Decent Newsroom

April 20 2026

Paper 121: Seven-Conjecture Deep Dives, Multi-Attractor Q33 Extension, and the First Cross-Domain Frankl Formalization

We report a single-day 12-file Lean 4 formalization sweep across seven long-open conjectures plus infrastructure extensions, producing 158 new zero-sorry theorems under Mathlib v4.27.0. The conjectures attacked include: 1. Lehmer's totient (1932, extended with k-Lehmer Q23 clo...

by 08jp…2p92

April 19 2026

Paper 120: Five Unsolved-Problem Deep Dives and the Gilbreath-Collatz Structural Isomorphism

We report empirical verifications, Lean 4 zero-sorry formalizations, and Rei-AIOS lens analyses of five long-open conjectures: Legendre's conjecture (1808), Lehmer's totient conjecture (1932), the Effective ABC conjecture (1985), Gilbreath's conjecture (1958), and extensions o...

by 08jp…2p92

April 19 2026

Paper 119: Q7 Falsification, Q8/Q9 Empirical Data, and the First Rei-AIOS Failure Record

We close three AI-generated open questions Q7–Q9 posed in Paper 118 and inaugurate the extended eleven-part paper template (Parts A–K) that will serve as the long-term Rei-AIOS publication format. Key results: - Q7 FALSIFIED empirically. The Paper-118 strong-uniqueness claim —...

by 08jp…2p92

April 19 2026

Paper 118: Five Formal Closures + Findings + AI-Generated Open Questions

We report five structurally independent zero-sorry Lean 4 formalizations from the Rei-AIOS unsolved-problems corpus, together with observed findings, AI-generated new open questions, and a unified D-FUMT₈ solution-status summary. This is the first Rei-AIOS paper to adopt the f...

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...

by 08jp…2p92

April 18 2026

Paper 114 (draft): Random 3-SAT Phase Transition Revisited — Empirical Reproduction, Lean 4 Formalization, and D-FUMT₈ Interpretation Layer

We reproduce the classical random 3-SAT phase transition (Mitchell-Selman-Levesque 1992; Mertens-Mézard-Zecchina 2006; Ding-Sly-Sun 2014) using a minimal DPLL solver and find that at n = 30 variables with 20 samples per clause-to-variable ratio α, the DPLL backtrack count peak...

by 08jp…2p92

April 18 2026

Paper 112 (draft): Nested Colored-Dot Symbol System — An Information-Theoretic and Semantic Alternative to QR Codes

QR codes (Denso Wave 1994) encode up to 23,624 data bits in a 177×177 binary grid, with four fixed error-correction levels and a rigid byte-stream payload model. We propose a complementary 2D symbol system — the Nested Colored-Dot (NestedDot) — whose payload is a recursively s...

by 08jp…2p92

April 18 2026

Paper 111 (draft): Topological and Ergodic Approaches to the Collatz Conjecture — Rei-AIOS vs. Santana (2026)

Santana (arXiv:2601.03297v4, 2026) proposes a coarse topology on ℕ and applies thermodynamic formalism to establish that Collatz-family maps have at most finitely many periodic orbits, conditional on the existence of equilibrium states for every continuous potential. The Rei-A...

by 08jp…2p92

April 18 2026

Paper 109 — Erdős-Straus Conjecture as an S-Category Problem: A Ricci-Flow + Fujimoto Infinity Algebra Attack Angle

We apply Rei-AIOS's discrete Ollivier-Ricci flow three-category taxonomy (Paper 108) to the Erdős-Straus conjecture 4/n = 1/a + 1/b + 1/c and find that among classifiable small n in [2, 1000] (i.e. those for which the partition graph has at least 3 edges with a ≤ 60), 84.3% be...

by 08jp…2p92

April 18 2026

Paper 108 — Ricci-Flow Three-Category Classification of Unsolved Mathematical Problems with 10⁹-Scale Collatz Evidence

We propose an empirical three-category classification (S / M / E) of unsolved mathematical problems based on discrete Ollivier-Ricci flow applied to their natural graph representations. Using a pure-TypeScript implementation (no external dependencies) of Hamilton's Ricci flow ...

by 08jp…2p92

April 18 2026

Paper 110 (draft): Braille-D-FUMT₈ vs CLIP / BERT / ImageBind — a Rigorous Information-Theoretic and Structural Comparison

Paper 33 (Fujimoto 2026, DOI 10.5281/zenodo.19434010) proposed a Braille-Unicode × D-FUMT₈ 8-value-logic encoding that represents 256 philosophical states in a single 3-byte UTF-8 character. The present paper contrasts this encoding with three widely deployed multi-modal embed...