)/c; " "absorption holds even at a = 4 (limit 11 pi/kappa_c): " "NO finite asymptotic ceiling (r169-SF4)") def G_num(T): # the HSW-corrected density envelope (r168/r169/r171/r172 # VERBATIM): G_lead + the HSW22 Cor. 1.2 correction terms al, be, cc = 0.1038, 0.2573, 9.3675 lg = math.log(T) ll = math.log(lg) t1 = (math.log(T / (2 * math.pi)) + 1) / (2 * math.pi * T) t2 = (al * (2 * lg + 1) / 2 + be * (ll + 1 / (2 * lg)) + cc) / T ** 2 t3 = (al * lg + be * ll + cc) / T ** 2 return t1 + t2 + t3 eps56 = math.sqrt(56.0) * G_num(float(T_PT)) / G_num(2 * math.pi * 56.0) amax = math.log(PIN_RATE_C / eps56) / math.log(56.0) pmax = 2 * (1 + amax) okN = abs(eps56 / PIN_EPS56 - 1) <= 5e-3 \ and abs(amax / PIN_AMAX - 1) <= 5e-3 \ and abs(pmax / PIN_PMAX - 1) <= 5e-3 okO = PIN_P_ALL <= pmax - 4.0 check("B3 admissibility RECOMPUTED: p_max = 10.27, margin >= 4", okN and okO, "eps_closed(56) = sqrt(56) G(T_PT)/G(2 pi 56) = %.6e " "(frozen 4.533792e-9); a_max = ln(0.0767/eps)/ln 56 = " "%.6f; p_max = 2(1 + a_max) = %.6f: the measured p_all = " "%.4f leaves %.1f powers of h of margin -- the census " "schedule absorbs the quartic law with room to exponent " "10" % (eps56, amax, pmax, PIN_P_ALL, pmax - PIN_P_ALL)) W = sp.Integer(1000) dpl = A2 * (W - 1) / (b2 - b1) A0w = c0 - (c1 + dpl) + (c2 + dpl) A2w = -(c1 + dpl) * b1 + (c2 + dpl) * b2 okP = sp.simplify(A0w - A0) == 0 okQ = sp.simplify(A2w - W * A2) == 0 okR = sp.simplify(sp.Abs(dpl) - sp.Abs(A2) * (W - 1) / db) == 0 okS = PIN_WIT_THETA_INFL > THETA_BAR \ and PIN_WIT_SCALE[13] <= -15.0 \ and abs(PIN_WIT_DNORM["infl"] / PIN_WIT_DNORM["defl"] - 1000.0) <= 1.0 check("B4 witness both directions: H3 refutable, TOPROOT not " "norm-continuous", okP and okQ and okR and okS, "inflation d+ = A_2(W-1)/(b_2-b_1): A_0'' == A_0 and " "y_t'' == W y_t EXACT generic (b_2 = b_1 + db); theta'' " "= %.3f > bar %.3f: H3 REFUTED IN THE WITNESS WORLD (the " "certificate is falsifiable); the price |d+|/max|c| = " "8.1e-2 (h=5) -> 10^%.1f (h=13): an EXPONENTIALLY small " "source perturbation moves y_t by ANY polynomial factor " "-- TOPROOT-NOT-NORM-CONTINUOUS (any proof must consume " "the arithmetic sign structure)" % (PIN_WIT_THETA_INFL, THETA_BAR, PIN_WIT_SCALE[13])) # ================================================ C: graphs section("C. THE ENDGAME GRAPHS (four loops; terminal chain)") chain_uni = {"RH": ["CENSUS_ALLK"], "CENSUS_ALLK": ["DTSTEP"], "DTSTEP": ["HCOF"], "HCOF": ["RH"]} chain_pin = {"SIGMAFLOOR": ["DTSTEP_K"], "DTSTEP_K": ["TAUPOS"], "TAUPOS": ["SIGMAFLOOR"]} chain_term = { "H3_PER_RUNG": ["RATE"], "H3_COFINAL": ["RATE"], "ENVJ-H1": ["JETMASS"], "CENSUS-H2": ["JETMASS"], "GONEK": ["WF"], "WF": ["JETMASS"], "RATE": ["JETMASS"], "CENSUS_K": ["DCLEG", "DTSTEP_K"], "DCLEG": ["SIGMAFLOOR"], "JETMASS": ["SIGMAFLOOR"], "SIGMAFLOOR": ["DTSTEP_K"], "DTSTEP_K": ["HCOF"], "HCOF": ["RH"]} okT = has_cycle(chain_uni) and has_cycle(chain_pin) \ and has_cycle(chain_a0) and not has_cycle(chain_term) okU = all("RH" in reachable(chain_term, sname) for sname in ("H3_COFINAL", "CENSUS_K", "GONEK")) check("C1 graphs: four loop routes flagged; TOPROOT-MEAS " "ancestor eliminated", okT and okU, "universalized-census, pinning-supply and A0-floor cycles " "DETECTED (+ tlaw-window: FOUR flagged routes, none " "consumed); the terminal chain with {H3_PER_RUNG, " "H3_COFINAL} -> RATE replacing TOPROOT-MEAS is ACYCLIC " "with RH reachable only from the counterfactual grants " "(AND-semantics); H3's ancestor set == {SOURCE}: same " "purity class as H1; NO RH CLAIM") # ================================================ D: pinned tables section("D. PINNED LADDERS (consistency arithmetic)") margins = [THETA_BAR / v for v in PIN_THETA_Y.values()] okth = all(0.03 < v < 0.12 for v in PIN_THETA_Y.values()) \ and min(margins) >= PIN_H3_MARGIN_MIN \ and PIN_THETA_Y[4] < PIN_THETA_Y[30] caps = {k: 1 + 2 * v for k, v in PIN_RHO.items()} okcap = all(1.15 < v < 1.45 for v in caps.values()) \ and all(PIN_CSTAR[k] <= caps[k] for k in PIN_CSTAR) check("D1 H3 certified 26/26 (margin >= 1.99) + TR-CAP vs H1", okth and okcap, "theta_y = %s in (0.03, 0.12) at all 25 rungs + holdout " "h = 30 (K = 128, deg-127); H3 margin bar/theta >= %.2f " "everywhere; rho == |J_2| (argmax 1) with cap 1 + 2 rho " "= %.2f -> %.2f vs certified c* = %s: ENVJ-SHARPER (the " "new cap never beats the certified half-plane constant)" % ({k: PIN_THETA_Y[k] for k in (4, 30)}, min(margins), min(caps.values()), max(caps.values()), PIN_CSTAR)) okgl = 3.0 < PIN_P_ALL < 5.5 and PIN_HOLD_RESID <= 0.08 \ and abs(PIN_P_ALL / 2 - 1 - 1.057) <= 0.25 \ and min(PIN_SEP_FACTORS) >= 10.0 check("D2 growth law + holdout + dictionary + size separator", okgl, "p_all = %.4f in the r143 window (3.0, 5.5); deep holdout " "h = 30 EXCLUDED from the fit, predicted with residual " "-%.3f dex; dictionary a_pred = p/2 - 1 = %.4f vs the " "r171 record 1.057 (closes within 0.093 tightened in " "v933); SIZE-SEPARATOR vs fake worlds: factors %s >= 10 " "(theta_w <= 1.9e-3 vs MAIN 0.045-0.078)" % (PIN_P_ALL, PIN_HOLD_RESID, PIN_P_ALL / 2 - 1, PIN_SEP_FACTORS)) print("\n [TYPED, BH7-F1 ADOPTED] THE RESIDUE: the composed " "per-block") print(" hypothesis is the TRIPLE {H1 AND H2 AND H3}-cofinal " "(one rung per") print(" dyadic block, all three at the same h -- NOT H3 " "alone) + {Gonek") print(" constants: priced v934} + {census-forall-k == LOOP} + " "{L1, WPD}.") print(" Census cardinality 4 UNCHANGED. NOT RH evidence. NO " "RH claim.") return 0 def run(): global CHECKS, FAILS CHECKS = [] FAILS = [] print("=" * 74) print("v932 -- PRIME.TOPROOT.THETA.01 (TOPROOT stated " "SEQ-cofinal, three locked") print("forms; rate dictionary a = p/2 - 1 proven; TR-CAP proven " "circular-for-") print("TOPROOT; H3 quartic certificate; round 172; 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("v932: %d/%d checks passed | verdict %s | runtime %.1f s" % (n_run - len(fails), n_run, verdict, time.time() - T_ALL)) print("PINNING: T1/TR-CAP/dictionary/admissibility/witness " "algebra recomputed") print("in-run; the theta/rho/lock ladders PINNED from " "toproot_theta_probe.py") print("(SPEC %s, 33/33, record 2813 s + deterministic re-run, " "all logs kept," % PIN_SPEC_R172) print("RE-RUN GREEN AS TYPED 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.TOPROOT.THETA.01 TOPROOT statement + quartic " "certificate: %d passed, %d failed ---" % (n_run - len(fails), len(fails))) return 0 if ok else 1 if __name__ == "__main__": raise SystemExit(run())