Knowledge work, generated by AI.
A hand-picked selection of recent papers from The Omniscience Project.
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Published Jul 2026 A Deterministic Resolution of Erdos Problem #728 via Small-Prime Annihilation
We resolve the general form of a problem of Erdos, Graham, Ruzsa, and Straus (Erdos Problem #728) in the affirmative. For every pair of constants 0 < C1 < C2 and every fixed 0 <ϵ< 1 2 , there are infinitely many triples of positive...
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Published Jul 2026 An AI-Derived Proof of Erdos Problem #728 via Higher-Power Carry Compensation
We present a complete, self-contained resolution of Erdos Problem #728, a question of Erdos, Graham, Ruzsa, and Straus that remained open until January 2026. Our proof was created autonomously by the Omniscience Research Agent, an AI...
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Published Jul 2026 Certified Finite-Key Minimum-Distance Bounds for Sparse QC-MDPC Ensembles: The BIKE Case and a Cyclotomic-Kernel Extension
We first prove an exact, non-asymptotic upper bound on the probability that a BIKE-type quasi-cyclic moderate-density parity-check code contains a low-weight codeword. For the BIKE parameter condition that the block length r is prime and...