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 \(L≥ L_0\), a closure packet that passes the public audit checklist and certifies\[κ_\*(k_\*,L) > 0, ηlift(k_\*,L) < κ_\*(k_\*,L), infL≥ L_0(κ_\*(k_\*,L)-ηlift(k_\*,L)) > 0,\]then the program’s EB\(2S\) closure holds uniformly and the Gate-B / quenched absorption conclusions follow, yielding the Collatz conjecture as a consequence. ## Included artifacts - `Collatz_Final_Gate_v6.0_QBHITrevB_patched.pdf` (this manuscript)- `Collatz_Final_Gate_v6.0_QBHITrevB_patched.tex` (LaTeX source, for reference)- `demo_closure_packet_Level2B_tiny_v6.0_realprep_strict_matrixdemo_testsweep_QBHIT_auditpass_revBclean.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\(_δ\) + budget fields sufficient to instantiate the reduction).- **Level-2B**: Level-2A plus a Gate-B witness bundle (certificate objects audited by `audit_gateb.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 \(S_L=Z/2^LZ\), 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 `closure_packet/` 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`, `cert_log.json`, `thresholds.json`, a `witnesses/` folder, and environment stamps (e.g. `env_stamp.json`, `pip_freeze.txt`), all SHA256-bound in `manifest.json`. 2. **Paper binding**: `paper_version.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. `delta_max`, `kappa_eff_min`); 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/audit_all.py --packet_dir . ========================= Author: Lee Byoungwoo leeclinic@protonmail.com