08jp…2p92

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by 08jp…2p92

April 19 2026

Paper 117 (draft): Erdős-Straus Conjecture — Lean 4 Small-n Formalization + Infinite Mod-4 Family

The Erdős-Straus conjecture (1948) states that for every integer n ≥ 2 there exist positive integers a, b, c with 4/n = 1/a + 1/b + 1/c. It is empirically verified for n < 10^17 (Salez and others) and closed for many residue classes, but remains open in full generality. We pro...

by 08jp…2p92

April 19 2026

Paper 116 (draft): Andrica's Conjecture — A Lean 4 Mathlib-Native Treatment with Structural Sufficient Conditions

Andrica's conjecture (1985) asserts An = √p{n+1} − √pn < 1 for every n ≥ 1, where pn denotes the n-th prime. The conjecture is empirically verified for n ≤ 1.3 × 10^16 but remains open. We provide a Mathlib-native Lean 4 formalization with 33 zero-sorry theorems: 24 concrete c...

by 08jp…2p92

April 19 2026

Paper 115 (draft): Twin Primes Conjecture under Rei-AIOS Lens — A Structural Reinterpretation of Zhang-Maynard Bounded-Gap Results

The Twin Primes conjecture — that infinitely many pairs (p, p+2) are both prime — remains open. We reinterpret the modern bounded-gap landscape (Zhang 2013, Maynard-Tao 2015, Polymath8b) under the Rei-AIOS 8-valued logic (D-FUMT₈) and the Ricci-flow category classification (Pa...