Collatz Final Gate v8.8: A Sealed Level-2B Certificate Interface (Non-Synthetic 𝐿0 = 16, Mandatory Proxy ⇒ ⇒Corr ( 𝛿 )/TwGap, Numeric-Model Audit, Hardened Replication)

## Overview This record releases **Collatz Final Gate v8.8** together with a **sealed Level–2B demo packet**implementing an *audited proof interface* for a certificate-triggered closure program. **Included components**- **Main paper:** *Collatz Final Gate v8.8* (PDF + TeX)- **Companion:** *Gate B Bottleneck v1.8b* (PDF + TeX)- **Sealed demo packet (ZIP):** a mechanically auditable artifact that produces and verifies a single **verdict certificate** with checked inequalities and sealed provenance. The v8.8 upgrade is designed to strengthen the reviewer-facing “completeness impression”while staying faithful to modern computational-proof norms:a finite sealed object + an auditable verification pipeline. --- ## Summary (v8.8) - **I4b is mandatory**: Proxy⇒Corr(δ)/TwGap is enforced as a required discharge item.- **Numeric-model guardrail**: the audit rechecks a curated set of core scalar inequalities under a declared `numeric_model.json`.- **Robustness trace**: adds at least one additional scale sweep (e.g. L=20) in the same audited format.- **Hardened replication**: semantic (contract-level) replication interface + hardened audit mode. --- ## What is new in v8.8 ### (1) I4b is always required (mandatory Proxy⇒Corr(δ)/TwGap binding) The Gate-B certificate check now enforces the binding item - **I4b: Proxy ⇒ Corr(δ)/TwGap** as a **mandatory** checked entry. Any packet claiming Level–2B closure must supply and pass theProxy⇒Corr(δ)/TwGap binding; otherwise the mechanical audit fails. In particular, the binder requires the companion theorem label - `companion.required_label = thm:proxy-to-corrdelta` and fails if the shipped companion artifacts do not contain that theorem label(or if hashes/binders are inconsistent). ### (2) Declared numeric model expanded to “core inequalities” v8.8 expands the numeric soundness layer: the audit rechecks a curated set of**core scalar inequalities** under a declared numeric model specified by `numeric_model.json`.The policy uses conservative decimal arithmetic (fixed precision + safety margins) to reducedependence on floating-point edge cases. This is intentionally scoped: rather than converting all computations to interval/rational arithmetic,v8.8 enforces a **minimal but decisive** numeric-model guardrail on the inequalities that drive the verdict. ### (3) Robustness trace (additional scale sweep, e.g. L=20) To leave a visible robustness trace, v8.8 adds at least one additional scale L (e.g. L=20)to the audited pipeline using the same script/spec format.The purpose is not to claim asymptotic coverage, but to demonstrate stable pipeline behaviorbeyond the L0=16 trigger instance. ### (4) Hardened replication interface The packet includes a semantic replication interface (reproduction contract + snapshot collection + comparator)and exposes a hardened audit mode that 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) This record provides a Level–2B-style closure interface in the following sense: - A **sealed ZIP packet** contains all scripts/specs/results needed to (re)generate and (re)verify a **verdict certificate**.- The audit fails if required artifacts, hashes, or required checked inequalities are missing.- The interface is designed so that once a nontrivial trigger instance is certified, analytic “All-L” promotion mechanisms can be invoked by the certificate rather than by ad-hoc arguments. --- ## Packet contents (inside the ZIP) Typical top-level components: - `scripts/` — compute + audit programs (including `audit_all.py`)- `tests/` — input specs (q-sweep specs, scale sweep specs, etc.)- `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 from the packet root: - 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 mode (includes replication-contract checks when runA/runB snapshots are present): - `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 main mathematical content is a reduction that isolatesa small family of checked inequalities (Gate-B bottleneck items) whose satisfaction triggers program closure. v8.8 focuses on:- strengthening **interface integrity** (mandatory I4b, packet–document binding, numeric-model audit), and- strengthening **reproducibility** (sealed manifests + contract-level replication). It does not claim that every remaining arithmetic bottleneck is fully resolved; rather, it supplies an auditablepipeline intended to host and validate decisive trigger instances. --- ## Files in this record - Main paper: - `Collatz_Final_Gate_v8.8.pdf` - `Collatz_Final_Gate_v8.8.tex`- Companion: - `GateB_Bottleneck_v1.8b.pdf` - `GateB_Bottleneck_v1.8b.tex`- L0=16 certificate checklist: - `L0_16_complete_certificate_checklist_v8.8.pdf` - `L0_16_complete_certificate_checklist_v8.8.tex`- Level–2B demo packet (sealed, hardened): - `Collatz_Demo_L2B_v8.8_sealed_full_nonsynth_HARDENEDPASS_manifestsha_docsync2.zip` --- ## Citation If you cite this record, cite the main paper version and reference the sealed packet filename above for reproducibility. ========================= Author: Lee Byoungwoo leeclinic@protonmail.com