Collatz Final Gate v8.5 — Main Paper + Auditable Level-2B Demo Packet + Replication Toolkit (GateB companion v1.7r2)

## Overview This record is a versioned “reduction + certification” package toward the Collatz conjecture.The main paper (v8.5) isolates the remaining arithmetic bottleneck into a finite, auditable attack surface(“Gate B”) and ships a sealed Level-2B proof-input packet that passes mechanical audit with`thresholds.json` enforcement enabled. **Core methodological claim (carefully stated):**the remaining hard input (Corr(δ)/TwGap/AP-dispersion, etc.) is not hidden inside prose;it is exposed as *checked inequalities with explicit margins* inside a hash-locked certificate object,so that progress is measurable, reproducible, and version-stable (Four-Color-style workflow). ## What is new in v8.5 - **Manifest-SHA sealing (cycle-avoidance + binder binding):** the verdict binder records `binder.manifest_sha256 = SHA256(manifest.json)` while excluding the binder itself from the manifest to avoid a hash cycle.- **Final Verdict Protocol (trigger instance at fixed base scale L0):** a single audited base-scale packet (e.g. L0 = 16) is treated as a *trigger instance*; once its one-line inequality is certified with positive margin, the analytic “All-L promotion” mechanism applies.- **Two-environment semantic replication toolkit:** contract-driven snapshot collection + comparison script + replication audit script. ## Included files (this Zenodo record) 1. `Collatz_Final_Gate_v8.5.pdf` — main paper.2. `GateB_Bottleneck_v1.7r2.pdf` — companion note (Gate-B bottleneck + certificate interface).3. `Collatz_Demo_L2B_v8.5_sealed_full_PASS_manifestsha.zip` — sealed Level-2B demo packet (mechanical audit PASS).4. `Collatz_Replication_Toolkit_v8.5.zip` — two-environment semantic replication toolkit.5. `L0_16_complete_certificate_checklist.pdf` — one-page checklist for a complete trigger instance at L0=16. **Minor naming note (cosmetic only):**inside the demo packet, `packet_id` may still read `...v8.4_replication_ready` for backward compatibility,while `paper_version.json` and the shipped paper hash bind to v8.5. The audits do not depend on this label. ## How to reproduce (mechanical audit) Unzip the demo packet and run: ```bashunzip Collatz_Demo_L2B_v8.5_sealed_full_PASS_manifestsha.zipcd <PACKET_DIR>python -B scripts/audit_all.py --mode sealed_full Expected outcome: PASS: all audits completed. How to run semantic replication Unzip Collatz_Replication_Toolkit_v8.5.zip and follow README_REPLICATION.txt.The toolkit includes: specs/repro_contract.json scripts/collect_minimal_run.py scripts/compare_runs.py scripts/audit_replication.py Scope & non-overstatement This record does not claim that Corr(δ)/TwGap is already proved.It claims that the remaining arithmetic burden is reduced to a finite, hash-locked,mechanically audited checklist (a concrete “attack surface” with explicit margins),and that the “All-L” amplification step is analytic once a trigger instance is certified. Keywords Collatz conjecture; certification; reproducibility; audited computation; Markov operators; contraction; spectral gap; hash-locked evidence; Gate B; TwGap; Corr(δ) ========================= Author: Lee Byoungwoo leeclinic@protonmail.com