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Random 3-SAT Phase Transition Revisited: Empirical Reproduction, Lean 4 Formalization, and D-FUMT8 Interpretation Layer

Nobuki Fujimoto1d ago • 10 min read

Random 3-SAT Phase Transition Revisited: Empirical Reproduction, Lean 4 Formalization, and D-FUMT8 Interpretation Layer

Reproduces classical 3-SAT phase transition. n=30 peak DPLL backtrack at α=4.267 EXACT match with Me...

#math#research#lean#algorithms

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A WebGL 3D Cube From First Principles — Handwritten 4x4 Matrices and Visible Shaders

SEN LLC5d ago • 3 min read

A WebGL 3D Cube From First Principles — Handwritten 4x4 Matrices and Visible Shaders

A WebGL 3D Cube From First Principles — Handwritten 4x4 Matrices and Visible Shaders Most...

#webgl#graphics#javascript#math

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Mandelbrot, Julia, and Burning Ship Fractals in a Progressive-Render Canvas

SEN LLC5d ago • 3 min read

Mandelbrot, Julia, and Burning Ship Fractals in a Progressive-Render Canvas

Mandelbrot, Julia, and Burning Ship Fractals in a Progressive-Render Canvas Each pixel...

#javascript#canvas#math#graphics

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Ricci-Flow Three-Category Classification of Unsolved Math Problems (with 10 -Scale Collatz Census)

Nobuki Fujimoto3d ago • 7 min read

Ricci-Flow Three-Category Classification of Unsolved Math Problems (with 10 -Scale Collatz Census)

Discrete Ollivier-Ricci flow on graphs sorts unsolved math conjectures into three categories: stable...

#math#lean#research#typescript

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Prime Factorization With Deterministic Miller-Rabin Up to 10^24

SEN LLC5d ago • 3 min read

Prime Factorization With Deterministic Miller-Rabin Up to 10^24

Prime Factorization With Deterministic Miller-Rabin Up to 10^24 Trial division works for...

#javascript#math#algorithms#primes

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To Teach AI How to Remember, First Teach It How to Forget 2/2

김이더6d ago • 9 min read

To Teach AI How to Remember, First Teach It How to Forget 2/2

Code on GitHub. Paper on arXiv. More posts at radarlog.kr. Part 1 covered MemoryBank's...

#ai#llm#memorybank#math

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Erdős-Straus Conjecture — Lean 4 Small-n Formalization + Infinite Mod-4 Family

Nobuki Fujimoto1d ago • 5 min read

Erdős-Straus Conjecture — Lean 4 Small-n Formalization + Infinite Mod-4 Family

Erdős-Straus 1948: 4/n = 1/a+1/b+1/c for n >= 2. Lean 4 Mathlib: 22 theorems, 0 sorry. Explicit witn...

#math#research#lean#algorithms

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Andrica's Conjecture — A Lean 4 Mathlib-Native Treatment with Structural Sufficient Conditions

Nobuki Fujimoto1d ago • 5 min read

Andrica's Conjecture — A Lean 4 Mathlib-Native Treatment with Structural Sufficient Conditions

Andrica 1985: A_n = sqrt(p_{n+1}) - sqrt(p_n) < 1. Lean 4 Mathlib formalization: 33 theorems, 0 sorr...

#math#research#lean#algorithms

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Five Formal Closures + Findings + AI-Generated Open Questions (Rei-AIOS Paper 118)

Nobuki Fujimoto1d ago • 12 min read

Five Formal Closures + Findings + AI-Generated Open Questions (Rei-AIOS Paper 118)

Five Lean 4 zero-sorry closures: Köthe commutative / Problem 007 FIA 6-axiom independence / Problem ...

#math#research#lean#collatz

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

Nobuki Fujimoto1d ago • 10 min read

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

Q7 (Paper 118) EMPIRICALLY FALSIFIED: 61 odd m ≤ 10000 have K(m)=41, not only m=911. Lean 4 zero-sor...

#math#collatz#lean#research

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Nested Colored-Dot Symbol System: An Information-Theoretic and Semantic Alternative to QR Codes

Nobuki Fujimoto1d ago • 9 min read

Nested Colored-Dot Symbol System: An Information-Theoretic and Semantic Alternative to QR Codes

Recursive 2D symbol system combining D-FUMT8 8-value logic + 24-bit RGB color on orthogonal axes. Le...

#math#research#lean#typescript

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Five Unsolved-Problem Deep Dives and the Gilbreath-Collatz Structural Isomorphism (Rei-AIOS Paper 120)

Nobuki Fujimoto20h ago • 13 min read

Five Unsolved-Problem Deep Dives and the Gilbreath-Collatz Structural Isomorphism (Rei-AIOS Paper 120)

94 new Lean 4 zero-sorry theorems across Legendre 1808, Lehmer totient 1932, Effective ABC 1985, Gil...

#math#collatz#gilbreath#lean

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Braille-D-FUMT8 vs CLIP / BERT / ImageBind: a Rigorous Information-Theoretic Comparison

Nobuki Fujimoto2d ago • 6 min read

Braille-D-FUMT8 vs CLIP / BERT / ImageBind: a Rigorous Information-Theoretic Comparison

5-axis comparison of Paper 33 Braille-D-FUMT8 8-value-logic encoding against CLIP, BERT, and ImageBi...

#math#ai#research#typescript

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Twin Primes Conjecture under Rei-AIOS Lens — A Structural Reinterpretation of Zhang-Maynard Bounded-Gap Results

Nobuki Fujimoto1d ago • 6 min read

Twin Primes Conjecture under Rei-AIOS Lens — A Structural Reinterpretation of Zhang-Maynard Bounded-Gap Results

Reinterprets Zhang 2013 (N<=70M), Maynard 2015 (N<=246), Elliott-Halberstam (N<=12) via Rei D-FUMT8 ...

#math#research#lean#algorithms

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

Nobuki Fujimoto2d ago • 7 min read

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

Comparative analysis of Rei-AIOS ergodic tooling (5 engines) against Santana (arXiv:2601.03297v4, 20...

#math#research#lean#algorithms

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A Roman Numeral Converter With Step-By-Step Breakdown and Strict Validation

SEN LLC5d ago • 3 min read

A Roman Numeral Converter With Step-By-Step Breakdown and Strict Validation

A Roman Numeral Converter With Step-By-Step Breakdown and Strict...

#javascript#math#webdev#tools

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Seven-Conjecture Deep Dives, Multi-Attractor Q33 Extension, and the First Cross-Domain Frankl Formalization (Rei-AIOS Paper 121)

Nobuki Fujimoto18h ago • 13 min read

Seven-Conjecture Deep Dives, Multi-Attractor Q33 Extension, and the First Cross-Domain Frankl Formalization (Rei-AIOS Paper 121)

Single-day 12-file Lean 4 sweep: 158 new zero-sorry theorems across 7 long-open conjectures. Lehmer/...

#math#collatz#frankl#lean

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A Loan Calculator With 元利均等 vs 元金均等 and Prepayment Simulation

SEN LLC5d ago • 3 min read

A Loan Calculator With 元利均等 vs 元金均等 and Prepayment Simulation

A Loan Calculator With 元利均等 vs 元金均等 and Prepayment Simulation Japanese mortgages let you...

#javascript#finance#calculator#math

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The whiteboard test: a FAANG-level gate applied to my own learning

Aman Bhandari1d ago • 6 min read

The whiteboard test: a FAANG-level gate applied to my own learning

Reciting a YouTube explanation is not derivation. Watching 3Blue1Brown on backpropagation and being....

#learning#ai#interview#math

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I Bought a Domain That Used to Sell Viagra. Here's My SEO Recovery Log.

levent çelik2d ago • 4 min read

I Bought a Domain That Used to Sell Viagra. Here's My SEO Recovery Log.

I Bought a Domain That Used to Sell Viagra. Now It Teaches Math. I have loved math since I...

#seo#equation#solver#math

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Erdős-Straus Conjecture as an S-Category Problem (Ricci Flow + Fujimoto Infinity Algebra)

Nobuki Fujimoto3d ago • 7 min read

Erdős-Straus Conjecture as an S-Category Problem (Ricci Flow + Fujimoto Infinity Algebra)

Applying Ricci-flow taxonomy to Erdős-Straus 4/n=1/a+1/b+1/c shows 84.3% of classifiable n in [2,100...

#math#lean#research#algorithms

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Active Inference, The Learn Arc — Part 17: Session §2.3 — The Cost of Being Wrong

ORCHESTRATE16h ago • 4 min read

Active Inference, The Learn Arc — Part 17: Session §2.3 — The Cost of Being Wrong

Chapter 2, §3. Free energy decomposes into complexity plus accuracy. What "cost" means when your gen...

#activeinference#bayesian#math#elixir

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Active Inference, The Learn Arc — Part 16: Session §2.2 — Why Free Energy, and What the Bound Buys You

ORCHESTRATE16h ago • 4 min read

Active Inference, The Learn Arc — Part 16: Session §2.2 — Why Free Energy, and What the Bound Buys You

Chapter 2's second session. Bayes' intractable evidence meets KL divergence. Variational free energy...

#activeinference#bayesian#math#elixir

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Active Inference, The Learn Arc — Part 3: Chapter 2 — The Low Road from Bayes to Free Energy

ORCHESTRATE16h ago • 5 min read

Active Inference, The Learn Arc — Part 3: Chapter 2 — The Low Road from Bayes to Free Energy

Chapter 2 derives variational free energy from one coin flip. Bayes' rule, the free-energy bound on ...

#activeinference#bayesian#math#elixir

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Tech Articles

Random 3-SAT Phase Transition Revisited: Empirical Reproduction, Lean 4 Formalization, and D-FUMT8 Interpretation Layer

A WebGL 3D Cube From First Principles — Handwritten 4x4 Matrices and Visible Shaders

Mandelbrot, Julia, and Burning Ship Fractals in a Progressive-Render Canvas

Ricci-Flow Three-Category Classification of Unsolved Math Problems (with 10 -Scale Collatz Census)

Prime Factorization With Deterministic Miller-Rabin Up to 10^24

To Teach AI How to Remember, First Teach It How to Forget 2/2

Erdős-Straus Conjecture — Lean 4 Small-n Formalization + Infinite Mod-4 Family

Andrica's Conjecture — A Lean 4 Mathlib-Native Treatment with Structural Sufficient Conditions

Five Formal Closures + Findings + AI-Generated Open Questions (Rei-AIOS Paper 118)

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

Nested Colored-Dot Symbol System: An Information-Theoretic and Semantic Alternative to QR Codes

Five Unsolved-Problem Deep Dives and the Gilbreath-Collatz Structural Isomorphism (Rei-AIOS Paper 120)

Braille-D-FUMT8 vs CLIP / BERT / ImageBind: a Rigorous Information-Theoretic Comparison

Twin Primes Conjecture under Rei-AIOS Lens — A Structural Reinterpretation of Zhang-Maynard Bounded-Gap Results

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

A Roman Numeral Converter With Step-By-Step Breakdown and Strict Validation

Seven-Conjecture Deep Dives, Multi-Attractor Q33 Extension, and the First Cross-Domain Frankl Formalization (Rei-AIOS Paper 121)

A Loan Calculator With 元利均等 vs 元金均等 and Prepayment Simulation

The whiteboard test: a FAANG-level gate applied to my own learning

I Bought a Domain That Used to Sell Viagra. Here's My SEO Recovery Log.

Erdős-Straus Conjecture as an S-Category Problem (Ricci Flow + Fujimoto Infinity Algebra)

Active Inference, The Learn Arc — Part 17: Session §2.3 — The Cost of Being Wrong

Active Inference, The Learn Arc — Part 16: Session §2.2 — Why Free Energy, and What the Bound Buys You

Active Inference, The Learn Arc — Part 3: Chapter 2 — The Low Road from Bayes to Free Energy