Experimental Constraints on Landau-Siegel Zeros: A 2-Billion Point Spectral Gap Analysis of Q47

We present experimental constraints on hypothetical Landau-Siegel zeros derived from high-precision spectral gap analysis of the polynomial prime sequence Q(n) = n^47 - (n-1)^47. Our dataset comprises 15.4 million verified primes across the asymptotic regime n ∈ [3×10^8, 2×10^9].

TWO-STAGE VERIFICATION PROTOCOL:
(1) Fast scanning algorithms for large-scale anomaly detection identified a candidate void at n ≈ 1.4×10^9
(2) Arbitrary-precision verification (gmpy2) resolved this as fine-structure primes below the initial resolution threshold

FINAL VERIFIED STATISTICS:
- Coefficient of Variation: 0.995 (Poisson: 1.000)
- Maximum Gap Ratio: 0.99 (Expected: 1.00)
- Cramér Ratio: < 1.5 (Bound: 2.0)
- Regional Anomalies: 0/100

CONCLUSION: No detectable perturbation from Landau-Siegel zeros within the analyzed range. The spectral gap distribution remains fully consistent with Generalized Riemann Hypothesis predictions, providing independent experimental support for GRH at the n ~ 10^9 scale.

REPOSITORY CONTENTS:
- Research paper (6 pages with figures)
- LaTeX source
- Verification figure (4-panel analysis)
- Statistical results (JSON)
- Analysis scripts (Python)

GitHub: https://github.com/Ruqing1963/Landau-Siegel-Q47-Constraints

Related publications:
- Q47 Prime Dataset: DOI 10.5281/zenodo.18305185
- Ouroboros Phase Transition: DOI 10.5281/zenodo.18306984