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https://github.com/blackboxprogramming/BlackRoad-Operating-System.git
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Create comprehensive research-lab pack structure with mathematical and quantum computing modules from blackroad-prism-console: Math Modules: - hilbert_core.py: Hilbert space symbolic reasoning - collatz/: Distributed Collatz conjecture verification - linmath/: Linear mathematics C library - lucidia_math_forge/: Symbolic proof engine - lucidia_math_lab/: Experimental mathematics Quantum Modules: - lucidia_quantum/: Quantum core - quantum_engine/: Circuit simulation Experiments: - br_math/: Gödel gap, quantum experiments Includes pack.yaml manifest and comprehensive README. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <noreply@anthropic.com>
84 lines
2.7 KiB
Python
84 lines
2.7 KiB
Python
"""Hilbert–Pólya / GUE spacing test.
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This script compares normalized spacing distributions of the
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first `nzeros` nontrivial zeros of the Riemann zeta function and
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random Gaussian Unitary Ensemble (GUE) eigenvalues against the
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Wigner surmise. It reports the Kolmogorov–Smirnov distance for
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both samples relative to the Wigner CDF.
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"""
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from __future__ import annotations
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import argparse
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import math
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from typing import Callable
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import mpmath as mp
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import numpy as np
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def wigner_cdf(s: np.ndarray) -> np.ndarray:
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"""CDF of the Wigner surmise for the GUE."""
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return np.vectorize(
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lambda x: math.erf(2 * x / math.sqrt(math.pi))
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- (4 * x / math.pi) * math.exp(-4 * x**2 / math.pi)
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)(s)
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def ks_distance(sample: np.ndarray, cdf: Callable[[np.ndarray], np.ndarray]) -> float:
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"""Return the two-sided Kolmogorov–Smirnov distance between a sample and a CDF."""
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x = np.sort(sample)
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n = x.size
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if n == 0:
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raise ValueError("sample must contain at least one element")
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cdf_vals = cdf(x)
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ecdf_right = np.arange(1, n + 1) / n
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ecdf_left = np.arange(0, n) / n
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d_plus = np.max(ecdf_right - cdf_vals)
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d_minus = np.max(cdf_vals - ecdf_left)
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return float(max(d_plus, d_minus))
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def riemann_zeros(n: int) -> np.ndarray:
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"""Return the imaginary parts of the first n Riemann zeta zeros."""
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mp.mp.dps = 30
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return np.array([float(mp.zetazero(k).imag) for k in range(1, n + 1)])
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def normalized_spacings(vals: np.ndarray) -> np.ndarray:
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"""Return consecutive spacings normalised to unit mean."""
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diffs = np.diff(vals)
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return diffs / np.mean(diffs)
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def gue_spacings(n: int, k: int) -> np.ndarray:
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"""Sample spacings from k random n×n GUE matrices."""
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spacings: list[float] = []
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for _ in range(k):
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a = np.random.normal(size=(n, n)) + 1j * np.random.normal(size=(n, n))
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h = (a + a.conj().T) / 2 # Hermitian
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eigvals = np.linalg.eigvalsh(h)
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spacings.extend(normalized_spacings(eigvals))
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return np.array(spacings)
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def main() -> None:
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parser = argparse.ArgumentParser(description=__doc__)
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parser.add_argument("--nzeros", type=int, default=200, help="number of zeta zeros")
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parser.add_argument("--gue_n", type=int, default=200, help="dimension of GUE matrix")
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parser.add_argument("--gue_k", type=int, default=20, help="number of GUE samples")
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args = parser.parse_args()
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zero_spacings = normalized_spacings(riemann_zeros(args.nzeros))
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gue_sample = gue_spacings(args.gue_n, args.gue_k)
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ks_zero = ks_distance(zero_spacings, wigner_cdf)
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ks_gue = ks_distance(gue_sample, wigner_cdf)
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print(f"KS distance (zeros vs Wigner): {ks_zero:.4f}")
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print(f"KS distance (GUE vs Wigner): {ks_gue:.4f}")
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if __name__ == "__main__":
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main()
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