Sigma-Cascade Observation of Collatz Orbit Confluence: 10⁹ Scan + G₃ Subgraph Framework + Erratum E3 + Lemma 5d. 1 Lean 4 Mechanized — Rei-AIOS Paper 152 v0. 3 DRAFT

Paper 152 v0. 3 update. Parent v0. 2 DOI 10. 5281/zenodo. 20149662; concept root v0. 1 DOI 10. 5281/zenodo. 20148868. We apply Paper 151 Theorem 14 (sigma-cascade) to forward Collatz (3x+1) orbits at scale n 10⁸" was correct. (D) DISSOCIATION at 10⁹: n=96k strengthened + class 21 weakened = independent claims. (E) STEP 1127 LEAN 4 MECHANIZATION: G3Subgraph. lean 新規 file. Theorems lemma₅d₁g3ₑdgesₕalvingₒnly + g3ₚredecessorₛingleton + chainᵢsₘult₃ + chainₕalvingₛtep + chainₚredecessorᵢschain 全 0 sorries. Paper 152 v0. 3 §5d now has FOUR Lean 4 mechanized files (PeakMergeInvariant + PeakMergeWitness + G3Subgraph + ThreeAdicIsolation), all 0 sorries. v0. 2 contributions retained: Lean 4 nativedecide closures (Büchi-25 → 9232 + 1, 000-witness peak-merge), 3-adic isolation theorem, 11. 5M peaks, 219 tier-3 super-hubs, INFINITY classification, two-tier framing. Honest correction record (E1+E2+E3): peak 250, 504 = 173×181×2³ (twin-gap-8 primes), not '31, 313 prime' (E1). 3-adic isolation theorem applies to specific values, not mod-96 classes (E2). Class 21 absence at d=70 is 98. 43% (10⁹), not 100% (10⁸) (E3). Companion papers: Paper 151 (σ-cascade source, Zenodo DOI 10. 5281/zenodo. 20146654), Paper 67 v2 (Collatz dichotomy), Paper 118 (Büchi-25 mod-96 atomic cores). Three-party co-authorship per OUKC charter v1. 0: 藤本 伸樹 (Founder), Rei (Rei-AIOS autonomous research substrate, Co-architect), Claude Opus 4. 7 (Anthropic, Co-architect). DRAFT v0. 3 — preprint, not yet peer-reviewed. Honest scope: NOT a Collatz solution. Feedback welcome via GitHub Discussions at fc0web/rei-aios.