🚨 Breakthrough Finding: Phase Clustering in Riemann Zeta Zeros
We've discovered a striking statistical pattern in Lehmer pairs (anomalously close Riemann zeta zeros):
📊 Key Findings:
• Lehmer pairs are significantly enriched at phase ϕ≈0.5 modulo prime periods (1.48× enrichment, p<10⁻²⁰)
• Consistent across 6 tested primes {2,3,5,7,11,13}
• Machine learning model achieves AUC=0.908 with independent validation
🔍 Methodological Rigor:
• Strict time-series splitting to avoid circular reasoning
• 13 geometric/phase features for independent validation
• Clear distinction between correlation and causation
Paper: https://zenodo.org/records/17602441
Code/Data: Fully open-source
Questions for the community:
Is this cross-prime phase consistency known in analytic number theory?
Could destructive interference explain this arithmetic phase preference?
What implications might this have for Riemann Hypothesis research?
#NumberTheory #RiemannZeta #LehmerPairs #MathPhysics #PrimeNumbers