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

## 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** (sealed_full_nonsynth) 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 \(η < κ_0\) and (ii) the Gate B trigger item **I4**, discharged in v8.7 via a **Proxy⇒Corr(\(δ\))/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 **sealed_full_nonsynth** Level–2B packet that passes mechanical audit.- A **Gate B certificate object** \( results/gateb_certificate.json \) whose binder locks: - the packet manifest hash (manifest_sha256), - paper/companion hashes, - and the Proxy⇒Corr(\(δ\))/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(\(δ\))/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 (sealed_full_nonsynth).- 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): `Collatz_Final_Gate_v8.7.*`- GateB companion (PDF/TeX): `GateB_Bottleneck_v1.8.*`- Demo packet (sealed_full_nonsynth, PASS): - `Collatz_Demo_L2B_v8.7_sealed_full_nonsynth_PASS_manifestsha.zip`- Replication toolkit: - `Collatz_Replication_Toolkit_v8.7.zip`- L0=16 complete certificate checklist (PDF/TeX): - `L0_16_complete_certificate_checklist_v8.7.*` ## Reproducibility / how to verify After unzipping the demo packet: - Run the mechanical audit: - `python -B scripts/audit_all.py --mode sealed_full_nonsynth` The audit checks manifest binding, certificate binder consistency (including the Proxy⇒Corr(\(δ\))/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