Collatz Final Gate v9.0.1 — Audited Proof Interface (Sealed Level-2B Packet, L0=16 Anchor, Gate-B I4 Mandatory)

# Overview This record releases **Collatz Final Gate v9. 0. 1** together with a **sealed Level-2B demo packet** implementing an *audited proof interface* for a certificate-triggered closure program. The core idea is to replace the last arithmetic bottleneck with a **public, mechanically auditable verdict certificate**: once a single nontrivial instance (here \ (L₀=16\) ) is sealed and audited, the paper’s analytic promotion mechanism upgrades the claim to **All-\ (L\) ** *within the program’s formal interface*. # Contents of this record - **Main paper (documentation / theory): ** - `CollatzFinalGateᵥ9. 0. 1. pdf`- **Companion (Gate B bottleneck / interface): ** - `GateBBottleneckᵥ2. 0. 1. pdf`- **Reviewer checklist (L0=16 anchor): ** - `L0₁6completecertificatechecklistᵥ9. 0. 1. pdf`- **Sealed Level-2B demo packet (ZIP): ** - `CollatzL2Bᵥ9. 0. 1. zip` # What is “closed” in this record (interface sense) The sealed packet is designed so that a reviewer can mechanically verify: 1. **Manifest / hash discipline** (no hidden state; checked digests; provenance seal). 2. **Non-synthetic origin claims** for required report files (per packet policy). 3. **Mandatory L0=16 anchor evidence bundle**: `results/L0₁6ₐnchor/*` is required, and audit fails if it is missing or inconsistent. 4. **Mandatory Gate-B I4 item** (Corr\ ( () \) /TwGap interface): it appears as a **checked inequality entry** in the verdict certificate (not a narrative claim). In other words: the program’s “closure step” is encoded as **PASS/FAIL** of a finite, auditable object (certificate + witnesses + scripts), not as an informal argument. # How to verify (quick start) Unzip `CollatzL2Bᵥ9. 0. 1. zip` and run: - `python3 -B scripts/auditₐll. py --mode sealedfullₙonsynthₕardened`- (optional, if enabled in `thresholds. json`) `python3 -B scripts/auditₐll. py --mode sealedfullₙonsynthₕardenedₗevel3` A successful run ends with an explicit `PASS` message and identifies the produced certificate objects in `results/`. # Scope instead, the record formalizes an *auditable interface* whose remaining pressure points are concentrated into named, checkable targets. # Program closure and targets The main remaining “hard content” is concentrated in the Gate-B interface, notably the Corr\ ( () \) /TwGap obligation: the record enforces it as a mandatory checked item, and the companion documents the proxy-to-target binding logic and the open targets to tighten. # Version note (v9. 0. 1) v9. 0. 1 emphasizes reviewer-facing hygiene and strict document–packet binding: - mandatory L0=16 anchor bundle, - mandatory I4 entry in the verdict certificate, - sealed provenance + manifest/certificate consistency checks. ========================= Author: Lee Byoungwoo leeclinic@protonmail. com