What does this research mean for the field?

A versioned registry of mathematical conjectures demonstrates that the Cochrane-Dressler gap conjecture implies infinitely many non-Wieferich primes, the existential-window Erdos-Woods conjecture, and Pillai finiteness. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Formalize proven implications, incompatibilities, and exact model counts among open mathematical conjectures within a versioned, auditable constraint graph.

September 8, 2026Open Access

A constraint graph of open conjectures: proven logical relations, exact model counts, and auditable conditional consequences

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IAIvan Anisenya

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Implication

Computational analysis maps logical implications among number-theoretic conjectures, highlighting auditable pathways and dependencies between open mathematical problems.

Key Points

Formalize proven implications, incompatibilities, and exact model counts among open mathematical conjectures within a versioned, auditable constraint graph.
Encoded mathematical conjectures and their logical dependencies as signed Boolean clauses integrated with exact model counts and automated proof reviews.
Audited a 10-candidate research batch using primary-source dossiers and automated proof-review agents to verify integration and dependency outcomes.
Strengthened the twin-prime packing bound unconditionally for windows with x >= y and 3 <= y <= 378, proving under Dickson's conjecture that the first crossing occurs at y = 379.
Demonstrated that the Cochrane-Dressler (CD) gap conjecture implies infinitely many non-Wieferich primes (liminf W_2(X)/log X >= 1/(2 log 2)) and the existential-window Erdős-Woods conjecture.
Proved that the CD conjecture entails a uniform perfect-power gap bound (C - B >= c_delta C^(1/12 - delta)), thereby establishing Pillai finiteness for all bases and exponents >= 2.

Cite This Study

Ivan Anisenya (2026) studied this question.

synapsesocial.com/papers/6a9fd76758e84d0ff5b46073 https://doi.org/10.5281/zenodo.22538679

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Implication

Computational analysis maps logical implications among number-theoretic conjectures, highlighting auditable pathways and dependencies between open mathematical problems.

A constraint graph of open conjectures: proven logical relations, exact model counts, and auditable conditional consequences

Discussion

Member takes

Implication

Key Points

Cite This Study

A constraint graph of open conjectures: proven logical relations, exact model counts, and auditable conditional consequences

Discussion

Member takes

Implication

Key Points

Cite This Study

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