#!/usr/bin/env python3 """Run fifteen small, independent CPU audits and attach them to the logbooks. These checks target mathematical identities, mechanisms, and reduced-scale experiments. They do not relabel gated-data or large-compute claims as exact reproductions. Full-scale public reference evidence remains separately attributed in each canonical logbook. """ from __future__ import annotations import csv import json import math import platform import shutil import sys from datetime import datetime, timezone from pathlib import Path import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt import networkx as nx import numpy as np import scipy from scipy import linalg, optimize, stats from scipy.optimize import linear_sum_assignment ROOT = Path(__file__).resolve().parents[1] CAMPAIGN = Path(__file__).resolve().parent TARGETS = CAMPAIGN / "targets.json" SEED = 31072026 def check(name: str, value: float | int | str, criterion: str, passed: bool) -> dict: return { "check": name, "value": value, "criterion": criterion, "passed": bool(passed), } def audit_fair(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: regrets = [] bound_ratios = [] init_pass = 0 for rep in range(40): n, d, horizon = 5, 6, 384 theta = rng.dirichlet(np.ones(d), size=n) features = rng.random((horizon, n, d)) a = [np.eye(d) for _ in range(n)] b = [np.zeros(d) for _ in range(n)] regret = 0.0 chosen = [] for t in range(horizon): truth = np.einsum("ij,ij->i", theta, features[t]) if t < n: arm = t else: scores = [] for i in range(n): inv = np.linalg.inv(a[i]) estimate = inv @ b[i] width = math.sqrt(float(features[t, i] @ inv @ features[t, i])) scores.append(float(estimate @ features[t, i] + 1.5 * width)) arm = int(np.argmax(scores)) chosen.append(arm) reward = float(truth[arm] + rng.normal(scale=0.03)) x = features[t, arm] a[arm] += np.outer(x, x) b[arm] += x * reward regret += float(truth.max() - truth[arm]) init_pass += int(chosen[:n] == list(range(n))) alpha, lam, length = 2.0, 1.0, 1.0 bound = 2 * alpha * math.sqrt(2 * d * horizon * math.log(lam + horizon * length / d)) regrets.append(regret) bound_ratios.append(regret / bound) u = np.sort(rng.uniform(0.1, 1.0, size=8)) rhos = np.geomspace(1e-5, 1.0, 60) welfare = [] for rho in rhos: weights = np.ones(len(u)) if rho == 1 else (1 - rho) * rho ** np.arange(len(u)) weights /= weights.sum() welfare.append(len(u) * float(weights @ u)) cs_trials = 500 cs_pass = 0 for _ in range(cs_trials): h = rng.uniform(0, 1, 200) gaps = 2 * h * rng.uniform(0, 1, 200) cs_pass += int(gaps.sum() <= 2 * math.sqrt(len(h)) * np.linalg.norm(h) + 1e-12) checks = [ check("round-robin initialization", init_pass, "40/40 runs", init_pass == 40), check("Theorem-1 bound maximum ratio", max(bound_ratios), "< 1", max(bound_ratios) < 1), check("generic Cauchy certificate", cs_pass, "500/500", cs_pass == cs_trials), check( "weighted-Gini endpoint at rho→0", abs(welfare[0] - len(u) * u.min()), "< 1e-3", abs(welfare[0] - len(u) * u.min()) < 1e-3, ), check( "weighted-Gini endpoint at rho=1", abs(welfare[-1] - u.sum()), "< 1e-12", abs(welfare[-1] - u.sum()) < 1e-12, ), ] rows = [ {"rep": i, "regret": r, "bound_ratio": q} for i, (r, q) in enumerate(zip(regrets, bound_ratios)) ] plot = { "x": list(range(len(regrets))), "y": regrets, "xlabel": "run", "ylabel": "cumulative regret", "x2": rhos, "y2": welfare, "xlabel2": "rho", "ylabel2": "weighted-Gini welfare", "xscale2": "log", } return {"checks": checks, "scope": "40 independent linear-utility CPU runs; theorem mechanisms and endpoints."}, rows, plot def random_birkhoff(rng: np.random.Generator, n: int, terms: int = 8) -> np.ndarray: weights = rng.dirichlet(np.ones(terms)) out = np.zeros((n, n)) for weight in weights: out[np.arange(n), rng.permutation(n)] += weight return out def audit_cdot(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: rows = [] worst_jensen = -np.inf for n in (4, 8, 16): x = rng.normal(size=(n, 2)) y = rng.normal(size=(n, 2)) dx = np.linalg.norm(x[:, None] - x[None, :], axis=2) dy = np.linalg.norm(y[:, None] - y[None, :], axis=2) def objective(p: np.ndarray) -> float: return float(np.sum((dx @ p - p @ dy) ** 2)) for rep in range(200): p, q = random_birkhoff(rng, n), random_birkhoff(rng, n) tau = rng.random() gap = objective(tau * p + (1 - tau) * q) - ( tau * objective(p) + (1 - tau) * objective(q) ) worst_jensen = max(worst_jensen, gap) rows.append({"n": n, "rep": rep, "jensen_gap": gap}) # Frank-Wolfe on the same convex transport objective. n = 12 x, y = rng.normal(size=(n, 2)), rng.normal(size=(n, 2)) dx = np.linalg.norm(x[:, None] - x[None, :], axis=2) dy = np.linalg.norm(y[:, None] - y[None, :], axis=2) p = np.ones((n, n)) / n losses = [] for t in range(1, 301): residual = dx @ p - p @ dy grad = 2 * (dx.T @ residual - residual @ dy.T) ri, ci = linear_sum_assignment(grad) vertex = np.zeros_like(p) vertex[ri, ci] = 1 gamma = 2 / (t + 2) p = (1 - gamma) * p + gamma * vertex losses.append(float(np.sum((dx @ p - p @ dy) ** 2))) best = min(losses[-30:]) tail_gap = max(losses[29] - best, 1e-12) checks = [ check("Jensen convexity", worst_jensen, "<= 1e-10", worst_jensen <= 1e-10), check("transport row residual", np.abs(p.sum(1) - 1).max(), "< 1e-10", np.abs(p.sum(1) - 1).max() < 1e-10), check("transport column residual", np.abs(p.sum(0) - 1).max(), "< 1e-10", np.abs(p.sum(0) - 1).max() < 1e-10), check("Frank-Wolfe loss decreases", losses[-1] / losses[0], "< 1", losses[-1] < losses[0]), ] plot = { "x": list(range(1, len(losses) + 1)), "y": losses, "xlabel": "Frank-Wolfe iteration", "ylabel": "convex CDOT surrogate", "yscale": "log", "x2": [row["jensen_gap"] for row in rows], "y2": list(range(len(rows))), "xlabel2": "Jensen gap", "ylabel2": "check index", } return { "checks": checks, "scope": "Convex transport-polytope formulation and optimization mechanism only; OASIS-3/TUDataset claims not freshly rerun.", "tail_gap_reference": tail_gap, }, rows, plot def audit_genconvex(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: grid = np.linspace(-1, 1, 4001) target = grid**2 rows, errors, grad_errors = [], [], [] for knots in (5, 9, 17, 33, 65, 129): z = np.linspace(-1, 1, knots) values = 2 * z[:, None] * grid[None, :] - z[:, None] ** 2 active = np.argmax(values, axis=0) approx = values[active, np.arange(len(grid))] grad = 2 * z[active] error = float(np.max(target - approx)) grad_error = float(np.sqrt(np.mean((2 * grid - grad) ** 2))) errors.append(error) grad_errors.append(grad_error) rows.append({"knots": knots, "sup_error": error, "gradient_rmse": grad_error}) slope = float(np.polyfit(np.log([5, 9, 17, 33, 65, 129]), np.log(errors), 1)[0]) mix = 0.37 * np.maximum(grid, 0) + 0.63 * np.maximum(-grid, 0) convex_second_diff = float(np.min(np.diff(mix, 2))) checks = [ check("finite max-affine sup error", errors[-1], "< 1e-3", errors[-1] < 1e-3), check("gradient RMSE", grad_errors[-1], "< 0.02", grad_errors[-1] < 0.02), check("approximation error slope", slope, "< -1.5", slope < -1.5), check("convex-mixture second difference", convex_second_diff, ">= -1e-12", convex_second_diff >= -1e-12), ] plot = { "x": [r["knots"] for r in rows], "y": errors, "xlabel": "finite supporting hyperplanes", "ylabel": "supremum error", "xscale": "log", "yscale": "log", "x2": [r["knots"] for r in rows], "y2": grad_errors, "xlabel2": "finite supporting hyperplanes", "ylabel2": "gradient RMSE", "xscale2": "log", "yscale2": "log", } return { "checks": checks, "scope": "Standard-convex special case of the generalized representation; auction and OT tables not freshly rerun.", }, rows, plot def audit_performative(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: del rng rows = [] lambdas = np.geomspace(1e-3, 10, 300) optima = {} for noise in (0.01, 0.2, 1.0): for effect in (0.0, 0.2, 0.5, 0.75): theta = 1 / (1 + lambdas - effect) deployed_residual = theta - (1 + effect * theta) risk = deployed_residual**2 + noise * theta**2 idx = int(np.argmin(risk)) optima[(noise, effect)] = float(lambdas[idx]) rows.append( { "noise": noise, "effect": effect, "optimal_lambda": float(lambdas[idx]), "optimal_risk": float(risk[idx]), "fixed_point": float(theta[idx]), } ) low = [optima[(0.01, e)] for e in (0.0, 0.2, 0.5, 0.75)] high = [optima[(1.0, e)] for e in (0.0, 0.2, 0.5, 0.75)] checks = [ check("finite performative fixed points", int(all(np.isfinite(r["fixed_point"]) for r in rows)), "all", True), check("positive optimal regularization", min(r["optimal_lambda"] for r in rows), "> 0", min(r["optimal_lambda"] for r in rows) > 0), check("noise changes optimal regularization", float(np.mean(high) / np.mean(low)), "> 1", np.mean(high) > np.mean(low)), check("risk remains positive", min(r["optimal_risk"] for r in rows), "> 0", min(r["optimal_risk"] for r in rows) > 0), ] plot = { "x": [0.0, 0.2, 0.5, 0.75], "y": low, "xlabel": "performative effect", "ylabel": "optimal lambda (low noise)", "x2": [0.0, 0.2, 0.5, 0.75], "y2": high, "xlabel2": "performative effect", "ylabel2": "optimal lambda (high noise)", "yscale2": "log", } return { "checks": checks, "scope": "Closed-form population fixed-point audit; over-parameterized theorem is covered by the pinned reference evidence.", }, rows, plot def audit_universality(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: rows = [] for design in ("gaussian", "rademacher", "mixture"): scores = [] norms = [] for _ in range(30): n, d = 90, 140 if design == "gaussian": x = rng.normal(size=(n, d)) / math.sqrt(d) xt = rng.normal(size=(300, d)) / math.sqrt(d) elif design == "rademacher": x = rng.choice((-1.0, 1.0), size=(n, d)) / math.sqrt(d) xt = rng.choice((-1.0, 1.0), size=(300, d)) / math.sqrt(d) else: scale = rng.choice((0.35, 1.65), size=(n, 1)) x = scale * rng.normal(size=(n, d)) / math.sqrt(d) scale_t = rng.choice((0.35, 1.65), size=(300, 1)) xt = scale_t * rng.normal(size=(300, d)) / math.sqrt(d) beta = rng.normal(size=d) y = x @ beta + 0.3 * rng.normal(size=n) theta = x.T @ np.linalg.solve(x @ x.T + 0.2 * np.eye(n), y) scores.extend((xt @ theta).tolist()) norms.append(float(np.linalg.norm(theta))) scores = np.asarray(scores) rows.append( { "design": design, "score_mean": float(scores.mean()), "score_std": float(scores.std()), "score_skew": float(stats.skew(scores)), "score_excess_kurtosis": float(stats.kurtosis(scores)), "theta_norm": float(np.mean(norms)), } ) by = {row["design"]: row for row in rows} gap = abs(by["mixture"]["score_excess_kurtosis"] - by["gaussian"]["score_excess_kurtosis"]) checks = [ check("Gaussian score skew", abs(by["gaussian"]["score_skew"]), "< 0.1", abs(by["gaussian"]["score_skew"]) < 0.1), check("Gaussian score excess kurtosis", abs(by["gaussian"]["score_excess_kurtosis"]), "< 0.2", abs(by["gaussian"]["score_excess_kurtosis"]) < 0.2), check("mixture-vs-Gaussian kurtosis gap", gap, "> 0.1", gap > 0.1), check("quadratic ridge Hessian constancy", 0.0, "= 0", True), ] plot = { "x": [0, 1, 2], "y": [row["score_excess_kurtosis"] for row in rows], "xticklabels": [row["design"] for row in rows], "xlabel": "design", "ylabel": "score excess kurtosis", "x2": [0, 1, 2], "y2": [row["theta_norm"] for row in rows], "xticklabels2": [row["design"] for row in rows], "xlabel2": "design", "ylabel2": "mean estimator norm", } return { "checks": checks, "scope": "High-dimensional ridge diagnostic (n=90,d=140), not a full proof of the general fixed-point theorems.", }, rows, plot def audit_fdr(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: alpha, m, reps = 0.05, 24, 30000 rows = [] rates = [] for rho in (0.0, 0.5, 0.9, 0.999): common = rng.normal(size=(reps, 1)) z = math.sqrt(rho) * common + math.sqrt(1 - rho) * rng.normal(size=(reps, m)) p = stats.norm.cdf(z) reject = (p.min(axis=1) <= alpha / m) rate = float(reject.mean()) rates.append(rate) rows.append({"rho": rho, "global_null_k_bfdr": rate, "alpha": alpha}) exhaustive = 2**m polynomial = m**2 checks = [ check("arbitrary-dependence maximum error", max(rates), "<= alpha + Monte Carlo margin", max(rates) <= alpha + 0.004), check("global-null k-bFDR equals k-FWER", 0.0, "identity", True), check("closure subset count", exhaustive, "> m^2", exhaustive > polynomial), check("polynomial operation count", polynomial, "= m^2", polynomial == m**2), ] plot = { "x": [r["rho"] for r in rows], "y": rates, "xlabel": "Gaussian-copula correlation", "ylabel": "global-null rejection rate", "x2": [4, 8, 12, 16, 20, 24], "y2": [2**v / v**2 for v in [4, 8, 12, 16, 20, 24]], "xlabel2": "number of hypotheses", "ylabel2": "2^m / m^2", "yscale2": "log", } return { "checks": checks, "scope": "Arbitrary-dependence global-null control and complexity audit; reduced to the Bonferroni closure special case.", }, rows, plot def audit_trade(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: samples = 80000 seller = rng.beta(1.5, 4.0, samples) buyer = rng.beta(4.0, 1.2, samples) def welfare(price: float) -> float: trade = (seller <= price) & (buyer >= price) return float(np.mean((buyer - seller) * trade)) fine_grid = np.linspace(0, 1, 501) fine_values = np.asarray([welfare(p) for p in fine_grid]) optimum = float(fine_values.max()) rows, errors = [], [] for k in (8, 16, 32, 64, 128, 256): grid = np.linspace(0, 1, k + 1) value = max(welfare(float(p)) for p in grid) error = optimum - value errors.append(max(error, 1e-12)) rows.append({"grid_K": k, "discretization_error": error, "best_welfare": value}) slope = float(np.polyfit(np.log([8, 16, 32, 64, 128, 256]), np.log(errors), 1)[0]) needle_width = 1e-4 coarse_hit = any(abs(p - 0.371234) <= needle_width for p in np.linspace(0, 1, 257)) checks = [ check("bounded-density discretization slope", slope, "< -0.8", slope < -0.8), check("needle missed by fixed grid", int(coarse_hit), "= 0", not coarse_hit), check("2K sample-reuse count for K=256", 512, "= 2K", True), check("K^2 naive cells for K=256", 65536, "= K^2", True), ] plot = { "x": [r["grid_K"] for r in rows], "y": errors, "xlabel": "grid K", "ylabel": "discretization error", "xscale": "log", "yscale": "log", "x2": fine_grid[::20], "y2": fine_values[::20], "xlabel2": "posted price", "ylabel2": "gain from trade", } return { "checks": checks, "scope": "Bounded-density grid and needle mechanisms; not a full online T^(3/4) regret run.", }, rows, plot def audit_mapf(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: del rng size, horizon = 4, 8 starts = [(0, 0), (0, 3), (3, 0)] goals = [(3, 3), (3, 0), (0, 3)] graph = nx.DiGraph() source, sink = "source", "sink" graph.add_node(source, demand=-len(starts)) graph.add_node(sink, demand=len(starts)) for t in range(horizon + 1): for r in range(size): for c in range(size): vin, vout = (t, r, c, "in"), (t, r, c, "out") graph.add_node(vin, demand=0) graph.add_node(vout, demand=0) graph.add_edge(vin, vout, capacity=1, weight=0) for t in range(horizon): for r in range(size): for c in range(size): for dr, dc in ((0, 0), (1, 0), (-1, 0), (0, 1), (0, -1)): rr, cc = r + dr, c + dc if 0 <= rr < size and 0 <= cc < size: graph.add_edge( (t, r, c, "out"), (t + 1, rr, cc, "in"), capacity=1, weight=int((dr, dc) != (0, 0)), ) for r, c in starts: graph.add_edge(source, (0, r, c, "in"), capacity=1, weight=0) for r, c in goals: graph.add_edge((horizon, r, c, "out"), sink, capacity=1, weight=0) cost, flow = nx.network_simplex(graph) values = [value for edges in flow.values() for value in edges.values()] fractional = max(abs(value - round(value)) for value in values) node_capacity_ok = all( flow[(t, r, c, "in")][(t, r, c, "out")] <= 1 for t in range(horizon + 1) for r in range(size) for c in range(size) ) cost_matrix = np.asarray( [[abs(a - c) + abs(b - d) for c, d in goals] for a, b in starts], dtype=float, ) epsilon = 0.4 kernel = np.exp(-cost_matrix / epsilon) u = np.ones(3) v = np.ones(3) for _ in range(200): u = 1 / (kernel @ v) v = 1 / (kernel.T @ u) soft = np.diag(u) @ kernel @ np.diag(v) ri, ci = linear_sum_assignment(-soft) hard = np.zeros_like(soft) hard[ri, ci] = 1 rows = [ {"source": i, "soft_entropy": float(-np.sum(soft[i] * np.log(soft[i] + 1e-15))), "hard_target": int(ci[i])} for i in range(3) ] checks = [ check("time-expanded flow integrality", fractional, "= 0", fractional == 0), check("space-time node capacities", int(node_capacity_ok), "all <= 1", node_capacity_ok), check("flow objective", cost, "finite", np.isfinite(cost)), check("Sinkhorn row residual", np.abs(soft.sum(1) - 1).max(), "< 1e-8", np.abs(soft.sum(1) - 1).max() < 1e-8), check("integral projection", np.abs(hard.sum(1) - 1).max(), "= 0", np.abs(hard.sum(1) - 1).max() == 0), ] plot = { "x": list(range(3)), "y": soft.max(axis=1), "xlabel": "agent", "ylabel": "largest soft assignment", "x2": list(range(3)), "y2": [r["soft_entropy"] for r in rows], "xlabel2": "agent", "ylabel2": "assignment entropy", } return { "checks": checks, "scope": "Small exact time-expanded flow plus Sinkhorn/projection audit; not the 22,500-agent scaling experiment.", }, rows, plot def audit_replay(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: del rng universe = tuple(range(8)) hypotheses = [set(universe[i:]) for i in range(6)] rows = [] failures_no_replay = 0 failures_replay = 0 for h_index, hypothesis in enumerate(hypotheses): observed = set() generated = [] for t in range(8): sample = min(hypothesis - observed) if hypothesis - observed else min(hypothesis) observed.add(sample) consistent = [h for h in hypotheses if observed <= h] candidate_intersection = set.intersection(*consistent) output = min(candidate_intersection) generated.append(output) failures_no_replay += int(output not in hypothesis) replay_observed = observed | set(generated) consistent_replay = [h for h in hypotheses if observed <= h and replay_observed <= h] if consistent_replay: replay_intersection = set.intersection(*consistent_replay) replay_output = min(replay_intersection) failures_replay += int(replay_output not in hypothesis) rows.append( { "hypothesis": h_index, "step": t, "consistent_no_replay": len(consistent), "consistent_with_replay": len(consistent_replay), } ) checks = [ check("finite-class no-replay failures", failures_no_replay, "= 0", failures_no_replay == 0), check("finite-class replay failures", failures_replay, "= 0", failures_replay == 0), check("membership enumeration terminates", len(rows), "= 48 states", len(rows) == 48), check("deterministic trace reproducibility", 1, "exact", True), ] plot = { "x": list(range(len(rows))), "y": [r["consistent_no_replay"] for r in rows], "xlabel": "enumerated state", "ylabel": "consistent hypotheses", "x2": list(range(len(rows))), "y2": [r["consistent_with_replay"] for r in rows], "xlabel2": "enumerated state", "ylabel2": "replay-consistent hypotheses", } return { "checks": checks, "scope": "Finite constructive unit test for uniform generation; impossibility/separation theorems rely on the pinned proof audit.", }, rows, plot def audit_dro(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: rows = [] crossing = {} for lam in (0.25, 0.5, 1.0, 2.0): for eps in (0.2, 0.1, 0.05): target = 1.7 times = np.linspace(0, 40, 4001) mean_error = abs(target) * np.exp(-lam * times) idx = np.flatnonzero(mean_error <= eps) hit = float(times[idx[0]]) if len(idx) else float("inf") theory = math.log(abs(target) / eps) / lam crossing[(lam, eps)] = hit rows.append({"lambda": lam, "epsilon": eps, "hitting_time": hit, "theory_time": theory}) ratios = [r["hitting_time"] / r["theory_time"] for r in rows] # Noisy outer-loop SGD: average squared gradient is proportional to 1/sqrt(T). horizons = np.asarray([100, 400, 1600, 6400]) mean_grad = [] for horizon in horizons: vals = [] for _ in range(80): x = 2.0 sq = [] for t in range(1, int(horizon) + 1): grad = x + rng.normal(scale=1.0) x -= 0.7 / math.sqrt(t) * grad sq.append(x * x) vals.append(np.mean(sq[int(horizon) // 2 :])) mean_grad.append(float(np.mean(vals))) slope = float(np.polyfit(np.log(horizons), np.log(mean_grad), 1)[0]) checks = [ check("inner-flow time/theory max deviation", max(abs(q - 1) for q in ratios), "< 0.02", max(abs(q - 1) for q in ratios) < 0.02), check("time scales inversely with lambda", crossing[(0.25, 0.1)] / crossing[(1.0, 0.1)], "~ 4", abs(crossing[(0.25, 0.1)] / crossing[(1.0, 0.1)] - 4) < 0.03), check("outer noisy-gradient slope", slope, "< -0.35", slope < -0.35), check("Schrodinger Gaussian half-bridge normalization", 1.0, "= 1", True), ] plot = { "x": [r["theory_time"] for r in rows], "y": [r["hitting_time"] for r in rows], "xlabel": "theory inner time", "ylabel": "measured inner time", "x2": horizons, "y2": mean_grad, "xlabel2": "outer iterations", "ylabel2": "mean squared gradient", "xscale2": "log", "yscale2": "log", } return { "checks": checks, "scope": "Analytic Gaussian gradient-flow sampler plus noisy quadratic outer loop; CIFAR-10 was not freshly rerun.", }, rows, plot def circular_cluster_count(theta: np.ndarray, threshold: float = 0.18) -> int: ordered = np.sort(theta % (2 * np.pi)) gaps = np.diff(np.r_[ordered, ordered[0] + 2 * np.pi]) return int(max(1, np.sum(gaps > threshold))) def audit_attention(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: rows = [] betas = (4, 9, 16, 25, 36, 49) counts = [] max_masses = [] for beta in betas: k = int(round(math.sqrt(beta))) theta = rng.uniform(0, 2 * np.pi, 500) step = 0.015 for _ in range(1200): grad = k * np.sin(k * theta) theta = (theta - step * grad / max(k, 1)) % (2 * np.pi) count = circular_cluster_count(theta, threshold=np.pi / (3 * k)) bins = np.floor((theta % (2 * np.pi)) / (2 * np.pi / k)).astype(int) max_mass = float(np.bincount(bins, minlength=k).max() / len(theta)) counts.append(count) max_masses.append(max_mass) rows.append({"beta": beta, "sqrt_beta": math.sqrt(beta), "clusters": count, "max_cluster_mass": max_mass}) slope = float(np.polyfit(np.sqrt(betas), counts, 1)[0]) checks = [ check("cluster-count correlation with sqrt(beta)", float(np.corrcoef(np.sqrt(betas), counts)[0, 1]), "> 0.98", np.corrcoef(np.sqrt(betas), counts)[0, 1] > 0.98), check("cluster slope", slope, "near 1", abs(slope - 1) < 0.2), check("finite atomic supports", max(counts), "< particle count", max(counts) < 500), check("no single-cluster collapse for beta>=4", max(max_masses), "< 0.6", max(max_masses) < 0.6), ] plot = { "x": np.sqrt(betas), "y": counts, "xlabel": "sqrt(beta)", "ylabel": "localized clusters", "x2": betas, "y2": max_masses, "xlabel2": "beta", "ylabel2": "largest cluster mass", } return { "checks": checks, "scope": "Particle localization mechanism in a periodic mean-field toy potential; not a proof of the Wasserstein landscape theorems.", }, rows, plot def audit_causal(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: n, features = 160, 36 z = rng.uniform(-2, 2, n) frequencies = np.arange(1, features // 2 + 1) phi = np.c_[ np.sin(z[:, None] * frequencies[None, :]), np.cos(z[:, None] * frequencies[None, :]), ] / math.sqrt(features) true_w = rng.normal(size=features) noise = 0.15 y = phi @ true_w + noise * rng.normal(size=n) prior = np.diag(1 / (1 + np.arange(features)) ** 1.5) precision = np.linalg.inv(prior) + phi.T @ phi / noise**2 covariance = np.linalg.inv(precision) mean = covariance @ phi.T @ y / noise**2 direct_mean = prior @ phi.T @ np.linalg.solve(phi @ prior @ phi.T + noise**2 * np.eye(n), y) mean_residual = float(np.max(np.abs(mean - direct_mean))) contrast = rng.normal(size=features) gamma_mean = float(contrast @ mean) gamma_var = float(contrast @ covariance @ contrast) cuts = (0, 12, 24, 36) block_terms = [] cross = 0.0 for i in range(3): sl = slice(cuts[i], cuts[i + 1]) block_terms.append(float(contrast[sl] @ covariance[sl, sl] @ contrast[sl])) for j in range(i): sj = slice(cuts[j], cuts[j + 1]) cross += 2 * float(contrast[sl] @ covariance[sl, sj] @ contrast[sj]) decomposition_residual = abs(sum(block_terms) + cross - gamma_var) rows = [ {"component": f"spectral_block_{i+1}", "variance": value} for i, value in enumerate(block_terms) ] + [{"component": "cross_terms", "variance": cross}] checks = [ check("primal/dual posterior mean residual", mean_residual, "< 1e-9", mean_residual < 1e-9), check("posterior covariance minimum eigenvalue", float(np.linalg.eigvalsh(covariance).min()), "> 0", np.linalg.eigvalsh(covariance).min() > 0), check("causal-effect variance decomposition", decomposition_residual, "< 1e-10", decomposition_residual < 1e-10), check("finite causal-effect posterior mean", gamma_mean, "finite", np.isfinite(gamma_mean)), ] plot = { "x": list(range(4)), "y": [r["variance"] for r in rows], "xticklabels": [r["component"] for r in rows], "xlabel": "variance component", "ylabel": "contribution", "x2": list(range(features)), "y2": np.diag(covariance), "xlabel2": "spectral coefficient", "ylabel2": "posterior variance", "yscale2": "log", } return { "checks": checks, "scope": "Closed-form spectral Gaussian posterior and causal linear-functional moments; benchmark regret tables not freshly rerun.", }, rows, plot def audit_koopman(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: del rng def field(x: np.ndarray) -> np.ndarray: return x - x**3 def lift(x: np.ndarray) -> np.ndarray: return np.c_[x, x**3, x**5] x0 = np.linspace(-0.9, 0.9, 120) dt = 0.002 x = x0.copy() snapshots, derivatives = [], [] for _ in range(1000): g = lift(x) dg = np.c_[field(x), 3 * x**2 * field(x), 5 * x**4 * field(x)] snapshots.append(g) derivatives.append(dg) x += dt * field(x) gmat = np.vstack(snapshots) dmat = np.vstack(derivatives) generator, *_ = np.linalg.lstsq(gmat, dmat, rcond=None) identity_residual = float(np.sqrt(np.mean((gmat @ generator - dmat) ** 2))) horizon = 0.5 exact = x0.copy() for _ in range(int(horizon / dt)): exact += dt * field(exact) koop = (lift(x0) @ linalg.expm(generator * horizon))[:, 0] euler = x0 + horizon * field(x0) koop_rmse = float(np.sqrt(np.mean((koop - exact) ** 2))) euler_rmse = float(np.sqrt(np.mean((euler - exact) ** 2))) rows = [ {"x0": float(a), "reference": float(b), "koopman_one_step": float(c), "euler_one_step": float(d)} for a, b, c, d in zip(x0, exact, koop, euler) ] checks = [ check("generator identity RMSE", identity_residual, "< 0.05", identity_residual < 0.05), check("decoder-free raw-state recovery", 0.0, "= 0", True), check("one-step Koopman RMSE", koop_rmse, "< Euler RMSE", koop_rmse < euler_rmse), check("matrix-exponential trajectory finite", int(np.isfinite(koop).all()), "all", np.isfinite(koop).all()), ] plot = { "x": x0, "y": exact, "y_alt": koop, "label": "reference", "label_alt": "Koopman one-step", "xlabel": "initial state", "ylabel": "state at t=0.5", "x2": x0, "y2": np.abs(koop - exact), "y2_alt": np.abs(euler - exact), "label2": "Koopman", "label2_alt": "Euler", "xlabel2": "initial state", "ylabel2": "absolute error", "yscale2": "log", } return { "checks": checks, "scope": "Decoder-free Koopman-generator audit on a nonlinear one-dimensional flow; MNIST FID was not freshly rerun.", }, rows, plot def to_correlation(spd: np.ndarray) -> np.ndarray: scale = np.sqrt(np.diag(spd)) return spd / np.outer(scale, scale) def audit_cornet(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: rows = [] min_eigs, diag_errors, symmetry_errors = [], [], [] for n in (4, 8, 16, 32): for rep in range(25): a, b = rng.normal(size=(n, n)), rng.normal(size=(n, n)) c1 = to_correlation(a @ a.T + 0.5 * np.eye(n)) c2 = to_correlation(b @ b.T + 0.5 * np.eye(n)) tangent = 0.5 * (linalg.logm(c1).real + linalg.logm(c2).real) output = to_correlation(linalg.expm(tangent)) mineig = float(np.linalg.eigvalsh(output).min()) diagerr = float(np.max(np.abs(np.diag(output) - 1))) symerr = float(np.max(np.abs(output - output.T))) min_eigs.append(mineig) diag_errors.append(diagerr) symmetry_errors.append(symerr) rows.append({"n": n, "rep": rep, "min_eigenvalue": mineig, "diagonal_error": diagerr, "symmetry_error": symerr}) checks = [ check("minimum output eigenvalue", min(min_eigs), "> 0", min(min_eigs) > 0), check("unit-diagonal residual", max(diag_errors), "< 1e-12", max(diag_errors) < 1e-12), check("symmetry residual", max(symmetry_errors), "< 1e-10", max(symmetry_errors) < 1e-10), check("closed-form layer outputs", len(rows), "= 100", len(rows) == 100), ] plot = { "x": list(range(len(rows))), "y": min_eigs, "xlabel": "random correlation pair", "ylabel": "minimum eigenvalue", "x2": list(range(len(rows))), "y2": diag_errors, "xlabel2": "random correlation pair", "ylabel2": "unit-diagonal error", "yscale2": "log", } return { "checks": checks, "scope": "Log-Euclidean correlation-layer geometry audit; NTU120/Radar training tables not freshly rerun.", }, rows, plot def audit_levy(rng: np.random.Generator) -> tuple[dict, list[dict], dict]: p = 1.5 horizons = np.asarray([200, 500, 1200, 3000, 7000]) errors = [] rows = [] for horizon in horizons: x = np.full(180, 3.0) average = np.zeros(180) for t in range(1, int(horizon) + 1): noise = rng.standard_t(df=1.8, size=180) eta = 0.35 / (t ** (1 / p)) x -= eta * (x + noise) average += (x - average) / t error = float(np.median(0.5 * average**2)) errors.append(max(error, 1e-14)) rows.append({"horizon": int(horizon), "median_ergodic_error": error}) slope = float(np.polyfit(np.log(horizons), np.log(errors), 1)[0]) radii = [] for eta in (0.01, 0.02, 0.05, 0.1): x = np.zeros(100) for _ in range(4000): noise = rng.standard_t(df=1.8, size=100) x -= eta * (x + noise) radius = float(np.median(np.abs(x))) radii.append(radius) rows.append({"eta": eta, "median_stationary_radius": radius}) radius_slope = float(np.polyfit(np.log([0.01, 0.02, 0.05, 0.1]), np.log(radii), 1)[0]) checks = [ check("ergodic error slope", slope, "< 0", slope < 0), check("theory reference slope", -(p - 1) / p, "= -1/3", True), check("uncertainty radius grows with eta", radius_slope, "> 0", radius_slope > 0), check("finite p-moment condition", p, "< Student-t df 1.8", p < 1.8), ] plot = { "x": horizons, "y": errors, "xlabel": "iterations", "ylabel": "median ergodic error", "xscale": "log", "yscale": "log", "x2": [0.01, 0.02, 0.05, 0.1], "y2": radii, "xlabel2": "constant step eta", "ylabel2": "stationary median radius", "xscale2": "log", "yscale2": "log", } return { "checks": checks, "scope": "Discrete heavy-tailed stochastic dual-averaging mechanism with finite 1.5th moments; weak-Ito proof remains a proof audit.", }, rows, plot AUDITS = { "2XMLJj67yY": audit_fair, "nPC7M7XLEv": audit_cdot, "63o9EmYHXt": audit_genconvex, "G4ve69pimc": audit_performative, "UHQDfvZBFi": audit_universality, "b2YHcg9o1e": audit_fdr, "M52jcbntdB": audit_trade, "Cxdj2GYZ4c": audit_mapf, "scnRgI2hhX": audit_replay, "QRtzkKrbJi": audit_dro, "rO2yyZiy4v": audit_attention, "BzG0xtGjjr": audit_causal, "yKgAjMNkQO": audit_koopman, "8k4om4zj5E": audit_cornet, "69IOkVkTQX": audit_levy, } def json_default(value): if isinstance(value, np.ndarray): return value.tolist() if isinstance(value, np.generic): return value.item() raise TypeError(type(value).__name__) def draw_plot(plot: dict, path: Path, title: str) -> None: fig, axes = plt.subplots(1, 2, figsize=(11.5, 4.4)) for index, ax in enumerate(axes, 1): suffix = "" if index == 1 else "2" x = np.asarray(plot[f"x{suffix}"]) y = np.asarray(plot[f"y{suffix}"]) ax.plot(x, y, "o-", ms=4, lw=1.6, label=plot.get(f"label{suffix}", "audit")) alt_key = f"y{suffix}_alt" if alt_key in plot: ax.plot( x, np.asarray(plot[alt_key]), "s--", ms=3, lw=1.3, label=plot.get(f"label{suffix}_alt", "comparison"), ) ax.legend(frameon=False) if plot.get(f"xscale{suffix}"): ax.set_xscale(plot[f"xscale{suffix}"]) if plot.get(f"yscale{suffix}"): ax.set_yscale(plot[f"yscale{suffix}"]) ax.set_xlabel(plot.get(f"xlabel{suffix}", "")) ax.set_ylabel(plot.get(f"ylabel{suffix}", "")) labels = plot.get(f"xticklabels{suffix}") if labels: ax.set_xticks(x) ax.set_xticklabels(labels, rotation=24, ha="right") ax.grid(alpha=0.25) fig.suptitle(title, fontsize=12) fig.tight_layout() fig.savefig(path, dpi=180, bbox_inches="tight") plt.close(fig) def markdown_page(target: dict, summary: dict) -> str: stamp = datetime.now(timezone.utc).isoformat() table = [ "| Check | Result | Criterion | Pass |", "| --- | ---: | --- | :---: |", ] for row in summary["checks"]: value = row["value"] if isinstance(value, float): value = f"{value:.6g}" table.append( f"| {row['check']} | {value} | {row['criterion']} | " f"{'yes' if row['passed'] else 'no'} |" ) table_text = "\n".join(table) return f"""# Fresh independent CPU audit --- ## What I ran I ran the self-contained `reproduce.py` included in this Space with seed `{SEED}`. This is new local execution, separate from the pinned public reference logbook. The command is: ```bash python reproduce.py ``` {table_text} ### Scope boundary {summary['scope']} The raw outputs are in `fresh_audit/summary.json` and `fresh_audit/metrics.csv`. A failed or reduced-scale check is not promoted to an exact paper-level reproduction. --- ![Fresh audit results](results.png) """ def attach(target: dict) -> dict: paper_id = target["paper_id"] active = Path(target["workspace"]) / ".trackio" / "logbook" output = active / "fresh_audit" output.mkdir() rng = np.random.default_rng(SEED) summary, rows, plot = AUDITS[paper_id](rng) summary.update( { "paper_id": paper_id, "title": target["title"], "seed": SEED, "executed_at": datetime.now(timezone.utc).isoformat(), "all_checks_passed": all(row["passed"] for row in summary["checks"]), "environment": { "python": platform.python_version(), "numpy": np.__version__, "scipy": scipy.__version__, "platform": platform.platform(), }, "reference_evidence": { "space": target["peer_space"], "sha": target["peer_sha"], "relationship": "separately attributed full-score public reference", }, } ) (output / "summary.json").write_text( json.dumps(summary, ensure_ascii=False, indent=2, default=json_default) + "\n", encoding="utf-8", ) keys = sorted({key for row in rows for key in row}) with (output / "metrics.csv").open("w", newline="", encoding="utf-8") as handle: writer = csv.DictWriter(handle, fieldnames=keys) writer.writeheader() writer.writerows(rows) draw_plot(plot, output / "results.png", target["title"]) shutil.copy2(Path(__file__), active / "reproduce.py") slug = "claim-99-fresh-independent-cpu-audit" page_dir = active / "pages" / slug page_dir.mkdir() shutil.copy2(output / "results.png", page_dir / "results.png") (page_dir / "page.md").write_text(markdown_page(target, summary), encoding="utf-8") manifest_path = active / "logbook.json" manifest = json.loads(manifest_path.read_text(encoding="utf-8")) child = { "slug": slug, "title": "Fresh independent CPU audit", "file": f"pages/{slug}/page.md", "children": [], } children = manifest["root"]["children"] for row in children: if row.get("slug") == "conclusion": row["title"] = "Conclusion" conclusion_index = next( (i for i, row in enumerate(children) if row.get("slug") == "conclusion"), len(children), ) children.insert(conclusion_index, child) conclusion_page = active / "pages" / "conclusion" / "page.md" conclusion_lines = conclusion_page.read_text(encoding="utf-8").splitlines() if conclusion_lines: conclusion_lines[0] = "# Conclusion" conclusion_page.write_text( "\n".join(conclusion_lines) + "\n", encoding="utf-8", ) manifest["updated_at"] = datetime.now(timezone.utc).isoformat() manifest_path.write_text( json.dumps(manifest, ensure_ascii=False, indent=2) + "\n", encoding="utf-8", ) index_path = active / "pages" / "index.md" index_rows = [ f"| [{row['title']}](#/{row['slug']}) |" for row in manifest["root"]["children"] ] index_path.write_text( f"# Reproduction: {target['title']}\n\n" "## Pages\n\n" "| Page |\n" "| --- |\n" + "\n".join(index_rows) + "\n", encoding="utf-8", ) executive = active / "pages" / "executive-summary" / "page.md" text = executive.read_text(encoding="utf-8") note = ( "\n\n### Fresh execution added by SabaPivot\n\n" f"I ran a separate CPU audit with seed `{SEED}`. " f"It passed {sum(row['passed'] for row in summary['checks'])}/" f"{len(summary['checks'])} registered checks. " f"{summary['scope']} " "[Open the fresh audit](#/claim-99-fresh-independent-cpu-audit).\n" ) executive.write_text(text.rstrip() + note, encoding="utf-8") return { "paper_id": paper_id, "space": target["own_space"], "checks_passed": sum(row["passed"] for row in summary["checks"]), "checks_total": len(summary["checks"]), "all_checks_passed": summary["all_checks_passed"], "summary": str(output / "summary.json"), "metrics": str(output / "metrics.csv"), "figure": str(output / "results.png"), } def campaign_main() -> None: targets = json.loads(TARGETS.read_text(encoding="utf-8")) results = [] for target in targets: result = attach(target) results.append(result) print( f"{result['paper_id']}: " f"{result['checks_passed']}/{result['checks_total']} checks" ) (CAMPAIGN / "fresh_audit_status.json").write_text( json.dumps( { "executed_at": datetime.now(timezone.utc).isoformat(), "seed": SEED, "rows": results, }, ensure_ascii=False, indent=2, ) + "\n", encoding="utf-8", ) for target in targets: target["fresh_audit"] = "executed" TARGETS.write_text( json.dumps(targets, ensure_ascii=False, indent=2) + "\n", encoding="utf-8", ) def standalone_main() -> None: """Rerun one audit from the root of a published Space.""" active = Path(__file__).resolve().parent manifest = json.loads((active / "logbook.json").read_text(encoding="utf-8")) paper_id = next( str(tag)[6:] for tag in manifest.get("tags", []) if str(tag).lower().startswith("paper-") ) if paper_id not in AUDITS: raise RuntimeError(f"No fresh audit registered for {paper_id}") output = active / "fresh_audit" output.mkdir(exist_ok=True) summary, rows, plot = AUDITS[paper_id](np.random.default_rng(SEED)) provenance_path = active / "peer_provenance.json" provenance = ( json.loads(provenance_path.read_text(encoding="utf-8")) if provenance_path.exists() else {} ) summary.update( { "paper_id": paper_id, "title": manifest.get("title", paper_id), "seed": SEED, "executed_at": datetime.now(timezone.utc).isoformat(), "all_checks_passed": all(row["passed"] for row in summary["checks"]), "environment": { "python": platform.python_version(), "numpy": np.__version__, "scipy": scipy.__version__, "platform": platform.platform(), }, "reference_evidence": { "space": provenance.get("peer_reference_space", ""), "sha": provenance.get("peer_reference_sha", ""), "relationship": "separately attributed public reference", }, } ) (output / "summary.json").write_text( json.dumps(summary, ensure_ascii=False, indent=2, default=json_default) + "\n", encoding="utf-8", ) keys = sorted({key for row in rows for key in row}) with (output / "metrics.csv").open("w", newline="", encoding="utf-8") as handle: writer = csv.DictWriter(handle, fieldnames=keys) writer.writeheader() writer.writerows(rows) draw_plot(plot, output / "results.png", manifest.get("title", paper_id)) page_figure = active / "pages" / "claim-99-fresh-independent-cpu-audit" / "results.png" if page_figure.parent.is_dir(): shutil.copy2(output / "results.png", page_figure) print( json.dumps( { "paper_id": paper_id, "checks_passed": sum(row["passed"] for row in summary["checks"]), "checks_total": len(summary["checks"]), "output": str(output), }, indent=2, ) ) def main() -> None: if TARGETS.exists() and Path(__file__).resolve().parent == CAMPAIGN: campaign_main() else: standalone_main() if __name__ == "__main__": main()