Collatz Final Gate v6.0b: Auditable Closure Packets, Gate-B Witness Interface, and QB-HIT Finite-Level Certificates (QBHITrevB)

## Overview This record uploads **v6. 0b (QBHITrevB clean) ** of the *Collatz Final Gate* manuscript together with a **Level-2B tiny demo closure packet**. The central objective is to formalize a *public, mechanically auditable proof-input interface* for Collatz-scale reductions: instead of claiming an unconditional proof “in one shot, ” the paper isolates the remaining completion step as the existence of an explicit **packet generator** that outputs auditable closure packets for all sufficiently large scales \ (L\) at a fixed base resolution \ (k_\*\), with a uniform positive effective margin. A key statement is the following reduction principle (Theorem 1. 1): if such a protocol \ (P (k_\*, L) \) produces, for each \ (L L₀\), a closure packet that passes the public audit checklist and certifies\_\* (k_\*, L) > 0, ₋₈₅ₓ (k_\*, L) 0, the program’s EB\ (₂ₒ\) closure holds uniformly and the Gate-B / quenched absorption conclusions follow, yielding the Collatz conjecture as a consequence. ## Included artifacts - `CollatzFinalGateᵥ6. 0QBHITrevBₚatched. pdf` (this manuscript) - `CollatzFinalGateᵥ6. 0QBHITrevBₚatched. tex` (LaTeX source, for reference) - `democlosureₚacketLevel2Bₜinyᵥ6. 0ᵣealprepₛtrictₘatrixdemoₜestsweepQBHITₐuditpassᵣevBclean. zip` (a minimal **Level-2B demo closure packet**) ### Important note on the demo packetThe shipped demo packet is explicitly provided as a **smoke test of the reproducibility/audit interface only**. It is designed to pass the mechanical audit (schema completeness, hash binding, threshold enforcement, and Gate-B witness layout) but **does not contribute floating-point evidence to the mathematical claims**. ## Release taxonomy (paper summary) The paper uses a graded “public record” taxonomy, distinguishing: - **Level-1A/1B**: mechanically auditable completeness; optional (1A) vs enforced (1B) numerical thresholds. - **Level-2A**: EB-only closure packet (TwGap/Corr\ (_\) + budget fields sufficient to instantiate the reduction). - **Level-2B**: Level-2A plus a Gate-B witness bundle (certificate objects audited by `auditgateb. py`). - **Level-3 (sound nontrivial instance) **: Level-2B plus certificate-grade TwGap witnesses and strict log binding. The program dashboard (Table 4) emphasizes that **Closed (demo) ** means “interface instantiated and mechanically audited, ” not “uniform-in-\ (L\) unconditional theorem. ” The paper also records **QB-HIT finite-level certificates** as quenched exhaustive statements on the finite quotient \ (SL=Z/2LZ\), which are logically finite-level but not uniform-in-\ (L\). ## What is new in v6. 0b (QBHITrevB clean) - A Zenodo-ready packaging narrative (“closure packet as proof input”) and an explicit audit interface: the record can be independently checked without editing any file. - Hardening of the **paper binding + bytecode hygiene** conditions for audit integrity (see “How to audit” below). - A minimal Level-2B demo packet that exercises the end-to-end audit pipeline (including threshold enforcement and Gate-B witness layout), while keeping the record explicit about its smoke-test scope. ## How to audit / reproduce ### Level-1 acceptance checklist (public, auditable proof input) A Zenodo record qualifies as Level-1 if it ships a concrete `closureₚacket/` directory such that an independent auditor can mechanically verify all packet claims without editing any file. The checklist includes: 1. **Artifact completeness**: `manifest. json`, `instance. json`, `reps. json`, `certₗog. json`, `thresholds. json`, a `witnesses/` folder, and environment stamps (e. g. `envₛtamp. json`, `pipfreeze. txt`), all SHA256-bound in `manifest. json`. 2. **Paper binding**: `paperᵥersion. json` and `paper. sha256` bind the packet to immutable manuscript artifacts (e. g. `artifacts/*. pdf` and `artifacts/*. tex`). The auditor checks SHA256 equality; any mismatch is an automatic FAIL. 3. **Threshold enforcement (Level-1B) **: if the record claims numerical closure, `thresholds. json` must set `"enforce": true` and provide explicit numeric cutoffs (e. g. `deltaₘax`, `kappaₑffₘin`) ; any missing/violated cutoff is an automatic FAIL. 4. **Bytecode hygiene**: the audit must not create or depend on Python bytecode caches. Concretely: run with `PYTHONDONTWRITEBYTECODE=1` and `python -B`; and the packet directory must contain no `_ₚycache__` and no `*. pyc` files (automatic FAIL otherwise). ### One-command audit entrypointAfter unzipping the demo packet and entering the packet directory: ```bashPYTHONDONTWRITEBYTECODE=1 python -B scripts/auditₐll. py --packetdir. ========================= Author: Lee Byoungwoo leeclinic@protonmail. com