Researchers developed AutoGraphForge, a computational pipeline for automated graph-theoretic conjecturing, refuting, formalizing, and proving. [1]
The repository PrimeGaps186 contains a Lean 4 formalization of the result that the limit inferior of the gap between consecutive primes is at most 186. [2]
A novelty filter of 559 classical and folklore relations decides via a linear program whether a candidate conjecture is already implied by known results. [3]
Surviving candidates are tested against a dataset of about 348,000 graphs, which includes the House of Graphs invariant export and exhaustive censuses of connected graphs on at most nine vertices. [4]
The pipeline yielded 6,522 conjectures that survived the refutation dataset, novelty filter, and active-search runs. [5]
The author states that the mathematical estimates and numerical computations have not been turned into Lean proofs of those inputs, meaning the result remains conditional. [6]
The axiom PrimeGap186.kloosterman3_bound assumes $| ext{Kl}_3(c;p)|
eq 3$ for every prime $p$ and all $c
eq 0$, a result attributed to Nicholas M. Katz. [7]
What this stands on
Researchers developed AutoGraphForge, a computational pipeline for automated graph-theoretic conjecturing, refuting, formalizing, and proving. · arXiv.org
The repository PrimeGaps186 contains a Lean 4 formalization of the result that the limit inferior of the gap between consecutive primes is at most 186. · GitHub
A novelty filter of 559 classical and folklore relations decides via a linear program whether a candidate conjecture is already implied by known results. · arXiv.org
Surviving candidates are tested against a dataset of about 348,000 graphs, which includes the House of Graphs invariant export and exhaustive censuses of connected graphs on at most nine vertices. · arXiv.org
The pipeline yielded 6,522 conjectures that survived the refutation dataset, novelty filter, and active-search runs. · arXiv.org
The author states that the mathematical estimates and numerical computations have not been turned into Lean proofs of those inputs, meaning the result remains conditional. · GitHub
The axiom PrimeGap186.kloosterman3_bound assumes $| ext{Kl}_3(c;p)|
eq 3$ for every prime $p$ and all $c
eq 0$, a result attributed to Nicholas M. Katz. · GitHub
We could not place any of them by their address. None is an official body: that part stands on reporting, not on the underlying document or transcript.
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