Collatz Final Gate v9.1 + Gate B Bottleneck v2.1 — Sealed Level-2B Packet (Level-3 Enabled) and Audited Certificate Interface

# Summary (v9.1) ## OverviewThis record releases a **certificate-oriented closure interface** for the Collatz conjecture, together with a **sealed Level-2B/Level-3 packet** that produces and verifies a *verdict certificate* under explicit thresholds and mechanically enforced audit rules. The program replaces an informal “last arithmetic bottleneck” with a **finite, hash-locked, mechanically auditable attack surface**:the Corr\((δ)\)/TwGap obligation is exposed as a **mandatory checked entry (I4)** in the Gate-B certificate, and the All-\(L\) promotion is triggered by a **single PASS event** rather than additional ad-hoc arithmetic arguments. Scope note: this is not a claim of a purely pen-and-paper proof. The statement is **certificate-graded** and conditional on the published verifier/auditor under its declared numeric model and thresholds (see “Trust base (TCB)”). --- ## Contents of this record ### Papers (PDF + TeX)- Collatz Final Gate v9.1 (main paper)- Gate B Bottleneck v2.1 (companion)- L0=16 Complete Certificate Checklist v9.1 (reviewer-facing checklist) ### Sealed packet (ZIP)- Collatz_L2B_v9.1.zip Unzips to a single root directory:- pkt_v9_1/ Key directories/files inside pkt_v9_1/:- scripts/ (auditors/verifiers)- results/ (certificates, reports, witnesses)- thresholds.json, numeric_model.json- packet_identity.json, paper_version.json- manifest.json (hash-locked canonical file list)- provenance/ (seal + environment/toolchain fingerprints)- replication/ (runA/runB semantic replication + comparator)- historical/ (archived legacy material; excluded from the manifest) Important:- historical/ is non-canonical archive storage; it is explicitly excluded from manifest.json and never participates in PASS. --- ## Quickstart (fresh unzip)Run exactly the following from a clean unzip: 1) unzip Collatz_L2B_v9.1.zip2) cd pkt_v9_13) python -B scripts/audit_all.py --mode sealed_full_nonsynth_hardened_level3 Expected result:- PASS If any mandatory field/inequality/file/hash is missing or inconsistent, the audit must FAIL (no partial acceptance). --- ## Closed results (interface-level, v9.1) ### Gate-A: budget trigger (certificate-grade)The program requires an explicit budget domination trigger inequality at the packet-declared base scale:\[ηₜₒₜₐₗ < κ_0,\]recorded as a checked entry in the verdict certificate. ### Gate-B: Corr(delta)/TwGap bottleneck as a mandatory checked entry (I4)- The Corr\((δ)\)/TwGap bottleneck is exposed as a mandatory Gate-B certificate obligation (I4).- The verifier enforces I4 as a checked inequality (not a narrative assumption).- The audit fails if the I4 entry is missing. Consumption rule (localization):- The deterministic map / finite validation grid enters the logic only via a certified grid-envelope scalar.- Corr\((δ)\)/TwGap is consumed solely through this finite-grid envelope plus enforced margins (no hidden global Corr\((δ)\) interpretation elsewhere). --- ## Frozen constants (prevents “definition shift”) The packet freezes a conservative max-extension rule for the q-sweep proxy via an audited coverage slack constant. Definitions:- Let \(τ\) be the audited q-sweep proxy maximum over the observed modulus keys.- Let \(scov≥ 0\) be the audited coverage slack.- Define the frozen worst-case proxy constant:\[τ_ := τ + scov.\] Semantic contract (soundness role of coverage slack):\[max_{q∈ Qdecl}MS(q) ≤ τ_.\] Certified margin (on PASS):- Let \(τₘₐₓ\) be the enforced threshold.- Define the proxy margin:\[mproxy := τₘₐₓ - τ_.\]On PASS, \(mproxy≥ 0\). Interpretation:- \(scov\) is fixed as the conservative slack needed to extend the observed maximum to the declared modulus set.- This makes the grid-envelope consumption explicit and auditable; no other Corr\((δ)\) semantics are assumed. --- ## What is new in v9.1 (reader-facing changes)- Dependency map (1 page): the main paper includes a compact table stating exactly where the certified grid-envelope is used (and nowhere else).- Frozen proxy/coverage constants: the companion paper fixes the semantic contract for coverage slack and proxy margin as certificate-grade constants.- Minimal packet hygiene: the sealed ZIP has a clean top-level surface (pkt_v9_1/); legacy artifacts are moved under historical/ and excluded from the manifest.- Audit-first interface: mandatory certificate entries are enforced mechanically (missing entry ⇒ FAIL). --- ## Trust base (TCB) and numeric soundnessThe main claim is certificate-graded and conditional on:- correctness of the published auditor/verifier implementation,- correctness of the declared numeric model for the checked inequalities,- correctness of the manifest/seal binding the verified objects. In the standard computational-proof sense, the implication“Level-3 PASS ⇒ program conclusion”is meaningful only under the above trust base. A key target going forward is reducing the TCB further:- interval/rational enforcement for critical scalars/inequalities, and/or- an independent verifier. --- ## Scope & non-toy statusThis record is intentionally scoped as an auditable closure interface:- it isolates the final attack surface into a finite certificate with explicit thresholds,- it provides a reproducible audit pipeline,- it separates artifact/documentation completeness (sealed packet + audit PASS) from remaining mathematical upgrades. --- ## Program closure and targets Closed (v9.1, interface-level):- Sealed packet with mechanical audit (PASS/FAIL) and mandatory Gate-B I4 enforcement.- Explicit dependency map localizing where the grid-envelope enters. Primary targets for stronger academic acceptance:- front-and-center “Level-3 PASS ⇒ conclusion” soundness statement (with explicit TCB scope),- tighter Proxy⇒Corr/TwGap bridge presentation with clearer domain declarations and error margins,- further TCB reduction (interval/rational checks and/or an independent verifier). --- ## Reproducibility notes- Designed for fresh unzip execution.- Any missing mandatory file/hash/checked inequality must trigger FAIL.- historical/ is for reference only; it is excluded from the canonical manifest and does not affect PASS. (End of description.) ========================= Author: Lee Byoungwoo leeclinic@protonmail.com