Mersenne Neighborhood Audit

Mersenne Neighborhood Audit Skill

This skill focuses on the high-resolution investigation of the exponent space immediately surrounding known Mersenne primes ($p_{prime} \pm \Delta p$).

🛠️ Core Capabilities

1. Neighborhood Mapping: Systematic scanning of exponents in a radius around certified primes.
2. Spectral Echo Detection: Identifying composite exponents that exhibit "prime-like" spectral rigidity ($H \to 0$) during the first $10^5$ iterations of the LL-test.
3. Ghost Locus Identification: Filtering candidates that GIMPS might have skipped due to thresholding artifacts.

📜 Laws & Contracts

• Baseline Law: Every scan MUST be anchored to a certified prime from the ua_ledger.sqlite.
• Detection Contract: A "Ghost Locus" is defined as any exponent $p$ where the PRP test is negative but the LL-test residue exhibits local stability $> P95$ of the baseline.