Collatz Final Gate v8.8 (docsync9) together with a sealed Level-2B demo packet implementing an audited proof interface for a certificate-triggered closure program.

# Overview This record releases **Collatz Final Gate v8.8 (docsync9)** together with a **sealed Level-2B demo packet**implementing an **audited proof interface** for a certificate-triggered closure program. The program separates:1) *Paper-level logic* (what must be shown, and why it implies Collatz convergence),2) *A finite auditable object* (a sealed packet that produces/validates a verdict certificate with checked inequalities). The aim of v8.8 is not to claim a completed proof by prose alone, but to provide a **reviewer-facing, mechanically auditable closure interface** aligned with modern computational-proof norms. # Included artifacts (this record) - Main paper (PDF): `Collatz_Final_Gate_v8.8_docsync9_statussheet.pdf`- Companion (PDF): `GateB_Bottleneck_v1.8b_docsync9_statussheet.pdf`- Checklist (PDF): `L0_16_complete_certificate_checklist_v8.8_docsync9_synced.pdf`- Sealed demo packet (ZIP, Level-2B): `Collatz_Demo_L2B_v8.8_sealed_full_nonsynth_HARDENEDPASS_manifestsha_docsync9_merged_mladder_tausweep.zip` Note: the ZIP contains its own `artifacts/` snapshot (paper PDFs/TeX used for binding), and the record also ships reviewer-facing PDFs as listed above. # Summary (v8.8 / docsync9) **Core idea.** The closure program is expressed as a *verdict-certificate interface*: a public packet must output a finite object whose checked entries include (i) a budget domination inequality and (ii) a Gate-B Corr\((δ)\)/TwGap item (discharged via auditable proxies). Once such an instance is mechanically verified, downstream analytic promotion mechanisms are triggered by the verdict, not by additional informal reasoning. **Budget template.** A representative closure gate is a verified domination inequality of the form\[η < κ_0,\]reported inside the certificate and enforced by the audit scripts. # Closed results - **Sealed Level-2B auditable packet.** The ZIP is self-contained, hash-manifested, and includes a mechanically verifiable pipeline (`scripts/`) plus witness/evidence files required by the protocol.- **Non-synthetic origin enforcement.** The packet is configured with a non-synthetic data-origin interface (see `provenance/` and `raw_inputs/`), and the stricter audit mode enforces origin + raw-input fingerprinting.- **Gate-B certificate interface.** The Gate-B I4 item (Corr\((δ)\)/TwGap) is discharged via an auditable proxy interface produced by q-sweep reports and a binding object that pins the proxy to the companion theorem label.- **Matrix-backed TwGap evidence.** TwGap witnesses are matrix-backed and recomputable, avoiding absolute paths and enabling deterministic recomputation checks.- **Two-environment semantic replication.** The packet includes a minimal semantic replication bundle (`replication/runA`, `replication/runB`, `replication/comparison_report.json`) and an audit that enforces a PASS on the comparator. # What is new in docsync9 1) **\(τ\)-lowering sweep promoted to audit.** A dedicated \(τ\)-sweep generator + auditor is included: - `scripts/compute_gateb_tau_sweep.py` - `scripts/audit_gateb_tau_sweep.py` - outputs under `results/gateb_tau_sweep_report.json` and `results/tau_sweep/` 2) **K-scaling loophole mitigation via conservative normalization.** The q-sweep proxy reports both raw and conservative statistics: - \(τraw\) (raw statistic) - \(τeff = τraw· max(1, K/Kref)\) where \(Kref\) is recorded in the report. This ensures that increasing \(K\) alone cannot artificially improve the audited proxy without paying the declared penalty factor. 3) **M-ladder promoted to audit.** A grid-size ladder diagnostic is included: - `scripts/compute_gateb_m_ladder.py` - `scripts/audit_gateb_m_ladder.py` - outputs under `results/gateb_m_ladder_report.json` and `results/m_ladder/` 4) **Numeric model audit.** A declared numeric model and its audit are included (`numeric_model.json`, `scripts/audit_numeric_model.py`), and `audit_all` enforces PASS. # How to reproduce (mechanical audit) Tested with Python 3.11 on Linux. 1) Unzip the sealed packet: - `unzip -q Collatz_Demo_L2B_v8.8_sealed_full_nonsynth_HARDENEDPASS_manifestsha_docsync9_merged_mladder_tausweep.zip`2) Run the hardened non-synthetic audit: - `python3 -B scripts/audit_all.py --mode sealed_full_nonsynth_hardened` Expected result: `[audit_all] PASS (sealed_full_nonsynth_hardened)`. Additional modes:- `python3 -B scripts/audit_all.py --mode sealed_full`- `python3 -B scripts/audit_all.py --mode sealed_full_nonsynth` # Technical notes (proxy and binding objects) Primary q-sweep report:- `results/gateb_qsweep_report.json`- `summary.mean_sq_norm_max_over_q_raw` (raw proxy)- `summary.mean_sq_norm_max_over_q` (effective proxy, i.e. \(τeff\))- `summary.K_ref`, `summary.tau_scale_factor` Raw-driven q-sweep (enforced in non-synthetic modes):- `results/gateb_qsweep_raw_report.json` Enforcement threshold:- `thresholds.json : gateb_qsweep.max_mean_sq_norm_max_over_q` Binding object (pins the interface to the companion theorem label and combine-mode):- `results/proxy2corr_binding.json` # Scope & non-toy status This record provides:- a rigorous *interface-level* closure program (what must be certified, and how it is audited),- a concrete non-synthetic Level-2B instance demonstrating the full audit pipeline,- reproducibility/replication artifacts aligned with computational-proof expectations. This record does **not** claim that Collatz is fully proved by this single packet alone. The intended closure pathway is:- produce a “complete certificate” instance at a declared base scale \(L_0\) (see checklist),- then trigger the program’s analytic promotion steps (All-\(L\) mechanisms) from that verdict. # Program closure and targets Immediate next milestone (reviewer-facing):- **L0=16 complete certificate (end-to-end).** Produce a fully non-synthetic, audited verdict certificate whose checked entries include: 1) the budget domination inequality, and 2) a Corr\((δ)\)/TwGap item (or a sufficient proxy-to-Corr/TwGap condition) recorded as a mandatory checked entry. Mid-term strengthening:- tighten the proxy-to-Corr/TwGap sufficiency conditions (reduce dependence on finite certified grids),- strengthen numeric soundness for decisive inequalities (interval/rational enclosure on critical checks),- expand robustness diagnostics (M-ladder and \(τ\)-sweep) into reviewer-readable dashboards. # Citation Zenodo will provide the canonical citation entry for this record. When referencing the software artifact, cite the record and mention the sealed Level-2B demo packet filename listed above. ========================= Author: Lee Byoungwoo leeclinic@protonmail.com