#!/usr/bin/env python3 # -*- coding: utf-8 -*- r"""v951 -- PRIME.CANCELLATION.FUNCTIONAL.01: THE ACF LAW + THE POLE SQUARE + THE ARCH LAW of round 195 -- the wall is a CLOSED TRUNCATED WEIL-EXPLICIT-FORMULA FUNCTIONAL of the positive-definite test function g_x, with per-atom manifest positivity PROVABLY IMPOSSIBLE (Wiener-Khinchin) and the measured sign law + localization; PLUS THE BUGHUNT-X KD PIN, RECOMPUTED IN-RUN: the arch kernel is THE CLASSICAL WEIL ARCHIMEDEAN KERNEL in the L -> infinity limit -- the arc's designated external handoff object. THE THREE EXACT LAWS (all recomputed in-run). (1) THE ACF LAW: for an atom (u, w) with u <= L = 2a, the atom's TOTAL wall contribution (the Loewner divided-difference off-diagonal PLUS the r189/v947 cosine diagonal shift) is ONE kernel w W(u) with x^T W(u) x = -2 int_0^{L-u} A_x(t) A_x(t + u) dt, A_x(t) = sum_k x_k cos(om_k t) -- MINUS TWICE THE APERIODIC AUTOCORRELATION of the windowed mode polynomial at lag log q: r189's 'both quadratures in different slots' IS ONE OBJECT. In-run: the generic convolution identity 2 int_0^u cos(om_i (u - t)) cos(om_j t) dt == (f_i - f_j)/(b_i - b_j) (sympy, no periodicity), the k = 0 slice x = e_0 ==> g(u) = L - u exactly (the norm-doubling wraparound in its simplest exact slice), and the FULL kernel-vs-quadrature ward at h = 4 AND h = 5 (own wall build, every atom, mp oscillation-split quadrature). (2) THE POLE SQUARE: x^T RawP x = 8 sinh^2(a/2) (int_0^infty e^{-t/2} A_x dt)^2 EXACTLY -- a manifest L^2 square (the v947 Herglotz point mass in integral form); recomputed SYMBOLICALLY GENERIC (any modes, via the Laplace closed form int e^{-t/2} cos(om t) dt = (1/2)/(1/4 + om^2)) and numerically at h = 4, 5. (3) THE ARCH LAW (closed the r189 open arch item): DeltaArch_k = -mult_k L (kappa(om_k) + c*) with kappa the Ci-regularized cosine transform of the arch measure and c* = (gamma + ln 2 pi)/2 EXACTLY, k-independent including k = 0 -- recomputed at h = 4 and h = 5 for EVERY mode k (own arch integrals; k-independence and the closed form gated). THE KD PIN (Bughunt X, F4 POSITIVE, note-only per precedent -- recomputed in-run HERE as the promoted surface): in the L -> infinity limit the arch kernel IS the classical Weil archimedean kernel, kappa(om) + c* --> -1/2 [Re psi(1/4 + i om/2) - ln pi] (verified in-run at L = 80 on om = 0.5, 1, 2, 5, 11 to <= 1e-14 class; Bughunt X's own verification 6e-18), with the finite-L corrections O(e^{-L/2}) TYPED NOT-SMALL at the reachable rungs -- the finite-rung wall is NOT the classical kernel, it LIMITS to it. This is the arc's cleanest external handoff object: the wall's arch leg speaks the textbook explicit-formula language exactly in the window limit. PER-ATOM POSITIVITY PROVABLY IMPOSSIBLE (Wiener-Khinchin): g_x-hat = |B_x-hat|^2 >= 0, so each atom samples a positive-definite function WITH A MINUS SIGN; the exhibit x = e_0 gives x^T W(u) x = 2(u - L) < 0 for u < L (exact in-run) -- the too-good outcome (per-atom manifest positivity) is EXCLUDED, not just unobserved. THE MEASURED ANATOMY (pinned): budgets at the collapsing direction (mp inverse iteration, every rung) pole P = 1.281 -> 2.632 > 0, arch A = -1.251 -> -2.517, prime Pr = -0.031 -> -0.115 across h = 4 -> 20 -- THE POLE ALONE CARRIES POSITIVITY; cancellation depth -11.11 -> -88.25 == the tau ladder (DEFINITIONAL); concentration CI = 11.3 -> 88.7 dex (TOTAL in the collapsing direction, O(1)-partial elsewhere). THE SIGN LAW (the round's cleanest measured finding): at v_0 EVERY resolvable atom contributes NEGATIVELY (n+ = 0 at ALL 14 rungs), decaying near-exponentially in log q, the commensurate q = h atom EXACTLY ZERO; LOCALIZATION m99 = 1..2 of 3..12 atoms (q = 2, sometimes + q = 3, carries the prime total); COMPENSATION IS ATOMS-VS-POLE, NOT ATOM-VS-ATOM. Complementarity rho_min = 1.16..2.91 >= 1 everywhere with finite margin -- and NECESSARY-NOT-SUFFICIENT (amendment A2 honest: rho_min >= 1 holds in the indefinite SCRARITH/EPSTEIN cells too); SMOOTH has an EMPTY L_f-negative subspace (the commensurability mechanism in anatomy coordinates); ATOMJET exactly linear; tau screens flat. RE-RUN GREEN AS TYPED AT PROMOTION: cancellation_functional_ probe.py round 195 (note DXVIII (518), contract PRIME. CANCELLATION.FUNCTIONAL.01), 24/24 gates, SPEC_SHA a50b85bb112513a1 (UNTOUCHED by the Bughunt-X corrections -- the KD pin is note-only per precedent, the spec hash verified unchanged), record 1036 s + 1061 s deterministic re-run (timing-normalized diff empty, all logs kept, FOUR pre-freeze amendments disclosed: A1 warded antiderivatives; A2 worlds enum corrected; A3 THE SUBSTANTIVE ONE -- float64 bottom eigenvectors are direction-noise below the tau gap, the pass-1 mixed-sign ladders were artifacts, reversed to one-signed after the mp cross-check, the anatomy moved to mp inverse iteration everywhere; A4 gap-limited invit ward bars), re-run at promotion 1102.8 s, 24/24 -- log kept as cancellation_functional_probe.promo_rerun.log. HONEST PRICING (adopted verbatim): the Weil-ACF rewrite is EXACT AND NEW but an ALGEBRAIC RESTATEMENT -- the residual object (the pole square dominating the weighted autocorrelation samples, cofinally) IS the wall: the relabeling barrier is NAMED, NOT CROSSED; WEIL-ALLTESTS <-> RH is a FLAGGED LOOP consumed by NOTHING. THE RESIDUE (canonical, notes DII/DXVI/DXXIV): {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 cancellation_functional_probe.py (round 195, 2026-08-21, note DXVIII); consumes v947 (the Loewner-Pick dictionary whose two slots this round unifies into one ACF object); externally covered by Bughunt X (round 199, note DXXIII: THE ACF/pole/arch laws reproduced in FULLY OWN CODE to <= 1e-61, c* exact, and the F4/KD positive pin -- the arch kernel is the classical Weil archimedean kernel in the L -> infinity limit, verified 6e-18; note DXXIV: KD note-only per precedent). Python-only per GATE.WOLFRAM.02. """ from __future__ import annotations import math import time import mpmath as mp T_ALL = time.time() # ---------------------------------------------------------------- pinned PIN_SPEC_R195 = "a50b85bb112513a1" PIN_ASM_DEV = 1.7e-61 # ACF law, all 14 rungs (record) PIN_QUAD_WARD = 2.7e-31 PIN_POLE_SQ = 4.5e-61 PIN_ARCH_KIND = 3.1e-61 # k-independence at h = 4, 5 PIN_BH10_OWN = 1e-61 # BH10 own-code recompute class PIN_KD_BH10 = 6e-18 # BH10 digamma-limit verification PIN_BUDGETS = ((1.281, 2.632), (-1.251, -2.517), (-0.031, -0.115)) PIN_DEPTH = (-11.11, -88.25) # == the tau ladder, definitional PIN_CI = (11.3, 88.7) PIN_SIGNS_NPLUS = 0 # at ALL 14 rungs PIN_M99 = (1, 2) PIN_RHO_MIN = (1.16, 2.91) PIN_CTRL_RHO = {"SCRARITH": 1.0992, "EPSTEIN": 1.1199} PIN_SMOOTH_NNEG = 0 PIN_JET_DEVS = (3.0e-61, 8.3e-61) PIN_SLOPES = (-0.005, 0.000, 0.001) # nneg/match/m99 -- all flat KD_L = 80 KD_OMS = (0.5, 1, 2, 5, 11) KD_BAR = 1e-13 ACF_BAR = 1e-25 ARCH_BAR = 1e-28 N_CHECKS = 10 EXPECTED = "WALL-IS-WEIL-ACF-FORM-EXACT" 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) # ------------------------------------------------- own wall ingredients def r_of(w): if w == 0: return mp.mpf("0.25") return mp.exp(-w / 2) / (-mp.expm1(-2 * w)) - 1 / (2 * w) def sieve_atoms(h): icap = int(h) comp = [False] * (icap + 1) nlist = [] for p in range(2, icap + 1): if comp[p]: continue for m in range(p * p, icap + 1, p): comp[m] = True q = p while q <= icap: nlist.append((q, p)) q *= p nlist.sort() return [(mp.log(q), mp.log(p) / mp.sqrt(q)) for q, p in nlist] def cell(h, dps): """Node lattice + atoms at rung h (r171-r198 conventions).""" with mp.workdps(dps): aa = mp.log(h) / 2 K = int(math.ceil(1.25 * h * math.log(h))) L = 2 * aa oms = [k * mp.pi / aa for k in range(K)] b = [o * o for o in oms] return dict(aa=aa, K=K, L=L, oms=oms, b=b, atoms=sieve_atoms(h)) def W_atom(u, oms, b, L, K): """The r195 ACF kernel W(u) (Raw coordinates).""" W = mp.zeros(K, K) for i in range(K): for j in range(i): W[i, j] = 2 * (oms[i] * mp.sin(oms[i] * u) - oms[j] * mp.sin(oms[j] * u)) / (b[i] - b[j]) W[j, i] = W[i, j] W[0, 0] = 2 * (u - L) for k in range(1, K): W[k, k] = mp.sin(oms[k] * u) / oms[k] \ + (u - L) * mp.cos(oms[k] * u) return W def acf_quad(x, u, oms, L, K): """-2 int_0^{L-u} A_x(t) A_x(t+u) dt by oscillation-split quad.""" om_max = oms[-1] if K > 1 else mp.mpf(1) def integrand(t): A1 = sum(x[k] * mp.cos(oms[k] * t) for k in range(K)) A2 = sum(x[k] * mp.cos(oms[k] * (t + u)) for k in range(K)) return A1 * A2 top = L - u npts = max(int(mp.floor(top * om_max / mp.pi)), 1) pts = [top * j / npts for j in range(npts + 1)] return -2 * mp.quad(integrand, pts) def kappa_of(om, L): """Ci-regularized cosine transform of the arch measure.""" if om == 0: npts = 8 pts = [L * j / npts for j in range(npts + 1)] return mp.log(L) / 2 + mp.quad(r_of, pts) npts = max(int(mp.floor(L * om / mp.pi)), 1) pts = sorted(set( [mp.mpf(0), L] + [j * mp.pi / om for j in range(1, npts + 1) if j * mp.pi / om < L])) integ = mp.quad(lambda w: mp.cos(om * w) * r_of(w), pts) return mp.ci(L * om) / 2 - (mp.euler + mp.log(om)) / 2 + integ def arch_diag(h, k, aa, L, om): """The builder arch diagonal entry (own transcription of the documented r171+ arch recipe; BH9/BH10 lineage).""" if k == 0: f0 = L psi_d = lambda w: L - w # noqa: E731 else: f0 = aa psi_d = (lambda w, o=om: (aa - w / 2) * mp.cos(o * w) - mp.sin(o * w) / (2 * o)) integrand = (lambda w, f0=f0, psi_d=psi_d: (f0 * mp.exp(-2 * w) - psi_d(w) * mp.exp(-w / 2)) / (-mp.expm1(-2 * w))) npts = max(int(mp.floor(L * om / mp.pi)), 1) if k else 1 base = [mp.mpf(0), mp.mpf("1e-6"), mp.mpf("1e-3"), mp.mpf("0.05"), L] if k: base += [j * mp.pi / om for j in range(1, npts + 1)] pts = sorted(set(p for p in base if p <= L)) body = mp.quad(integrand, pts) tail = -f0 / 2 * mp.log1p(-mp.exp(-2 * L)) return -f0 * (mp.euler + mp.log(mp.pi)) + 2 * (body + tail) def farch_prime(k, om, L, aa): """Canonical Loewner diagonal f_arch'(b_k) = J/om + J' at the node (sin(L om_k) = 0); k = 0 by the exact limit.""" if k == 0: npts = 8 pts = [L * j / npts for j in range(npts + 1)] iwr = mp.quad(lambda w: w * r_of(w), pts) return 2 * iwr + L npts = max(int(mp.floor(L * om / mp.pi)), 1) pts = sorted(set( [mp.mpf(0), L] + [j * mp.pi / om for j in range(1, npts + 1) if j * mp.pi / om < L])) J = mp.quad(lambda w: mp.sin(om * w) * r_of(w), pts) \ + mp.si(L * om) / 2 Jp = mp.quad(lambda w: w * mp.cos(om * w) * r_of(w), pts) return J / om + Jp def part(): import sympy as sp # ================================================ A: exact layer section("A. THE EXACT LAYER (sympy generic)") u_, t_ = sp.symbols("u t", positive=True) oi, oj = sp.symbols("omega_i omega_j", positive=True) integrand = 2 * sp.cos(oi * (u_ - t_)) * sp.cos(oj * t_) # explicit product-to-sum antiderivative, WARDED by symbolic # differentiation (the r195 amendment-A1 route: sympy's own # integrate returns a Piecewise that defeats simplify) F = -sp.sin(oi * u_ - (oi + oj) * t_) / (oi + oj) \ - sp.sin(oi * u_ - (oi - oj) * t_) / (oi - oj) ward = sp.simplify(sp.expand_trig(sp.diff(F, t_) - integrand)) conv = F.subs(t_, u_) - F.subs(t_, 0) f_i, f_j = 2 * oi * sp.sin(oi * u_), 2 * oj * sp.sin(oj * u_) okA = ward == 0 and sp.simplify(sp.expand_trig(sp.expand( (conv - (f_i - f_j) / (oi ** 2 - oj ** 2)) * (oi ** 2 - oj ** 2)))) == 0 check("A1 the generic convolution identity (the ACF law's " "engine, exact)", okA, "2 int_0^u cos(om_i(u - t)) cos(om_j t) dt == (f_i - " "f_j)/(b_i - b_j) with f = 2 om sin(om u) (sympy, no " "periodicity assumed; explicit antiderivative warded by " "differentiation, the probe's amendment-A1 route): the " "Loewner divided difference IS a convolution of the two " "modes -- the off-diagonal slot of the ACF law") a_ = sp.symbols("a", positive=True) L_ = 2 * a_ # k = 0 slice: x = e_0, A(t) = 1: g(u) = int_0^{L-u} 1 = L - u g_e0 = sp.integrate(sp.Integer(1), (t_, 0, L_ - u_)) okB = sp.simplify(g_e0 - (L_ - u_)) == 0 check("A2 the k = 0 wraparound slice: x = e_0 ==> g(u) = L - u " "(exact)", okB, "W(u)[0, 0] = 2(u - L) == -2 int_0^{L-u} 1 dt exactly " "(the mult_0 = 2 norm-doubling IS the wraparound of the " "k = 0 mode): per-atom manifest positivity is already " "impossible here -- x = e_0 gives x^T W x = 2(u - L) < 0 " "for every interior lag (the Wiener-Khinchin kill's " "exact exhibit)") b_ = sp.symbols("b", positive=True) om_ = sp.sqrt(b_) lap = sp.integrate(sp.exp(-t_ / 2) * sp.cos(om_ * t_), (t_, 0, sp.oo)) okC = sp.simplify(lap - sp.Rational(1, 2) / (sp.Rational(1, 4) + b_)) == 0 x1, x2, x3 = sp.symbols("x1 x2 x3", real=True) b1, b2, b3 = sp.symbols("b1 b2 b3", positive=True) s2 = 2 * sp.sinh(a_ / 2) ** 2 xs, bs = (x1, x2, x3), (b1, b2, b3) quad_form = sum( xs[i] * xs[j] * s2 / ((sp.Rational(1, 4) + bs[i]) * (sp.Rational(1, 4) + bs[j])) for i in range(3) for j in range(3)) lap_sq = 8 * sp.sinh(a_ / 2) ** 2 * sum( xs[i] * sp.Rational(1, 2) / (sp.Rational(1, 4) + bs[i]) for i in range(3)) ** 2 okD = sp.simplify(quad_form - lap_sq) == 0 check("A3 THE POLE SQUARE, generic (a manifest L^2 square, " "exact)", okC and okD, "int_0^inf e^{-t/2} cos(om t) dt == (1/2)/(1/4 + b) " "(Laplace closed form) and x^T RawP x == 8 sinh^2(a/2) " "(int_0^inf e^{-t/2} A_x dt)^2 for generic 3-mode data " "(sympy exact): the pole block is EXACTLY the square of " "the Laplace transform of the mode polynomial -- the " "v947 Herglotz point mass in integral form, manifestly " "PSD") # ================================================ B: h = 4, 5 wards section("B. THE LAWS AT h = 4 AND h = 5 (own wall build, mp)") acf_worst = mp.mpf(0) pole_worst = mp.mpf(0) for h in (4, 5): dps = 60 with mp.workdps(dps): ce = cell(h, dps) K, L, oms, b = ce["K"], ce["L"], ce["oms"], ce["b"] phi = (1 + mp.sqrt(5)) / 2 xg = [mp.frac((k + 1) * phi) - mp.mpf("0.5") for k in range(K)] for (u, w) in ce["atoms"]: W = W_atom(u, oms, b, L, K) form = sum(xg[i] * W[i, j] * xg[j] for i in range(K) for j in range(K)) quadv = acf_quad(xg, u, oms, L, K) rel = abs(form - quadv) / max(abs(form), mp.mpf("1e-30")) acf_worst = max(acf_worst, rel) # pole square numeric s2v = mp.sinh(ce["aa"] / 2) ** 2 formP = sum(xg[i] * xg[j] * 2 * s2v / ((mp.mpf(1) / 4 + b[i]) * (mp.mpf(1) / 4 + b[j])) for i in range(K) for j in range(K)) lapv = sum(xg[k] / (2 * (mp.mpf(1) / 4 + b[k])) for k in range(K)) sq = 8 * s2v * lapv ** 2 pole_worst = max(pole_worst, abs(formP - sq) / abs(formP)) okE = acf_worst < ACF_BAR and pole_worst < 1e-45 check("B1 THE ACF LAW + THE POLE SQUARE at h = 4, 5 (every " "atom, mp)", okE, "x^T W(u_q) x == -2 int_0^{L-u} A_x A_x(. + u) dt at " "EVERY atom of both rungs for the golden probe vector " "(worst rel dev %.1e, bar %.0e; oscillation-split " "quadrature, dps 60) and the pole square holds " "numerically (worst %.1e): the probe gates the same " "objects at all 14 rungs to <= %.1e (assembly) / %.1e " "(quad wards) / %.1e (pole square); Bughunt X reproduced " "them in fully own code to <= 1e-61" % (float(acf_worst), ACF_BAR, float(pole_worst), PIN_ASM_DEV, PIN_QUAD_WARD, PIN_POLE_SQ)) arch_worst = mp.mpf(0) kind_spread = mp.mpf(0) for h in (4, 5): dps = 60 with mp.workdps(dps): cstar = (mp.euler + mp.log(2 * mp.pi)) / 2 ce = cell(h, dps) K, L, oms, aa = ce["K"], ce["L"], ce["oms"], ce["aa"] cvals = [] for k in range(K): adiag = arch_diag(h, k, aa, L, oms[k]) fap = farch_prime(k, oms[k], L, aa) delta = adiag - fap mult = 2 if k == 0 else 1 ck = -delta / (mult * L) - kappa_of(oms[k], L) cvals.append(ck) arch_worst = max(arch_worst, abs(ck - cstar)) kind_spread = max(kind_spread, max(cvals) - min(cvals)) okF = arch_worst < ARCH_BAR and kind_spread < ARCH_BAR check("B2 THE ARCH LAW at h = 4, 5 (every mode k incl. k = 0; " "c* exact)", okF, "DeltaArch_k = RawA[k, k] - f_arch'(b_k) == -mult_k L " "(kappa(om_k) + c*) with kappa the Ci-regularized cosine " "transform and c* = (gamma + ln 2 pi)/2: recomputed at " "EVERY mode of h = 4 (K = 7) and h = 5 (K = 11) -- " "worst |c*_k - (gamma + ln 2pi)/2| = %.1e, k-spread " "%.1e (bar %.0e; probe: k-independence <= %.1e, c* " "exact at working precision): the r189 open arch item " "is CLOSED -- the wall is a closed truncated Weil form" % (float(arch_worst), float(kind_spread), ARCH_BAR, PIN_ARCH_KIND)) # ================================================ C: the KD pin section("C. THE KD PIN: THE ARCH KERNEL IS THE CLASSICAL WEIL " "KERNEL (L -> inf)") kd_worst = mp.mpf(0) with mp.workdps(40): cst = (mp.euler + mp.log(2 * mp.pi)) / 2 for om in KD_OMS: omv = mp.mpf(om) lhs = kappa_of(omv, mp.mpf(KD_L)) + cst rhs = -(mp.re(mp.digamma(mp.mpf(1) / 4 + mp.mpc(0, 1) * omv / 2)) - mp.log(mp.pi)) / 2 kd_worst = max(kd_worst, abs(lhs - rhs)) okG = kd_worst < KD_BAR check("C1 KD RECOMPUTED: kappa + c* --> -1/2 [Re psi(1/4 + " "i om/2) - ln pi]", okG, "at L = %d and om in %s: worst |kappa(om) + c* - " "classical| = %.1e (bar %.0e; Bughunt X's own " "verification %.0e at higher dps): THE ARCH KERNEL IS " "THE CLASSICAL WEIL ARCHIMEDEAN KERNEL IN THE L -> " "infinity LIMIT -- the finite-L corrections are " "O(e^{-L/2}) and TYPED NOT-SMALL at the reachable rungs " "(L = log h <= 3): the finite-rung wall is not the " "classical kernel, it LIMITS to it -- the arc's external " "handoff pin (the wall's arch leg speaks the textbook " "explicit-formula language exactly in the window limit)" % (KD_L, str(KD_OMS), float(kd_worst), KD_BAR, PIN_KD_BH10)) # ================================================ D: pinned anatomy section("D. THE MEASURED ANATOMY (pinned, typed measured)") okH = PIN_BUDGETS[0][0] > 0 and PIN_BUDGETS[0][1] > 0 \ and PIN_BUDGETS[1][1] < PIN_BUDGETS[1][0] < 0 \ and PIN_BUDGETS[2][1] < PIN_BUDGETS[2][0] < 0 \ and PIN_DEPTH[1] < PIN_DEPTH[0] < 0 check("D1 THE POLE ALONE CARRIES POSITIVITY (budgets at v_0; " "depth == tau)", okH, "budgets at the collapsing direction (mp inverse " "iteration): pole P = %.3f -> %.3f > 0, arch A = %.3f -> " "%.3f, prime Pr = %.3f -> %.3f across h = 4 -> 20, " "cancelling to depth %.2f -> %.2f == the tau ladder " "(DEFINITIONAL, typed); concentration CI = %.1f -> %.1f " "dex: the cancellation is TOTAL in the collapsing " "direction, O(1)-partial elsewhere" % (PIN_BUDGETS[0][0], PIN_BUDGETS[0][1], PIN_BUDGETS[1][0], PIN_BUDGETS[1][1], PIN_BUDGETS[2][0], PIN_BUDGETS[2][1], PIN_DEPTH[0], PIN_DEPTH[1], PIN_CI[0], PIN_CI[1])) okI = PIN_SIGNS_NPLUS == 0 and PIN_M99 == (1, 2) check("D2 THE SIGN LAW + LOCALIZATION (n+ = 0 at all 14 " "rungs)", okI, "at v_0 EVERY resolvable atom contributes NEGATIVELY " "(n+ = %d at ALL 14 rungs -- each autocorrelation sample " "g_v(log q) > 0), near-exponential decay in log q, the " "commensurate q = h atom EXACTLY ZERO; localization " "m99 = %d..%d of 3..12 atoms (q = 2, sometimes + q = 3, " "carries the prime total): COMPENSATION IS ATOMS-VS-" "POLE, NOT ATOM-VS-ATOM" % (PIN_SIGNS_NPLUS, PIN_M99[0], PIN_M99[1])) okJ = PIN_RHO_MIN[0] >= 1 \ and all(v >= 1 for v in PIN_CTRL_RHO.values()) \ and PIN_SMOOTH_NNEG == 0 \ and all(abs(s) <= 0.30 for s in PIN_SLOPES) \ and max(PIN_JET_DEVS) < 1e-28 check("D3 complementarity NECESSARY-NOT-SUFFICIENT; worlds; " "screens flat", okJ, "rho_min = %.2f..%.2f >= 1 everywhere (finite margin) -- " "and >= 1 ALSO in the indefinite SCRARITH/EPSTEIN cells " "(%s: amendment A2 honest -- NOT a world detector); " "SMOOTH has an EMPTY L_f-negative subspace (n_neg = %d: " "the v949 commensurability mechanism in anatomy " "coordinates); ATOMJET exactly linear (devs %s); tau " "screens %s ALL FLAT; the identity itself is world-blind " "linear algebra (typed, never sold)" % (PIN_RHO_MIN[0], PIN_RHO_MIN[1], str(PIN_CTRL_RHO), PIN_SMOOTH_NNEG, str(PIN_JET_DEVS), str(PIN_SLOPES))) okK = True # adjudication/pricing check("D4 HONEST PRICING: an ALGEBRAIC RESTATEMENT -- the " "barrier named, not crossed", okK, "the Weil-ACF rewrite is exact and NEW as structure, but " "the residual object it exposes (the pole square " "dominating the weighted autocorrelation samples, " "cofinally) IS the wall again -- the relabeling barrier " "is NAMED, NOT CROSSED; WEIL-ALLTESTS <-> RH is a " "FLAGGED LOOP consumed by NOTHING; per-atom manifest " "positivity is PROVABLY IMPOSSIBLE (Wiener-Khinchin: " "hat-g = |hat-B|^2 >= 0, each atom samples a PD function " "with a minus sign) -- the too-good outcome excluded, " "not just unobserved; census cardinality 4 UNCHANGED; " "NOT RH evidence") print("\n [TYPED] THE WALL IS A CLOSED TRUNCATED WEIL FORM of") print(" g_x; the arch kernel LIMITS to the classical Weil") print(" archimedean kernel (KD, recomputed); per-atom positivity") print(" provably impossible; the pole alone carries positivity.") print(" An algebraic restatement, typed honestly. NO RH claim.") return 0 def run(): global CHECKS, FAILS CHECKS = [] FAILS = [] print("=" * 74) print("v951 -- PRIME.CANCELLATION.FUNCTIONAL.01 (the ACF law; " "the pole square;") print("the arch law with c* = (gamma + ln 2 pi)/2; the KD " "classical-Weil-kernel") print("pin recomputed; the sign law; round 195; 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("v951: %d/%d checks passed | verdict %s | runtime %.1f s" % (n_run - len(fails), n_run, verdict, time.time() - T_ALL)) print("PINNING: the convolution/wraparound/Laplace algebra " "(sympy generic), the") print("ACF/pole/arch laws at h = 4, 5 (own wall build, every " "atom/mode) and the") print("KD digamma limit recomputed in-run; the anatomy/sign/" "world tables PINNED") print("from cancellation_functional_probe.py (SPEC %s, 24/24," % PIN_SPEC_R195) print("record 1036 s + 1061 s deterministic re-run, four " "pre-freeze amendments") print("disclosed, SPEC verified UNTOUCHED by the Bughunt-X " "corrections, RE-RUN") print("GREEN AS TYPED AT PROMOTION 1102.8 s, 24/24). 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.CANCELLATION.FUNCTIONAL.01 Weil-ACF form + KD " "pin: %d passed, %d failed ---" % (n_run - len(fails), len(fails))) return 0 if ok else 1 if __name__ == "__main__": raise SystemExit(run())