What question did this study set out to answer?

This work aims to improve the certification process of the Collatz Final Gate program with a focus on auditability and non-synthetic origins.

February 10, 2026Open Access

Collatz Final Gate v8.6: Non-synthetic 𝐿 0 = 16 Trigger Certification, Proxy→Corr(𝛿)/TwGap Interface, and Portable Level-2B Demo Packet

Key Points

This work aims to improve the certification process of the Collatz Final Gate program with a focus on auditability and non-synthetic origins.
Introduced a portable Level-2B demo packet with mechanical auditing features.
Implemented an audit mode enforcing non-synthetic origin and raw-input binding.
Developed a report creation mechanism under a non-synthetic audit mode.
Formalized a Proxy→Corr(δ)/TwGap interface within the Gate-B companion.
The demo packet supports mechanical audits with guaranteed SHA-256 integrity.
Certificate-first approach successful in reducing the global statement to auditable inequalities.
Non-synthetic provenance methods enhance trust in audit results.

Abstract

#### OverviewThis record bundles the **v8. 6** release of the *Collatz Final Gate* program (main paper + Gate-B companion) together with a **portable, mechanically auditable Level-2B demo packet** and a **one-page \ (L₀=16\) complete-certificate checklist**. The program is **certificate-first**: the global statement is reduced to a finite list of **checked inequalities** (Gate-B certificate), each with explicit margins and evidence pointers, and verified by deterministic audit scripts under hash-locked packet integrity. #### What is new in v8. 6- **Non-synthetic provenance hooks**: the packet includes an audit mode that enforces a non-synthetic origin declaration and raw-input binding. - **Raw-driven q-sweep witness path**: an additional *raw-driven* q-sweep report is generated and required under the non-synthetic audit mode. - **Proxy→Corr (\ (\) ) /TwGap interface (template level) **: the Gate-B companion formalizes a theorem-level interface for upgrading a measured proxy to a Corr (\ (\) ) /TwGap-sufficient condition (with version/label binding into the certificate metadata). - **Portable packet hygiene**: absolute paths are disallowed in witnesses; bytecode artifacts are excluded; the binder enforces a manifest SHA-256 seal. #### Included artifacts (4 files) 1. **Main paper (PDF) **: *Collatz Final Gate v8. 6*2. **Companion paper (PDF) **: *GateB Bottleneck v1. 8r2*3. **One-page checklist (PDF) **: \ (L₀=16\) complete certificate checklist (v8. 6r2) 4. **Portable Level-2B demo packet (ZIP) **: sealed packet with manifest SHA-256 binding and `sealedfullₙonsynth` audit support #### Reproducibility (mechanical audit) Unzip the demo packet and run: - `python -B scripts/auditₐll. py --mode sealedfull`- `python -B scripts/auditₐll. py --mode sealedfullₙonsynth` The audit enforces: - manifest SHA-256 integrity and binder sealing, - no shipped/generated bytecode artifacts during audit (bytecode hygiene), - non-synthetic provenance binding (in `sealedfullₙonsynth`), - required report presence and threshold checks for the Gate-B certificate. #### Scope and caveatsThis release **does not claim** that Corr (\ (\) ) /TwGap is already proved. Instead, it claims that the remaining arithmetic burden is reduced to a **finite, auditable checklist** with explicit margins and evidence pointers, and provides a **portable** packet interface intended for third-party reproduction and incremental strengthening. #### Near-term targets (v8. 6 → v8. 7) - Produce a genuinely **non-synthetic** end-to-end \ (L₀=16\) trigger instance (raw inputs → reports → certificate → seal → audit PASS). - Upgrade the **Proxy→Corr (\ (\) ) /TwGap** implication from template level to a fully theorem-backed certificate item, with audit-enforced version/label binding. ========================= Author: Lee Byoungwoo leeclinic@protonmail. com

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