Collatz Final Gate v9.0.1 — Certificate-Triggered Closure Program with a Sealed Level-2B Audit Packet v9.0.1 (L0=16 Anchor, I4 Corr(δ)/TwGap Mandatory)

# OverviewThis record releases an **unconditional reduction-to-certificate** program for the Collatz conjecture, centered on a *sealed, mechanically auditable* **Level-2B** packet and companion manuscripts. The guiding idea is: instead of attempting to close the final arithmetic bottleneck purely in prose, we **fix a proof interface** (a list of checked inequalities + witness objects) and provide a **public sealed packet** that (i) reproduces the reports, (ii) outputs the certificate objects, and (iii) fails audit if any required items are missing or inconsistent. Crucially, this is **not “conditional on external conjectures”** (e.g. RH/GRH). The remaining requirement for proof completion is the existence of a **finite audited trigger instance** satisfying the program’s certificate specification. # Contents of this record- **Main paper (documentation / theory):** - `Collatz_Final_Gate_v9.0.1.pdf`- **Companion (Gate B bottleneck / interface):** - `GateB_Bottleneck_v2.0.1.pdf`- **Reviewer checklist (L0=16 anchor):** - `L0_16_complete_certificate_checklist_v9.0.1.pdf`- **Sealed Level-2B demo packet (ZIP):** - `Collatz_L2B_v9.0.1.zip` ## Important note on version binding (artifact identity)The sealed packet **v9.0.1** is the **audited computation artifact**. It binds the paper artifacts shipped inside the ZIP (including the main paper and the GateB companion PDFs) via explicit SHA256 references recorded in:- `paper_version.json`- `manifest.json`- `provenance/seal.json` This is the core “computational proof” promise of the record: the certificate objects are tied to a specific, immutable artifact set. # Reproducibility: mechanical audit (main entrypoint)Unzip `Collatz_L2B_v9.0.1.zip`, then run (from the packet root): - Full sealed audit: - `python -B scripts/audit_all.py --mode sealed_full`- Non-synthetic origin enforced: - `python -B scripts/audit_all.py --mode sealed_full_nonsynth`- Hardened mode (adds mandatory L0=16 anchor + tau-sweep + extra GateB checks): - `python -B scripts/audit_all.py --mode sealed_full_nonsynth_hardened` The packet includes a SHA256 manifest (`manifest.json`), provenance seals (`provenance/seal.json`), and an auditable scripts tree. The audit is designed to FAIL if any required file/field is missing or mismatched. # Status taxonomy: interface-complete vs proof-complete- **Level-2B (interface-complete):** a sealed, mechanically auditable packet that enforces the verdict-certificate interface and produces certificate objects with mandatory checked items (including Gate-B I4).- **Level-3 (proof-complete / trigger instance):** a Level-2B packet plus a **single base-scale trigger instance** (e.g. at L0=16) whose verdict certificate satisfies the program’s proof-completion criteria (including a positive trigger margin and certified witness bundles). In this program, proof completion is defined by such a finite audited trigger instance. This record releases **Level-2B** artifacts (interface-complete), but does not claim proof completion as of v9.0.1. # Closed results (Level-2B: proof-interface closure)The sealed packet v9.0.1 implements a **Level-2B verdict-certificate interface**: - **I4 (Corr(δ)/TwGap) is mandatory** as a checked inequality entry in the GateB certificate object.- **L0=16 anchor evidence bundle is mandatory** in hardened mode (directory `results/L0_16_anchor/*`). ## Anti-loophole proxy normalization (K-inflation penalty)To prevent a loophole where one inflates \(K\) to artificially lower the proxy, the packet enforces:\[τeff=τraw· max\!(1,{K}{Kref}),\]with audited report fields (examples of the canonical fields used by the packet):- `results/gateb_qsweep_report.json: summary.mean_sq_norm_max_over_q_raw` (τ_raw)- `results/gateb_qsweep_report.json: summary.mean_sq_norm_max_over_q` (τ_eff)- plus `summary.K`, `summary.K_ref`, `summary.tau_scale_factor`. In non-synthetic mode, a raw-driven proxy report is also required:- `results/gateb_qsweep_raw_report.json` (same field conventions). When enabled (hardened), grid-coverage slack is audited:- `results/grid_coverage_report.json: summary.coverage_slack`. ## Certified-grid discharge quantitiesThe certified-grid discharge values are recomputable from the bound report quantities:\[Corrᶜᵉʳᵗ=√{M\,τeff},ᶜᵉʳᵗ=1-(Corrᶜᵉʳᵗ)^2,\]where \(M\) (grid size) is read from the q-sweep report (e.g. `summary.r_samples` in the canonical schema). # What is new in v9.0.1 (documentation / interface clarity)- Aligns the exposition with an **unconditional reduction-to-certificate** viewpoint: the program’s statements do not rely on external conjectural inputs; closure is defined by a finite audited trigger instance.- Introduces an explicit interface-level **grid-sufficiency** viewpoint: the engine consumes certified-grid inputs, not a global Corr\((δ)\) theorem.- Makes the “certificate-triggered All-\(L\) promotion” narrative explicit: one sealed base instance at \(L_0=16\) is treated as a public trigger object, and the analytic promotion mechanism is framed as a deterministic upgrade step activated by the audited certificate interface.- Synchronizes the I4 terminology with packet-facing fields and hardened checks (tau normalization, raw-driven report, and coverage slack). # Scope & non-toy status (what this is and is not)- This record does **not** claim a traditional pen-and-paper closure of Collatz in one manuscript.- It provides a **computational-proof style framework**: a finite, audited object (the sealed packet) + a fixed certificate interface + a deterministic verification/audit pipeline.- The sealed packet is configured for **non-synthetic origin** (raw input provenance recorded under `raw_inputs/` and `provenance/`), and hardened audit fails if the L0=16 anchor evidence directory is missing or inconsistent. # Program closure and targets (next steps)- **Primary closure target (Level-3 trigger):** strengthen the GateB witness pipeline so that the mandatory I4 item (Corr\((δ)\)/TwGap) is satisfied at the required strength within the same audited interface.- **Strengthening target:** enlarge/rigorize certified-grid coverage (coverage slack control, ladder closures), and improve numeric soundness (interval/rational enclosure for selected inequalities).- **Replication target:** multi-environment semantic replication contracts with strict audit enforcement. # Suggested citationLee Byoungwoo, “Collatz Final Gate v9.0.1 — Certificate-Triggered Closure Program with a Sealed Level-2B Audit Packet v9.0.1 (L0=16 Anchor, I4 Corr(δ)/TwGap Mandatory)”, Zenodo, 2026. ========================= Author: Lee Byoungwoo leeclinic@protonmail.com