Collatz Final Gate v6.4: Reduction-and-Certification Program with Auditable Level-2B Closure Packet (QBHITrevB)

## Overview This deposit contains a programmatic reduction toward the Collatz conjecture, organized as a **reduction + certification pipeline** rather than an unconditional proof at the current version \(v6.4\) (stepwise19). **At-a-glance status (v6.4):**- This paper is a reduction + certification program; it is **not** an unconditional proof at v6.4.- **Closed(demo) \(≠\) Closed(full)**: the included demo packet is a **synthetic** demonstration of an auditable pipeline.- Main open targets: **Gate B** (APD0/dispersion at scale with uniform margin), **scale promotion**, and the **annealed \(→\) quenched transfer** (carry-cone influence control). The technical aim is to isolate the remaining proof bottleneck(s) into explicitly checkable “gate” statements and to provide a reproducible, mechanically auditable interface for finite certificates (TwGap/Corr\(δ\)/Budget and optional QB-HIT). ## Contents of this Zenodo record **Main paper (PDF):**- `Collatz_Final_Gate_v6.4_stepwise19.pdf` **Main paper (LaTeX):**- `Collatz_Final_Gate_v6.4_stepwise19.tex` **Demo closure packet (ZIP):**- `Collatz_Demo_L2B_v6.4_stepwise19.zip` The demo packet is aligned to the paper’s certification schema:- SHA256 manifest bindings for file immutability,- threshold enforcement via `thresholds.json` (automatic FAIL on missing/violated required inequalities),- certification logs (`cert_log.json`) with the minimal required fields,- optional small-scale sweep tests (QMC/Walsh) and auxiliary QB-HIT data,- and a “ledger” summary binding named constants to packet fields. ## How to verify (mechanical audit) Unzip the demo packet and follow `README_AUDIT.txt` inside the ZIP.The audit checks:- presence and JSON well-formedness of required objects,- SHA256 bindings recorded in the manifest/logs,- and enforcement of declared thresholds in `thresholds.json`. Important: the demo is meant to verify **auditability and schema correctness** at a tiny fixed scale; it does not claim to close the “full” (asymptotic) targets. ## Release-level taxonomy (summary) The protocol uses the following public release levels:- **Level-0**: layout only.- **Level-1A**: schema consistency (auditor PASS).- **Level-1B**: threshold enforcement enabled (automatic FAIL on violations).- **Level-2A**: EB-only closure at a declared instance \((k_, L)\) with certified TwGap/Corr\(δ\) and budget fields sufficient to instantiate the EB closure theorem interface.- **Level-2B**: Level-2A plus a Gate-B witness bundle (complete witness files; auditable).- **Level-3**: sound nontrivial instance (certificate-grade). This deposit includes a **Level-2B tiny demo packet** (synthetic) to demonstrate the end-to-end mechanical audit pipeline. ## What is new in v6.4 - Shortened artifact names for readable citation in the paper and Zenodo.- Updated bindings inside the demo packet to match the v6.4 paper artifacts (paper_version/sha/manifest/cert_log).- The paper/pipeline integrates the recent analytic interface upgrades: (i) Fourier-side \(L^1\) spectral diffusion diagnostics, (ii) large-sieve/bilinear “power-saving” ledger targeting Gate B, (iii) \(L^1\)/TV-contraction viewpoint for \(δ_0\)-uniformity as a corollary route, and (iv) carry-scattering / low-degree retention fields as measurable schema entries. ## Open targets (proof-completion bottlenecks) The paper isolates three principal bottlenecks:1) **Gate B**: APD0/dispersion-at-scale with a uniform positive margin.2) **Scale promotion**: uniform ledger bounds that survive \(L → ∞\) (e.g. via Mosco/\(Γ\)-convergence templates).3) **Annealed \(→\) quenched transfer**: controlling the carry-cone influence/defect budget to lift averaged statements to deterministic orbit statements. ## Keywords Collatz conjecture; 3x+1 problem; certification; reproducibility; auditable proof inputs; spectral gap; Markov kernels; conductance/Cheeger bounds; finite certificates; verification. ## Notes on scope This record is intentionally structured for third-party auditability.The demo packet is a reproducibility artifact, not a claim of full proof closure. ========================= Author: Lee Byoungwoo leeclinic@protonmail.com