What question did this study set out to answer?

The aim is to create an auditable verdict certificate while reducing complex arithmetic to a clear interface.

February 12, 2026Open Access

Collatz Final Gate v8.7: Certificate-grade reduction with an audited non-synthetic L0=16 trigger instance (Level–2B packet)

Key Points

The aim is to create an auditable verdict certificate while reducing complex arithmetic to a clear interface.
Compiled the main paper and companion into a bundled record.
Introduced a mechanical audit to ensure integrity of the verdict objects.
Established a theorem-level discharge rule to enhance audit robustness.
Successfully created a sealed full nonsynthetic packet that passes mechanical audit checks.
The Gate B certificate was validated against strict binding conditions.
The integration of raw data inputs is mandated for verdict pathways.

Abstract

## Overview This record bundles the **Collatz Final Gate** main paper (v8. 7) and its **Gate B bottleneck companion** (v1. 8) together with a **sealed, certificate-grade Level–2B demo packet** (sealedfullₙonsynth) and a replication toolkit. The program reframes Collatz as a **reduction to a finite, auditable verdict object**: a public packet must output a single **verdict certificate** whose checked inequalities include (i) the budget domination \ (< ₀\) and (ii) the Gate B trigger item **I4**, discharged in v8. 7 via a **Proxy⇒Corr (\ (\) ) /TwGap theorem-level rule** (not a template). The intent is to separate the “hard arithmetic content” into a **sharply located, certificate-facing interface** and to align the workflow with modern computational-proof norms: a finite auditable object + reproducible verification pipeline. ## Closed results (what is mechanically audited here) - A **sealedfullₙonsynth** Level–2B packet that passes mechanical audit. - A **Gate B certificate object** \ (results/gateb\certificate. json \) whose binder locks: - the packet manifest hash (manifestₛha256), - paper/companion hashes, - and the Proxy⇒Corr (\ (\) ) /TwGap binding. - **I4 is discharged by a theorem-level proxy rule** (required label: `thm: proxy-to-corrdelta` in the companion), and the audit fails if this binding is missing or inconsistent. ## What is new in v8. 7 / v1. 8 - **Proxy⇒Corr (\ (\) ) /TwGap is promoted to a theorem-level discharge rule for I4**, minimizing “template-only” assumptions. - **Non-synthetic raw data path is audit-enforced**: raw q-sweep inputs are required to affect the I4 discharge / verdict pathway (sealedfullₙonsynth). - Full doc-sync between: - main paper text (I4/dashboard/certificate wording), - companion theorem label requirements, - and the packet binder schema. ## Contents of this Zenodo record - Main paper (PDF/TeX): `CollatzFinalGateᵥ8. 7. *`- GateB companion (PDF/TeX): `GateBBottleneckᵥ1. 8. *`- Demo packet (sealedfullₙonsynth, PASS): - `CollatzDemoL2Bᵥ8. 7ₛealedfullₙonsynthPASSₘanifestsha. zip`- Replication toolkit: - `CollatzReplicationToolkitᵥ8. 7. zip`- L0=16 complete certificate checklist (PDF/TeX): - `L0₁6completecertificatechecklistᵥ8. 7. *` ## Reproducibility / how to verify After unzipping the demo packet: - Run the mechanical audit: - `python -B scripts/auditₐll. py --mode sealedfullₙonsynth` The audit checks manifest binding, certificate binder consistency (including the Proxy⇒Corr (\ (\) ) /TwGap required label), and fails on missing or inconsistent provenance / hashes. ## Scope & non-toy status (program statement) This work is intentionally “certificate-facing”: it reduces the global claim to a finite, auditable trigger instance and a formally stated upgrade interface. The Gate B companion isolates (i) an unconditional deterministic baseline and (ii) the exact remaining obstruction for certificate-grade uniformity, making the research target concrete and testable within an auditable pipeline. ========================= Author: Lee Byoungwoo leeclinic@protonmail. com

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