#!/usr/bin/env python3 """v713 -- PRIME.L1MONTAGE.01: L1-MONTAGE -- the first explicit assembly of the CONTINUUM candidate of the Z1 operator and the machine test of the scaling limit in the CORRECT normalization. EXPLORATION ONLY (experiments/ firewall): nothing here is a verification claim; no verification/, paper, ledger or website surface is touched; no marker moves; NO RH statement. CONTEXT (the chain this probe closes into one object): * S-C (chain_deck_sector_probe): the arch density rho(t) = e^{-t/2}/(1 - e^{-2t}) is EXACTLY the sum of the three deck-sector channels of the 48-site NS cover lift; the lattice operator read converges with ~N^-2 and joint scalar s* -> 0.9999 at N = 192. * S-D (chain_weyl_mass_probe): the flow alpha ARE the Schur parameters [E]; the arch+pole background alone is not Caratheodory (PD death between the n=2 and n=3 cell). * 5b (z1_jacobi_probe) M2.2: NO h-stable alpha ladder in RAW normalization (min r_env = -0.13) -- the negative this probe re-examines in the correct (fixed-frequency) normalization. * 5c (z1_uvarov_probe): atoms are single-lag insertions (duality point), slot identity exact, stabilization law. * v679 (orbifold continuum OS): the continuum template -- fixed continuum data over a discretization ladder, difference-ratio rates, geometric extrapolants with bands, honest typing of what stays open for the formal limit. * v695 S1.4: the comb sequence c + pole is positive-feasible; the deployed signedness IS the pole subtraction. THE CORE IDEA (the 5b repair): the window measure lives on the circle with cell width D(h) -> 0. The continuum candidate is the measure on the t-axis (window symbol PER BANDWIDTH). Coefficient-level ladders (raw alpha_k, or alpha at matched u = kD) need not converge -- the right object is the m-/Schur-FUNCTION side: the window transform W_h(s, t) = sum_{d >= 1} p_d e^{(-s + i t) d D_h} at FIXED band points (t = band position, s = Abel depth in t-units), i.e. F_h(z) at fixed test points z = e^{(-s+it)D_h} in the band. Sections and PREREGISTERED BARS (declared before the assembled run; all bars were set from an interactive calibration scan of the same formulas on 2026-08-03, documented in CALIBRATION below): G0 guards. G0.1 AST firewall (banned names: zetazero, nzeros, zeta, second_sheet_zero) -- construction path is counting data + closed expressions only. G0.2 5-window family (identical 5b/5c selection, 67 complete frame-A windows), full-depth Levinson PD on all 5. G0.3 THE CONTINUUM DICTIONARY, locked by machine: (a) the arch lag read is c_ar,d = -D rho(dD) (SIGN MEASURED: the arch half couples NEGATIVELY in the deployed background; the positive-density object is rho + pole, the deployed one is 2cosh - rho = the pole-subtraction reading of v695 S1.4) [rel <= 1e-3 coarse / 1e-4 at window 4, tau ~ 1]; (b) the pole lag read is +D 2cosh(dD/2) [same bars]; (c) every INTERIOR atom (u <= 2 alpha - 2D) reads a total of exactly -mu_n/2 [<= 1e-12], while the reach-edge atom (u/D = M) reads partially -- the reach boundary is a slot, mirror of the UV cell (measured, typed); (d) the deployed diagonal cell obeys c_ar,0 ~ ln(1/D): increments per D-halving = ln 2 within 2% -- the d = 0 cell is the UV/renormalization slot, carried closed below. M1 the continuum arch operator (the S-C limit object, explicit). M1.1 [E] the continuum object NAMED: the diagonal operator with spectrum {2k + 1/2} (deck channels {6k + b}, b in {1/2, 5/2, 9/2}); heat trace == rho and the three deck channels exact [<= 1e-12]. M1.2 [E] the N-ladder of the cover lift (N = 48..768): joint scalar s*(N) and max-rel-dev(N) with difference-ratio rates in [1.8, 2.3] (~N^-2) and geometric extrapolant |s*(inf) - 1| <= 1e-6, dev(768) <= 1e-3 -- the lift converges to the continuum object, s* -> 1. M1.3 [E] per-mode spectral convergence: eps_m(N) extrapolates to m/2 [rel <= 1e-5 for m <= 25] -- operator data, not only traces. M1.4 [E] the explicit multiplication/Jacobi object of the arch+pole half: multiplication by tau on L^2([tau_min, T_max], (rho(tau) + 2cosh(tau/2)) dtau) with tau_min = D_4 (the declared UV cell) and T_max = 2 alpha_4; Stieltjes/Lanczos Jacobi matrix K = 48; Gauss quadrature reproduces direct integrals [<= 1e-12] and the coefficients are quadrature-refinement stable [<= 1e-12]; spectrum inside [0.9 tau_min, 1.001 T_max]. M2 the scaled limit (the 5b-M2.2 re-examination). M2.1 [measured anchor, both readings side by side] RAW normalization: the family alpha ladder fails the 5b bar r_env >= 0.80 (min r_env reproduced, was -0.13), AND the FIXED-MEASURE pair (synthetic rung M = 2048 vs window 4, same measure, D halved) also fails [r_env < 0.80]: the raw coefficient ladder is not h-stable even without reach effects -- the normalization, not only the measure, is the issue. M2.2 [central] the D-ladder in fixed-frequency normalization: synthetic dyadic ladder (fixed measure = window 4's: T = 2 alpha_4, all ka_4 atoms; M = 256..4096, reference M = 8192); renormalized transform W-hat = W - c_UV(D), c_UV = (1/2) ln(1 - e^{(-s+it)D}) (the CLOSED UV term of the -1/(2 tau) arch divergence); gates at every battery point (s in {0.25, 0.5, 1.0} x t in {5, 12, 27, 45}): |W-hat_j - W-hat_ref| strictly decreasing, LSQ D-rate in [0.5, 1.7] (first order, edge-dominated -- measured, understood), err at M = 4096 <= 0.04. The D/UV limit exists at EVERY band point including s < 1/2. M2.3 [E, must-fail] WITHOUT the closed UV renormalization the ladder is NOT Cauchy: the last raw increment equals the UV drift (1/2) ln 2 = 0.3466 within [0.28, 0.42] and is >= 4x the renormalized increment, at every battery point. M2.4 [central, THE REPAIR] the true family ladder converges in fixed-frequency normalization: for each window h a D-MATCHED reference rung (same D, full window-4 measure) is built; then W-hat_syn(D_h) - W-hat_h == closed montage tail (atoms ka_h..ka_4 as point masses + closed pole integral + closed arch-tower integral over [2 alpha_h, 2 alpha_4]) to |dev| <= 3e-3 at all s in {0.75, 1.0, 1.5} x t battery -- combined with M2.2 the window ladder converges as a FUNCTION limit at fixed band points for s > 1/2. THIS is the repair of the 5b-M2.2 negative by correct normalization (both readings documented side by side in M2.1). M2.5 [measured] WHERE it diverges: the s-anatomy at t = 27. (a) the parts: at s = 1/4 the pole tail and the atom tail are individually large and cancel; gate: |pole tail| >= 3 x |combined tail| on the two coarsest windows; (b) the montage-prediction residual grows monotonically as s drops (0.75 -> 0.5 -> 0.25) -- the missing piece at s <= 1/2 is the zero-side fluctuation (PNT-level cancellation measured, residual named, never loaded). The divergence is NOT in D (M2.2 converges at s = 0.25); it sits in the REACH tails at s <= 1/2 -- the half-plane boundary is the critical line, typed, firewalled. M3 the montage. M3.1 [E] the tent read converges to the POINT-MASS reading: for single atoms (n = 2 and a late prime), the transform of the deployed <= 2-cell tent read minus the exact point value -(mu_n/2) e^{(-s+it)u_n} falls with LSQ D-rate in [1.7, 2.6] (~D^2), dev at M = 8192 <= 2e-4 -- the 5c duality point (lag insertion vs measure point mass) is a DISCRETIZATION artifact: in the limit the atoms are genuine point masses of the t-line montage measure. M3.2 [central] THE ASSEMBLED OBJECT: background density 2cosh(tau/2) - rho(tau) on (0, T] (dictionary G0.3; the S-C cover-limit operator supplies rho geometrically, M1) + point masses -mu_n/2 at u_n = log n (counting data) + ONE closed UV slot (c_UV(D) + the ln(1/D) diagonal). Its truncations predict the window operators (M2.4, gated); the limit values W_inf(s, t) = extrapolated ladder + closed beyond-window-4 tail are TABLED with honest bands; gate: |tail beyond window 4| <= 0.05 at s >= 0.75 (the montage is reach-complete at the battery depth). M3.3 [C, honest typing] what is still MISSING for the contract as theorems (the v679 O5.1 template, cited): locally uniform bounds (measured: finitely many battery points), tightness/equicontinuity of the transform family, the limit Hilbert space (GNS on the limit moment data), Mosco/strong resolvent convergence of the CMV/Jacobi truncations (not only transform values), positivity transport in the limit (PD per window is measured; the limit-PD statement is the RP-in-the-limit analogue of v679 O2), and the s -> 1/2 boundary object (the comb measure itself) -- named, not claimed. M4 verdict (preregistered): L1-ASSEMBLED-MEASURED iff guards + M1.2 + M1.4 + M2.2 + M2.3 + M2.4 + M3.1 + M3.2 all pass; L1-SCALING-REPAIRED-PARTIAL iff M2.2 + M2.3 + M2.4 pass (the function-limit exists = the 5b repair) but an M1/M3 gate fails; L1-OBSTRUCTED otherwise, with the precise location. Plus the PRIME.Z1.OPERATOR.01 contract note (report only). CALIBRATION (honesty first, recorded before the assembled run): all bars above were set from an interactive calibration scan of the same formulas (2026-08-03). The scan fixed one SIGN in the construction: the arch lag read carries -rho (measured, G0.3a), so the UV term inside W is +(1/2) ln(1 - e^{zD}) and the renormalization SUBTRACTS it; the first calibration pass had added it (drift doubled instead of removed). No gate was weakened after seeing assembled results. Run 1 (2026-08-03, 15/16, G0.3 check-wiring): the sampled "last atom" in G0.3c sits exactly AT the reach edge (u/D = M), where the tent read is partial BY CONSTRUCTION (measured ratio 0.0002); the gate was re-scoped to interior atoms (u <= 2 alpha - 2D, still <= 1e-12 exact) and the reach-edge partial read is now printed and typed as the boundary slot (mirror of the UV cell d = 0). No bar moved; no measurement changed. FIREWALL: AST-checked -- no zetazero/nzeros/zeta/second_sheet_zero anywhere; the battery band points t in {5, 12, 27, 45} are arbitrary declared band positions (NOT zero ordinates); counting data (v563 U_ALL/MU_ALL) enters only as the montage's atom layer -- that is this route's point (v695 S6.1). The kill criterion stands: any construction loading zeros or zeta values is a renaming. Provenance (read-only): v563 core (window geometry, arch/atom lags, counting atoms), chain_deck_sector_probe (S-C), chain_weyl_mass_probe (S-D), z1_jacobi_probe (5b), z1_uvarov_probe (5c), v679 (continuum template), v695 (Z1 census, S1.4 pole layer). PROVENANCE: discovery probe l1_montage_probe.py (2026-08-03, 16/16 PASS, verdict L1-ASSEMBLED-MEASURED: the continuum candidate of the Z1 operator is assembled -- cover limit 6.2e-8, the point masses converge at the D^2 rate, exactly one UV slot; the 5b negative was a normalization artifact; the divergence sits exactly at s <= 1/2 (the critical line as the boundary of the construction); the missing theorems are NAMED, not claimed). Promoted verbatim; numbers unchanged. """ import ast import cmath import math import os import sys import time import numpy as np _here = os.path.dirname(os.path.abspath(__file__)) for _cand in (_here, os.path.join(_here, "..", "..", "verification")): if os.path.exists(os.path.join(_cand, "v563_paper2_readouts.py")): sys.path.insert(0, os.path.abspath(_cand)) break T0 = time.time() FAILS = [] N_CHK = 0 BANNED = ("zetazero", "nzeros", "zeta", "second_sheet_zero") def check(name, ok, detail=""): global N_CHK N_CHK += 1 if not ok: FAILS.append(name.split()[0]) print("[%s] %s%s" % ("PASS" if ok else "FAIL", name, (": " + detail) if detail else "")) def ast_firewall(src_path): with open(src_path, "r", encoding="utf-8") as fh: tree = ast.parse(fh.read()) for node in ast.walk(tree): if isinstance(node, ast.Attribute) and node.attr in BANNED: return False if isinstance(node, ast.Name) and node.id in BANNED: return False return True import v563_paper2_readouts as core # noqa: E402 (READ-ONLY import) import scipy.linalg as sla # noqa: E402 from scipy.ndimage import median_filter # noqa: E402 # ---------------------------------------------------------------- bars BAR_EXACT = 1e-12 # closed identities (tower, deck, atoms) BAR_DICT_COARSE = 1e-3 # dictionary rel dev at M = 256 BAR_DICT_FINE = 1e-4 # dictionary rel dev at window 4 BAR_DIAG_LAW = 0.02 # |d c_ar,0 / ln 2 - 1| per D-halving RATE_N_LO, RATE_N_HI = 1.8, 2.3 # N-ladder difference-ratio rates BAR_SSTAR = 1e-6 # |s*(inf) - 1| BAR_DEVN = 1e-3 # joint dev at N = 768 BAR_MODE = 1e-5 # per-mode extrapolant rel dev K_JAC = 48 # Jacobi depth of the continuum object BAR_GAUSS = 1e-12 # Gauss-vs-direct functionals BAR_JSTAB = 1e-12 # quadrature-refinement stability R_LADDER = 0.80 # the 5b h-stability bar (cited) RUNGS = (256, 512, 1024, 2048, 4096) M_REF = 8192 T_BATT = (5.0, 12.0, 27.0, 45.0) # arbitrary declared band points S_DLAD = (0.25, 0.50, 1.00) # Abel depths, D-ladder S_FAM = (0.75, 1.00, 1.50) # Abel depths, family (s > 1/2) S_ANAT = (0.25, 0.50, 0.75) # the s-anatomy scan (t = 27) SLOPE_D_LO, SLOPE_D_HI = 0.5, 1.7 # W-hat LSQ D-rate band BAR_ERR4096 = 0.04 # |W-hat(4096) - W-hat(8192)| RAW_UV_LO, RAW_UV_HI = 0.28, 0.42 # raw UV drift ~ (1/2) ln 2 RAW_X = 4.0 # raw increment >= 4x renormalized BAR_MATCH = 3e-3 # matched-rung montage-tail deviation CANCEL_X = 3.0 # pole-vs-sum cancellation at s = 1/4 SLOPE_PM_LO, SLOPE_PM_HI = 1.7, 2.6 # tent -> point-mass D-rate BAR_PM_FINE = 2e-4 # point-mass dev at M = 8192 BAR_TAIL_INF = 0.05 # |montage tail beyond window 4| K_LO = 8 # skip boundary coefficients (5b) K_ARCH = 300 # arch tower terms in closed integrals T_GRID = np.linspace(0.5, 3.0, 51) # S-C trace grid N_LADDER = (48, 96, 192, 384, 768) # ------------------------------------------------- window machinery def window_geometry(kz): alpha = float(core.U_ALL[kz]) D_k = 0.5 * float(core.G_ALL[kz]) / float(core.NU_MAIN) M = int(math.ceil(alpha / D_k - 1.0e-9)) + 1 if M % 2: M += 1 return alpha, M def g_pole(tv): tv = abs(tv) return -4.0 * (math.exp(tv / 2) + math.exp(-tv / 2) - 2.0) def pole_lags(M, D): return np.array([-(g_pole((d - 1) * D) - 2.0 * g_pole(d * D) + g_pole((d + 1) * D)) / D for d in range(M)]) def build_lags(alpha, M, ka): """Full deployed lag build at (alpha, M): arch + atoms + pole.""" D = 2.0 * alpha / M c_ar = core.arch_lags(M, D) c_at, _ = core.atom_lags_at(alpha, M, core.U_ALL[:ka], core.MU_ALL[:ka]) cp = pole_lags(M, D) return dict(D=D, c_ar=c_ar, c_at=c_at, cp=cp, p=c_ar + c_at + cp) def rho_arch(tau): tau = np.asarray(tau, float) return np.exp(-tau / 2.0) / (1.0 - np.exp(-2.0 * tau)) # ------------------------------------------------- S-C lift machinery def channel(b, t): return np.exp(-b * t) / (1.0 - np.exp(-6.0 * t)) def sector_trace_lat(N, r, t): ms = np.arange(1, N, 2) ms = ms[ms % 12 == r] eps = (N / math.pi) * np.sin(ms * math.pi / (2.0 * N)) return np.exp(-np.outer(t, eps)).sum(axis=1) def joint_fit(traces, chans): Tv = np.concatenate(traces) Cv = np.concatenate(chans) s = float(Tv @ Cv) / float(Tv @ Tv) dev = float(np.max(np.abs(s * Tv - Cv) / np.abs(Cv))) return s, dev # --------------------------------------------- v679 template utilities def seq_rates(vals): d = np.diff(np.asarray(vals, dtype=float)) r = [] for k in range(len(d) - 1): if d[k] == 0 or d[k + 1] == 0 or d[k] * d[k + 1] <= 0: r.append(float("nan")) else: r.append(math.log2(abs(d[k]) / abs(d[k + 1]))) return d, r def geo_extrap(f1, f2, f3): d1, d2 = f2 - f1, f3 - f2 if d1 == 0 or d2 == 0 or d1 * d2 <= 0: return float("nan"), float("nan") q = d2 / d1 if not (0.0 < q < 1.0): return float("nan"), float("nan") return f3 + d2 * q / (1.0 - q), -math.log2(q) def geo_extrap_c(v1, v2, v3): aR, _ = geo_extrap(v1.real, v2.real, v3.real) aI, _ = geo_extrap(v1.imag, v2.imag, v3.imag) if math.isnan(aR): # rate-1 Richardson q=1/2 aR = v3.real + (v3.real - v2.real) if math.isnan(aI): aI = v3.imag + (v3.imag - v2.imag) return complex(aR, aI) # --------------------------------------------- transform machinery def W_of(p, D, s, t): """The fixed-frequency window transform sum_{d>=1} p_d e^{z d D}, z = -s + i t (t = band position, s = Abel depth in t-units).""" d = np.arange(1, len(p)) return complex(np.sum(p[1:] * np.exp((-s + 1j * t) * D * d))) def c_uv(D, s, t): """The CLOSED UV term of the -1/(2 tau) arch divergence inside W: sum_d (D/(2 d D)) e^{z d D} -> -(1/2) ln(1 - e^{zD}) with the measured arch sign (-rho) giving +(1/2) ln(1 - e^{zD}).""" return 0.5 * cmath.log(1.0 - cmath.exp((-s + 1j * t) * D)) def pole_int(z, a, b): """Closed: int_a^b 2 cosh(tau/2) e^{z tau} d tau.""" return ((cmath.exp((z + 0.5) * b) - cmath.exp((z + 0.5) * a)) / (z + 0.5) + (cmath.exp((z - 0.5) * b) - cmath.exp((z - 0.5) * a)) / (z - 0.5)) def arch_int(z, a, b, K=K_ARCH): """Closed tower sum: int_a^b rho(tau) e^{z tau} d tau.""" acc = 0j for k in range(K): bk = 2.0 * k + 0.5 acc += (cmath.exp((z - bk) * b) - cmath.exp((z - bk) * a)) \ / (z - bk) return acc def montage_tail(z, ka_lo, ka_hi, a, b): """The closed montage tail between reaches: point-mass atoms ka_lo..ka_hi + pole integral + arch-tower integral on [a, b].""" u = core.U_ALL[ka_lo:ka_hi] mu = core.MU_ALL[ka_lo:ka_hi] atoms = -0.5 * complex(np.sum(mu * np.exp(z.real * u) * np.exp(1j * z.imag * u))) return atoms + pole_int(z, a, b) - arch_int(z, a, b) # --------------------------------------------- Jacobi machinery (M1.4) def gl_nodes(a, b, npan, deg): x, wq = np.polynomial.legendre.leggauss(deg) edges = np.linspace(a, b, npan + 1) xs, ws = [], [] for i in range(npan): mid = 0.5 * (edges[i] + edges[i + 1]) half = 0.5 * (edges[i + 1] - edges[i]) xs.append(mid + half * x) ws.append(half * wq) return np.concatenate(xs), np.concatenate(ws) def lanczos_jacobi(xs, ws, K): """Stieltjes/Lanczos: Jacobi coefficients of the discretized measure sum ws_i delta(xs_i) (one re-orthogonalization pass).""" b0 = float(ws.sum()) q = np.sqrt(ws / b0) q_prev = np.zeros_like(q) beta = 0.0 aJ, bJ = [], [] for _k in range(K): v = xs * q - beta * q_prev alpha_k = float(q @ v) v = v - alpha_k * q v -= q * float(q @ v) beta = float(np.linalg.norm(v)) aJ.append(alpha_k) bJ.append(beta) q_prev, q = q, v / beta return np.array(aJ), np.array(bJ[:-1]), b0 # --------------------------------------------- OPUC machinery (M2.1) def levinson(r, N): r = np.asarray(r, float) a = np.zeros(N + 1) a[0] = 1.0 E = float(r[0]) ks = np.zeros(N) for n in range(1, N + 1): acc = r[n] + (float(a[1:n] @ r[n - 1:0:-1]) if n > 1 else 0.0) k = -acc / E ks[n - 1] = k a[1:n + 1] = a[1:n + 1] + k * a[n - 1::-1][:n] E *= (1.0 - k * k) if not (abs(k) < 1.0) or E <= 0.0: return ks[:n], n return ks, None def envelope(x, width): e = median_filter(np.abs(x), size=max(5, width | 1), mode="nearest") return np.maximum(e, 1e-300) def pearson(x, y): x = np.asarray(x, float) y = np.asarray(y, float) x = x - x.mean() y = y - y.mean() d = math.sqrt(float(x @ x) * float(y @ y)) return float(x @ y) / d if d > 0 else 0.0 def uprof_r_env(alA, DA, alB, DB): """5b M2.2 envelope-normalized u-profile correlation, verbatim convention (u = k D, mask u >= K_LO D_A).""" ua = np.arange(len(alA)) * DA ub = np.arange(len(alB)) * DB ea = envelope(alA, int(0.15 / DA)) eb = envelope(alB, int(0.15 / DB)) m_ = ua >= K_LO * DA ref_env = np.interp(ua[m_], ub, alB / eb) return pearson(alA[m_] / ea[m_], ref_env) def run(): print("=" * 78) print("L1-MONTAGE -- the continuum candidate of the Z1 operator:") print("assembly + the scaling limit in fixed-frequency " "normalization") print("=" * 78) # ================================================================ G0 print("\nG0 -- guards, family, the continuum dictionary") check("G0.1 [E] AST firewall: banned names %s nowhere in this " "probe; construction path = counting data + closed " "expressions only" % (BANNED,), ast_firewall(os.path.abspath(__file__))) zones = core.frame_a_zones() fam = [] for kz in zones: alpha, M = window_geometry(kz) if math.exp(2.0 * alpha) <= core.ATOM_MAX + 0.5: fam.append((kz, alpha, M)) hs = np.array([t[2] // 2 for t in fam], float) picks = [fam[0]] for qq in (0.25, 0.5, 0.75, 1.0): tgt = float(np.quantile(hs, qq)) cand = min(fam, key=lambda t_: abs(t_[2] // 2 - tgt)) if all(cand[0] != p_[0] for p_ in picks): picks.append(cand) picks = sorted(picks, key=lambda t_: t_[2]) wins = [] for (kz, alpha, M) in picks: ka = core.atoms_in(alpha) w = build_lags(alpha, M, ka) w.update(kz=kz, alpha=alpha, M=M, h=M // 2, ka=ka) ks, bd = levinson(w["p"], M - 1) w["al"] = -ks w["bd"] = bd wins.append(w) print(" family: " + ", ".join( "h=%d (alpha=%.4f, D=%.6f, X=%.0f)" % (w["h"], w["alpha"], w["D"], math.exp(2 * w["alpha"])) for w in wins)) check("G0.2 [E] 5-window family (identical 5b/5c selection, %d " "complete frame-A windows); full-depth Levinson PD on all " "5 (reproduces 5b M1.1)" % len(fam), len(picks) == 5 and len(fam) == 67 and all(w["bd"] is None for w in wins)) w4 = wins[-1] alpha4, ka4 = w4["alpha"], w4["ka"] T4 = 2.0 * alpha4 D4 = w4["D"] # the synthetic dyadic ladder (fixed measure = window 4's) lads = {} for M in RUNGS + (M_REF,): lads[M] = build_lags(alpha4, M, ka4) # dictionary dev_ar, dev_cp = {}, {} for M, bar_tag in ((256, "coarse"), (w4["M"], "win4")): w = lads[256] if M == 256 else w4 D = w["D"] d = int(round(1.0 / D)) tau_d = d * D dev_ar[bar_tag] = abs(w["c_ar"][d] / D + float(rho_arch(tau_d))) \ / float(rho_arch(tau_d)) dev_cp[bar_tag] = abs(w["cp"][d] / D - 2.0 * math.cosh(tau_d / 2.0)) \ / (2.0 * math.cosh(tau_d / 2.0)) dev_atom = 0.0 i_int = int(np.searchsorted(core.U_ALL, T4 - 2.0 * D4)) - 1 for i in (0, 1, 10, 100, 1000, i_int): c1, _ = core.atom_lags_at(alpha4, w4["M"], core.U_ALL[i:i + 1], core.MU_ALL[i:i + 1]) dev_atom = max(dev_atom, abs(float(np.sum(c1)) / (-float(core.MU_ALL[i]) / 2.0) - 1.0)) c1b, _ = core.atom_lags_at(alpha4, w4["M"], core.U_ALL[ka4 - 1:ka4], core.MU_ALL[ka4 - 1:ka4]) r_edge = float(np.sum(c1b)) / (-float(core.MU_ALL[ka4 - 1]) / 2.0) print(" reach-edge cell: the last atom (u/D = %.2f = M) reads " "PARTIALLY, ratio %.4f -- the reach boundary is a slot, " "mirror of the UV cell d = 0 (typed, measured)" % (float(core.U_ALL[ka4 - 1]) / D4, r_edge)) diag = [lads[M]["c_ar"][0] for M in (256, 512, 1024, 2048, 4096)] dev_diag = max(abs((diag[i + 1] - diag[i]) / math.log(2.0) - 1.0) for i in range(4)) print(" diagonal cell c_ar,0 over D-halvings: %s (increments " "/ ln 2 dev <= %.4f)" % (["%.4f" % x for x in diag], dev_diag)) check("G0.3 [E] THE CONTINUUM DICTIONARY locked: (a) arch lag = " "-D rho(dD) (rel dev %.1e coarse / %.1e win4; the arch " "half couples with the MINUS sign -- the deployed " "background density is 2cosh(tau/2) - rho(tau), the pole-" "subtraction reading of v695 S1.4); (b) pole lag = " "+D 2cosh(dD/2) (rel %.1e / %.1e); (c) every INTERIOR atom " "(u <= 2 alpha - 2D) reads EXACTLY -mu_n/2 in total (max " "dev %.1e; the reach-edge atom reads partially -- boundary " "slot, printed); (d) the diagonal " "cell obeys the closed UV law c_ar,0 ~ ln(1/D) " "(increment/ln2 dev %.3f <= %.2f) -- d = 0 is the " "renormalization slot" % (dev_ar["coarse"], dev_ar["win4"], dev_cp["coarse"], dev_cp["win4"], dev_atom, dev_diag, BAR_DIAG_LAW), dev_ar["coarse"] <= BAR_DICT_COARSE and dev_ar["win4"] <= BAR_DICT_FINE and dev_cp["coarse"] <= BAR_DICT_COARSE and dev_cp["win4"] <= BAR_DICT_FINE and dev_atom <= BAR_EXACT and dev_diag <= BAR_DIAG_LAW) # ================================================================ M1 print("\nM1 -- the continuum arch operator (the S-C limit " "object, explicit)") t = T_GRID rho_t = rho_arch(t) tow = sum(np.exp(-(2.0 * k + 0.5) * t) for k in range(400)) dev_tow = float(np.max(np.abs(tow - rho_t) / rho_t)) dev_deck = 0.0 for b in (0.5, 2.5, 4.5): ch = channel(b, t) tw = sum(np.exp(-(6.0 * k + b) * t) for k in range(140)) dev_deck = max(dev_deck, float(np.max(np.abs(tw - ch) / ch))) check("M1.1 [E] the continuum object NAMED: diagonal operator " "with spectrum {2k + 1/2} (deck channels {6k + b}, b in " "{1/2, 5/2, 9/2}); heat trace == rho (rel %.1e) and deck " "split exact (rel %.1e), both <= %.0e -- the S-C anchor " "re-verified" % (dev_tow, dev_deck, BAR_EXACT), dev_tow <= BAR_EXACT and dev_deck <= BAR_EXACT) chans = [channel(b, t) for b in (0.5, 2.5, 4.5)] svals, devs = [], [] for N in N_LADDER: traces = [sector_trace_lat(N, r, t) for r in (1, 5, 9)] s_star, dev = joint_fit(traces, chans) svals.append(s_star) devs.append(dev) print(" N = %3d: s* = %.9f, joint max rel dev %.3e" % (N, s_star, dev)) _, r_s = seq_rates(svals) _, r_d = seq_rates(devs) s_inf, _ = geo_extrap(*svals[2:]) check("M1.2 [E] N-ladder of the cover lift: s*(N) rates %s and " "dev rates %s all in [%.1f, %.1f] (~N^-2); geometric " "extrapolant s*(inf) = %.9f, |s*(inf) - 1| = %.1e <= %.0e; " "dev(768) = %.1e <= %.0e -- the lift converges to the " "continuum object with the measured N^-2 rate and the " "joint scalar goes to 1" % (["%.2f" % x for x in r_s], ["%.2f" % x for x in r_d], RATE_N_LO, RATE_N_HI, s_inf, abs(s_inf - 1.0), BAR_SSTAR, devs[-1], BAR_DEVN), all(RATE_N_LO <= x <= RATE_N_HI for x in r_s + r_d) and abs(s_inf - 1.0) <= BAR_SSTAR and devs[-1] <= BAR_DEVN) dev_mode = 0.0 for m in range(1, 26, 2): vals = [(N / math.pi) * math.sin(m * math.pi / (2.0 * N)) for N in (192, 384, 768)] a_m, _ = geo_extrap(*vals) dev_mode = max(dev_mode, abs(a_m - m / 2.0) / (m / 2.0)) check("M1.3 [E] per-mode spectral convergence: eps_m(N) " "extrapolates to m/2 for all odd m <= 25 (worst rel dev " "%.1e <= %.0e) -- operator data converge, not only traces" % (dev_mode, BAR_MODE), dev_mode <= BAR_MODE) def w_plus(tau): return rho_arch(tau) + 2.0 * np.cosh(tau / 2.0) xs, wq0 = gl_nodes(D4, T4, 3000, 12) ws = wq0 * w_plus(xs) aJ, bJ, mass = lanczos_jacobi(xs, ws, K_JAC) ev, U = sla.eigh_tridiagonal(aJ, bJ) wg = mass * U[0] ** 2 dev_g = 0.0 for s in (0.3, 1.0, 3.0): exact = float(np.sum(ws * np.exp(-s * xs))) gq = float(np.sum(wg * np.exp(-s * ev))) dev_g = max(dev_g, abs(gq - exact) / abs(exact)) xs2, wq02 = gl_nodes(D4, T4, 6000, 12) aJ2, bJ2, _ = lanczos_jacobi(xs2, wq02 * w_plus(xs2), K_JAC) stab = max(float(np.max(np.abs(aJ2 - aJ))), float(np.max(np.abs(bJ2 - bJ)))) print(" Jacobi head: aJ = %s, bJ = %s" % (["%.4f" % x for x in aJ[:4]], ["%.4f" % x for x in bJ[:4]])) check("M1.4 [E] the explicit multiplication/Jacobi object of the " "arch+pole half: measure (rho + 2cosh(tau/2)) dtau on " "[tau_min = D_4 = %.4f, T_max = 2 alpha_4 = %.4f] (mass " "%.4f; tau_min = the declared UV cell, typed [O]); K = %d " "Jacobi coefficients via Stieltjes/Lanczos; Gauss " "quadrature == direct integrals (rel %.1e <= %.0e), " "refinement-stable (%.1e <= %.0e), spectrum [%.4f, %.4f] " "inside the support -- the continuum operator EXISTS as an " "explicit matrix" % (D4, T4, mass, K_JAC, dev_g, BAR_GAUSS, stab, BAR_JSTAB, ev.min(), ev.max()), dev_g <= BAR_GAUSS and stab <= BAR_JSTAB and ev.min() >= 0.9 * D4 and ev.max() <= 1.001 * T4) # ================================================================ M2 print("\nM2 -- the scaled limit (the 5b-M2.2 re-examination)") # ---- M2.1 the raw reading, reproduced honestly r_fam = [] for w in wins[1:-1]: r_fam.append(uprof_r_env(w["al"], w["D"], w4["al"], w4["D"])) ks_syn, bd_syn = levinson(lads[2048]["p"], 2047) r_fix = uprof_r_env(-ks_syn, lads[2048]["D"], w4["al"], w4["D"]) \ if bd_syn is None else float("nan") print(" raw family r_env vs window 4: %s (5b bar %.2f)" % (["%+.4f" % r for r in r_fam], R_LADDER)) print(" raw FIXED-measure pair (rung M=2048 vs window 4, same " "measure, D halved): r_env = %+.4f" % r_fix) check("M2.1 [E, the raw negative, both readings side by side] " "RAW normalization has no h-stable ladder: family min " "r_env = %+.4f (reproduces the 5b M2.2 negative, was " "-0.13) AND the fixed-measure pair gives r_env = %+.4f -- " "both < %.2f: the coefficient-level comparison fails even " "WITHOUT reach effects; the normalization is the issue, " "which is what the function-level ladder (M2.2/M2.4) " "repairs" % (min(r_fam), r_fix, R_LADDER), min(r_fam) < R_LADDER and r_fix < R_LADDER) # ---- M2.2 the renormalized D-ladder (fixed measure) print(" M2.2 D-ladder (fixed measure, M = 256..4096, ref " "8192): W-hat = W - (1/2) ln(1 - e^{zD})") ok_mono, ok_last = True, True slopes = [] raw_last, ren_last = [], [] Dv = np.array([lads[M]["D"] for M in RUNGS]) for s in S_DLAD: for tb in T_BATT: Wref = W_of(lads[M_REF]["p"], lads[M_REF]["D"], s, tb) \ - c_uv(lads[M_REF]["D"], s, tb) errs, raws, rens = [], [], [] for M in RUNGS: Wv = W_of(lads[M]["p"], lads[M]["D"], s, tb) raws.append(Wv) rens.append(Wv - c_uv(lads[M]["D"], s, tb)) errs.append(abs(rens[-1] - Wref)) errs = np.array(errs) ok_mono &= bool(np.all(np.diff(errs) < 0.0)) ok_last &= errs[-1] <= BAR_ERR4096 sl = float(np.polyfit(np.log2(Dv), np.log2(errs), 1)[0]) slopes.append(sl) raw_last.append(abs(raws[-1] - raws[-2])) ren_last.append(abs(rens[-1] - rens[-2])) print(" s=%.2f t=%4.1f: |W-hat - ref| = %s D-rate " "%.2f" % (s, tb, ["%.1e" % e for e in errs], sl)) check("M2.2 [central] the D/UV limit EXISTS at every band point " "(incl. s < 1/2): after the closed UV renormalization the " "ladder error falls strictly monotonically at all %d " "battery points, LSQ D-rates in [%.2f, %.2f] (band " "[%.1f, %.1f]: first order, edge-dominated -- measured, " "understood), worst err(4096) <= %.0e -- the " "discretization limit of the window transform is CLEAN" % (len(S_DLAD) * len(T_BATT), min(slopes), max(slopes), SLOPE_D_LO, SLOPE_D_HI, BAR_ERR4096), ok_mono and ok_last and all(SLOPE_D_LO <= x <= SLOPE_D_HI for x in slopes)) ratio_uv = min(rl / max(re, 1e-300) for rl, re in zip(raw_last, ren_last)) check("M2.3 [E, must-fail] WITHOUT the renormalization the " "ladder is NOT Cauchy: last raw increments in [%.3f, " "%.3f] == the closed UV drift (1/2) ln 2 = %.4f (band " "[%.2f, %.2f]), and raw/renormalized increment ratio >= " "%.1f (bar %.1f) at every battery point -- the UV term is " "real, closed, and exactly one term" % (min(raw_last), max(raw_last), 0.5 * math.log(2.0), RAW_UV_LO, RAW_UV_HI, ratio_uv, RAW_X), all(RAW_UV_LO <= x <= RAW_UV_HI for x in raw_last) and ratio_uv >= RAW_X) # ---- M2.4 the family repair: D-matched rungs + closed tails print(" M2.4 family ladder, fixed-frequency normalization " "(D-matched reference rungs + closed montage tails):") match = {} for w in wins[:-1]: M_syn = int(round(T4 / w["D"])) match[w["h"]] = build_lags(alpha4, M_syn, ka4) dev_match = [] for s in S_FAM: for tb in T_BATT: z = complex(-s, tb) row = [] for w in wins[:-1]: syn = match[w["h"]] Wh = W_of(w["p"], w["D"], s, tb) - c_uv(w["D"], s, tb) Wsyn = W_of(syn["p"], syn["D"], s, tb) \ - c_uv(syn["D"], s, tb) tail = montage_tail(z, w["ka"], ka4, 2.0 * w["alpha"], T4) row.append(abs((Wsyn - Wh) - tail)) dev_match.append(max(row)) print(" s=%.2f t=%4.1f: |(W-hat_syn - W-hat_h) - " "closed tail| per window = %s" % (s, tb, ["%.1e" % x for x in row])) check("M2.4 [central, THE 5b REPAIR] the family ladder CONVERGES " "in fixed-frequency normalization: at every battery point " "(s in %s x t in %s) the D-matched reference rung minus " "the true window equals the CLOSED montage tail (point-" "mass atoms + pole integral + arch-tower integral) to " "worst dev %.1e <= %.0e -- combined with M2.2 the window " "ladder has a function limit at fixed band points for " "s > 1/2; the 5b M2.2 negative was the NORMALIZATION " "(raw alpha), not the limit" % (list(S_FAM), list(T_BATT), max(dev_match), BAR_MATCH), max(dev_match) <= BAR_MATCH) # ---- M2.5 the s-anatomy: where it diverges print(" M2.5 s-anatomy at t = 27 (window 0 row, reach " "%.2f -> %.2f):" % (2 * wins[0]["alpha"], T4)) res_s = {} canc = [] for s in S_ANAT: z = complex(-s, 27.0) w = wins[0] syn = match[w["h"]] Wh = W_of(w["p"], w["D"], s, 27.0) - c_uv(w["D"], s, 27.0) Wsyn = W_of(syn["p"], syn["D"], s, 27.0) \ - c_uv(syn["D"], s, 27.0) tail = montage_tail(z, w["ka"], ka4, 2.0 * w["alpha"], T4) res_s[s] = abs((Wsyn - Wh) - tail) u = core.U_ALL[w["ka"]:ka4] mu = core.MU_ALL[w["ka"]:ka4] at = -0.5 * complex(np.sum(mu * np.exp(z.real * u) * np.exp(1j * z.imag * u))) pl = pole_int(z, 2.0 * w["alpha"], T4) if s == 0.25: canc = [abs(at), abs(pl), abs(tail)] print(" s=%.2f: |atom tail| %.4f |pole tail| %.4f " "|combined| %.4f prediction residual %.4f" % (s, abs(at), abs(pl), abs(tail), res_s[s])) check("M2.5 [measured] WHERE it diverges -- located: NOT in D " "(M2.2 converges at s = 0.25); in the REACH tails at " "s <= 1/2: at s = 1/4 atom and pole tails are individually " "large (%.3f / %.3f) and cancel to %.3f (pole/combined = " "%.1fx >= %.1fx, the PNT-level cancellation, measured); " "the montage-prediction residual grows monotonically as s " "drops (%.4f -> %.4f -> %.4f for s = 0.75/0.50/0.25) -- " "the missing piece at s <= 1/2 is the zero-side " "fluctuation, NAMED and firewalled (never loaded); the " "half-plane boundary s = 1/2 is the critical line, typed" % (canc[0], canc[1], canc[2], canc[1] / canc[2], CANCEL_X, res_s[0.75], res_s[0.50], res_s[0.25]), canc[1] / canc[2] >= CANCEL_X and res_s[0.25] > res_s[0.50] > res_s[0.75]) # ================================================================ M3 print("\nM3 -- the montage") # ---- M3.1 tent read -> point mass print(" M3.1 tent read -> point mass (D-ladder, single atoms):") ok_pm = True for (i_at, lab) in ((0, "n=2"), (28, "n~%d" % round(math.exp( float(core.U_ALL[28]))))): u_n = float(core.U_ALL[i_at]) mu_n = float(core.MU_ALL[i_at]) for (s, tb) in ((0.5, 12.0), (1.0, 45.0)): devs_pm, Dl = [], [] for M in RUNGS + (M_REF,): D = 2.0 * alpha4 / M c1, _ = core.atom_lags_at(alpha4, M, core.U_ALL[i_at:i_at + 1], core.MU_ALL[i_at:i_at + 1]) Wa = W_of(c1, D, s, tb) exact = -(mu_n / 2.0) * cmath.exp((-s + 1j * tb) * u_n) devs_pm.append(abs(Wa - exact)) Dl.append(D) sl = float(np.polyfit(np.log2(Dl), np.log2(devs_pm), 1)[0]) ok_pm &= (SLOPE_PM_LO <= sl <= SLOPE_PM_HI and devs_pm[-1] <= BAR_PM_FINE) print(" atom %-7s s=%.2f t=%4.1f: dev %s LSQ D-rate " "%.2f" % (lab, s, tb, ["%.1e" % x for x in devs_pm], sl)) check("M3.1 [E] THE DUALITY POINT DISSOLVES IN THE LIMIT: the " "deployed <= 2-cell tent read converges to the exact " "point-mass value -(mu_n/2) e^{z u_n} with LSQ D-rate in " "[%.1f, %.1f] (~D^2) and dev(8192) <= %.0e on both test " "atoms x both battery points -- the 5c lag-insertion vs " "measure-point-mass duality is a discretization artifact; " "in the continuum the atoms are genuine point masses of " "the t-line montage measure" % (SLOPE_PM_LO, SLOPE_PM_HI, BAR_PM_FINE), ok_pm) # ---- M3.2 the assembled limit values + reach completeness print(" M3.2 the assembled limit W_inf(s, t) = extrapolated " "D-ladder + closed tail beyond window 4:") ka_end = len(core.U_ALL) U_MAX = float(core.U_ALL[-1]) ok_tail = True print(" %-5s %-6s %22s %10s %10s" % ("s", "t", "W_inf", "|tail4inf|", "band")) for s in S_FAM: for tb in T_BATT: z = complex(-s, tb) v1 = W_of(lads[2048]["p"], lads[2048]["D"], s, tb) \ - c_uv(lads[2048]["D"], s, tb) v2 = W_of(lads[4096]["p"], lads[4096]["D"], s, tb) \ - c_uv(lads[4096]["D"], s, tb) v3 = W_of(lads[M_REF]["p"], lads[M_REF]["D"], s, tb) \ - c_uv(lads[M_REF]["D"], s, tb) W_lim = geo_extrap_c(v1, v2, v3) tail = montage_tail(z, ka4, ka_end, T4, U_MAX) tail += -cmath.exp((z - 0.5) * U_MAX) / (z - 0.5) u_oct = core.U_ALL[core.U_ALL >= U_MAX - math.log(2.0)] mu_oct = core.MU_ALL[core.U_ALL >= U_MAX - math.log(2.0)] at_oct = -0.5 * complex( np.sum(mu_oct * np.exp(z.real * u_oct) * np.exp(1j * z.imag * u_oct))) sm_oct = -(cmath.exp((z + 0.5) * U_MAX) - cmath.exp((z + 0.5) * (U_MAX - math.log(2.0)))) \ / (z + 0.5) band = abs(v3 - v2) + abs(at_oct - sm_oct) ok_tail &= abs(tail) <= BAR_TAIL_INF print(" %-5.2f %-6.1f %10.5f%+10.5fj %10.5f %10.5f" % (s, tb, (W_lim + tail).real, (W_lim + tail).imag, abs(tail), band)) check("M3.2 [central] THE L1 CANDIDATE IS ASSEMBLED at the " "measured level: ONE fixed, zero-free-described continuum " "object -- background density 2cosh(tau/2) - rho(tau) on " "the lag line (rho = the S-C cover-limit heat trace, M1; " "sign = the v695 pole-subtraction slot), counting-data " "point masses -mu_n/2 at log n (M3.1), ONE closed UV slot " "(c_UV(D) + the ln(1/D) diagonal, G0.3d) -- whose " "truncations reproduce the window operators (M2.4) and " "whose limit values are tabled above with honest bands " "(atom table to u = %.2f = ln %d, smooth remainder closed, " "band = extrapolation + last-octave fluctuation); reach " "completeness: |tail beyond window 4| <= %.2f at all " "s >= 3/4 battery points" % (U_MAX, core.ATOM_MAX, BAR_TAIL_INF), ok_tail) check("M3.3 [C, honest typing] WHAT IS STILL MISSING FOR THE " "CONTRACT AS THEOREMS (v679 O5.1 template, cited): (i) " "locally uniform convergence bounds -- measured here at " "finitely many battery points only; (ii) tightness/" "equicontinuity of the transform family in (s, t); (iii) " "the limit Hilbert space (GNS on the limit moment data) " "and MOSCO/STRONG-RESOLVENT convergence of the CMV/Jacobi " "truncations -- transform-value convergence (this probe) " "is weaker than operator convergence; (iv) positivity " "transport: PD is measured per window (5b M1.1), the " "limit-PD statement is the RP-in-the-limit analogue of " "v679 O2 and is OPEN; (v) the s -> 1/2 boundary object " "(the comb measure itself) and the UV cell as a theorem " "(Pf/diagonal renormalization, S-C D6) -- all NAMED, none " "claimed; GATE stays where it is", True) # ================================================================ M4 print("\nM4 -- verdict + contract note") central = [f for f in FAILS if f.startswith(("M2.2", "M2.3", "M2.4"))] if not FAILS: verdict = "L1-ASSEMBLED-MEASURED" elif not central: verdict = "L1-SCALING-REPAIRED-PARTIAL (at %s)" \ % ", ".join(FAILS) else: verdict = "L1-OBSTRUCTED (at %s)" % ", ".join(FAILS) check("M4.1 [E] preregistered verdict logic: ASSEMBLED iff all " "gates; REPAIRED-PARTIAL iff the scaling repair " "(M2.2/M2.3/M2.4) stands but an assembly gate fails; " "OBSTRUCTED otherwise with location", True) print("\n VERDICT: %s" % verdict) print(""" contract note PRIME.Z1.OPERATOR.01 (report only, no ledger row): L1-MONTAGE (this run): der Kontinuums-Kandidat ist MONTIERT auf Mess-Ebene -- ein festes, zeta-frei beschriebenes Objekt: (1) Hintergrund: Dichte 2cosh(tau/2) - rho(tau) auf der Lag-Achse; rho ist per S-C die Waermespur des expliziten Cover-Limes-Operators (Spektrum {2k+1/2}, N-Leiter extrapoliert s* -> 1 auf %.1e, Raten ~N^-2, M1.2); das Minuszeichen der Arch-Haelfte ist GEMESSEN (G0.3) und ist der v695-S1.4-Pol-Abzugs-Slot; die Multiplikations-/ Jacobi-Lesart der positiven rho+Pol-Haelfte existiert als explizite K=%d-Jacobi-Matrix (Gauss-Konsistenz %.0e). (2) Atome: echte PUNKTMASSEN -mu_n/2 bei log n im Limes -- der 5c-Dualitaetspunkt (Lag-Insertion vs. Mass-Punkt) verschwindet mit Rate ~D^2 (M3.1). (3) UV: EIN geschlossener Slot -- c_UV(D) = (1/2) ln(1 - e^{zD}) im Transform + ln(1/D) in der Diagonalzelle (G0.3d, S-C-D6-Slot). DER GRENZUEBERGANG: in fester Frequenz-Normierung (F_h an festen Bandpunkten z, NICHT rohe alpha_k) konvergiert die h-Leiter: D-Limes sauber an ALLEN Bandpunkten inkl. s < 1/2 (M2.2, must-fail M2.3: ohne den UV-Term keine Cauchy-Folge); Reichweiten-Leiter = geschlossener Zaehldaten-Tail auf <= 3e-3 fuer s > 1/2 (M2.4). Das 5b-M2.2-Negativ war die NORMIERUNG: roh gibt es keine h-stabile Leiter, selbst bei festem Mass (r_env = %+.2f) -- beide Lesarten dokumentiert (M2.1). WO es divergiert: nicht in D; in den Reichweiten-Tails bei s <= 1/2 (Atome und Pol einzeln divergent, Ausloeschung auf PNT-Niveau gemessen, Faktor %.0fx; das Prediktions-Residuum waechst monoton Richtung s = 1/2) -- die Halbebenen-Grenze ist die kritische Linie, getypt, nie geladen (M2.5). FEHLENDE SAETZE fuer den Vertrag (benannt, M3.3): lokal uniforme Schranken, Straffheit, GNS-Limes-Hilbertraum, Mosco-/ stark-resolvente Konvergenz der CMV/Jacobi-Trunkierungen, Positivitaets-Transport im Limes (RP-Analogon v679 O2), das s=1/2-Randobjekt und die Pf/Diagonal-UV als Satz. Kill-Kriterien unveraendert (AST-erzwungen).""" % ( abs(s_inf - 1.0), K_JAC, BAR_GAUSS, r_fix, canc[1] / canc[2])) # ------------------------------------------------------------ final print("\n" + "=" * 72) dt = time.time() - T0 if FAILS: print("RESULT: %d/%d checks passed -- FAILURES: %s (%.1f s)" % (N_CHK - len(FAILS), N_CHK, ", ".join(FAILS), dt)) print("VERDICT: %s" % verdict) return 1 print("RESULT: ALL %d CHECKS PASSED (%.1f s)" % (N_CHK, dt)) print("VERDICT: %s" % verdict) return 0 if __name__ == "__main__": raise SystemExit(run())