Collatz Final Gate v8.8 — Sealed Level-2B Demo Packet for a Certificate-Triggered Closure Program (Main + Gate B Companion)

# Overview This record releases **Collatz Final Gate v8.8 (docsync3)** together with a **sealed Level-2B demo packet** implementing an auditable *certificate interface* for a certificate-triggered closure program. The release follows the modern computational-proof norm: a finite sealed object (ZIP) + a mechanical audit pipeline. The audit fails if required artifacts, hashes, or required checked inequalities are missing or inconsistent. # What is new in v8.8 (docsync3) ## (1) I4b is always required: mandatory Proxy⇒Corr(δ)/TwGap binding The Gate-B certificate audit now enforces the binding item - **I4b: Proxy ⇒ Corr(δ)/TwGap** as an **unconditional required checked inequality** (independent of any instance-origin flag). Any packet claiming Level-2B closure must supply and pass this entry; otherwise the mechanical audit fails. ## (2) Expanded numeric soundness layer for core inequalities Version v8.8 expands the **declared numeric model** (`numeric_model.json`) so that a curated set of *core scalar inequalities* is rechecked under conservative decimal arithmetic (fixed precision + safety margins). The intent is a minimal but decisive guardrail against floating-point edge cases, focused on inequalities that drive the verdict. ## (3) Robustness trace: additional scale sweep To provide a visible robustness trace, v8.8 adds at least one additional scale \(L\) (e.g. \(L=20\)) to the same audited test pipeline. This is not an asymptotic claim; it is a stability trace showing the pipeline behavior beyond the \(L_0=16\) trigger instance. ## (4) Hardened replication interface (semantic replication) The packet includes a **semantic replication interface** (reproduction contract + snapshot collector + comparator). A hardened audit mode can require agreement of two independent runs/environments at the contract level (field-wise semantic equivalence), not merely byte equality. # Closed results (certificate-interface status) The record provides a Level-2B style closure interface in the following sense: - The sealed ZIP contains all scripts/specs/results needed to generate and verify a **verdict certificate**.- The audit enforces required checked inequalities (including mandatory I4b), file provenance, and hash consistency (manifest + seal).- The interface is designed so that once a nontrivial trigger instance is certified, the analytic “All-\(L\)” promotion mechanism is triggered by the certificate, not by ad-hoc manual steps. # Packet contents (ZIP) Typical top-level components inside the sealed packet: - `scripts/` — compute + audit programs (including `audit_all.py`)- `tests/` — input specs (q-sweep specs, scale sweep specs)- `results/` — generated reports and the verdict certificate- `provenance/` — seal data, environment fingerprints, script digests- `manifest.json` — SHA256 manifest for the sealed payload- `numeric_model.json` — declared numeric model for core-inequality rechecks- `specs/repro_contract.json` and `replication/` — semantic replication tools # How to run (mechanical verification) Unzip the demo packet and run one of the audited modes: - Standard non-synthetic sealed audit: - `PYTHONDONTWRITEBYTECODE=1 python -B scripts/audit_all.py --mode sealed_full_nonsynth` - Numeric-model recheck: - `PYTHONDONTWRITEBYTECODE=1 python -B scripts/audit_all.py --mode sealed_full_nonsynth_numeric` - Hardened audit (includes replication contract checks): - `PYTHONDONTWRITEBYTECODE=1 python -B scripts/audit_all.py --mode sealed_full_nonsynth_hardened` # Scope & non-toy status This work is structured as a **certificate interface**: the program isolates a small family of checked inequalities (Gate-B bottleneck items) whose satisfaction triggers program closure. The v8.8 (docsync3) release strengthens: - interface integrity (mandatory I4b, packet–document binding, numeric-model audit), and- reproducibility (sealed manifests + semantic replication interface). It does not claim that every remaining arithmetic bottleneck is fully resolved; instead it supplies an auditable pipeline intended to host and validate decisive trigger instances. # Files in this record - Main paper: `Collatz_Final_Gate_v8.8_docsync3.pdf`, `Collatz_Final_Gate_v8.8_docsync3.tex`- Companion: `GateB_Bottleneck_v1.8b_docsync3.pdf`, `GateB_Bottleneck_v1.8b_docsync3.tex`- Checklist: `L0_16_complete_certificate_checklist_v8.8_docsync3.pdf`, `L0_16_complete_certificate_checklist_v8.8_docsync3.tex`- Sealed demo packet: - `Collatz_Demo_L2B_v8.8_sealed_full_nonsynth_HARDENEDPASS_manifestsha_docsync3.zip` # Citation If you cite this record, please cite the main paper version (v8.8) and include the sealed packet filename above for reproducibility. ========================= Author: Lee Byoungwoo leeclinic@protonmail.com