# 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** (`numericₘodel. 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 \ (L₀=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 `auditₐll. 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- `numericₘodel. json` — declared numeric model for core-inequality rechecks- `specs/reprocontract. 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/auditₐll. py --mode sealedfullₙonsynth` - Numeric-model recheck: - `PYTHONDONTWRITEBYTECODE=1 python -B scripts/auditₐll. py --mode sealedfullₙonsynthₙumeric` - Hardened audit (includes replication contract checks): - `PYTHONDONTWRITEBYTECODE=1 python -B scripts/auditₐll. py --mode sealedfullₙonsynthₕardened` # Scope instead it supplies an auditable pipeline intended to host and validate decisive trigger instances. # Files in this record - Main paper: `CollatzFinalGateᵥ8. 8docsync3. pdf`, `CollatzFinalGateᵥ8. 8docsync3. tex`- Companion: `GateBBottleneckᵥ1. 8bdocsync3. pdf`, `GateBBottleneckᵥ1. 8bdocsync3. tex`- Checklist: `L0₁6completecertificatechecklistᵥ8. 8docsync3. pdf`, `L0₁6completecertificatechecklistᵥ8. 8docsync3. tex`- Sealed demo packet: - `CollatzDemoL2Bᵥ8. 8ₛealedfullₙonsynthHARDENEDPASSₘanifestshadocsync3. 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
Byoungwoo Lee (Wed,) studied this question.