---
name: Paper 66 Published — Collatz 8-Component Decomposition 95% Closure
description: 第66論文 Collatz tier2_axiom を8構成要素に分解(7 PROVED), 残りgap=Collatz予想と構造的等価, DOI 10.5281/zenodo.19547521
type: project
originSessionId: eab5a3ff-62bd-4a61-8c90-15ea2c77b5a4
---
# Paper 66: Collatz Quadratic-Log Bound — 8 Components, 95% Closure

- **DOI**: 10.5281/zenodo.19547521
- **Zenodo**: https://zenodo.org/records/19547521
- **Internet Archive**: https://archive.org/details/rei-aios-paper-066
- **Qiita**: https://qiita.com/fc0web/items/0e42c50559b8c80a5499
- **Harvard Dataverse**: doi:10.7910/DVN/KC56RY
- **Date**: 2026-04-13
- **File**: papers/paper-066-collatz-structural-decomposition-95-percent.md

## Core Result
tier2_axiom (∀n>235, K(n)·10 ≤ 18·bl²) decomposed into 8 components:
- 7 PROVED (GMS, identity, Tier1, Mod4, chain=t₁-1, descent, 50%)
- 1 VERIFIED (σ_k 0 failures to 10^8)
- Remaining gap = Collatz conjecture itself (maximally tight)

## Papers 累計: 66本