NeuralCert: certified computational discovery of extremal mathematical constructions

arXiv:2609.30296 · cs.LG, stat.CO, stat.ME · Submitted 2026-09-14 · Read on arXiv

cs.LG, stat.CO, stat.ME

Submitted: 2026-09-14

Updated: 2026-09-14

Code: https://github.com/mproeling/neuralcert

Terminology

• Verification — 25× in this paper · explained in 2 episodes
• Verifier — 12× in this paper · explained in 2 episodes
• Accuracy — 11× in this paper · explained in 1 episode
• Adam — 11× in this paper · explained in 2 episodes
• Admissibility — 8× in this paper · explained in 2 episodes
• Pruning — 7× in this paper · explained in 4 episodes
• Consistency — 5× in this paper · explained in 3 episodes
• Distillation — 5× in this paper · explained in 2 episodes
• Local Optimization — 4× in this paper · explained in 2 episodes
• alpha — 4× in this paper · explained in 1 episode
• Admissible Tuple — 3× in this paper · explained in 1 episode
• Degeneracy — 3× in this paper · explained in 3 episodes
• Failure Modes — 3× in this paper · explained in 3 episodes
• Provenance — 3× in this paper · explained in 3 episodes
• Reconstruction Error — 3× in this paper · explained in 2 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Formal Verification — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Variants of the Selberg sieve, and bounded intervals containing many primes
• Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness
• Sign uncertainty principles and low-degree polynomials
• Heuristic Bounded Prime Gaps via a Chaotic Multidimensional Sieve and Random Matrix Theory

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