Collatz Final Gate (v5.7) — Proof-completion reduction via an EB-only closure packet

# Collatz Final Gate v5.7 — Zenodo Description ## OverviewThis record accompanies **“Collatz Final Gate v5.7: Proof-completion reduction via an EB-only closure packet (Level-2A/2B schema; Gate B auditable interface)”** (Lee Byoungwoo, January 18, 2026). We recast the Collatz map as a Markov-type dynamics on a 2-adic moduli space \(M_C\) with a canonical stationary measure, and develop an operator-theoretic absorption framework for deterministic Collatz convergence. The core reversible object is a self-adjoint contraction \(K\) (and twisted variants), with an associated Dirichlet form controlling escape from nested absorbing neighborhoods of the terminal cycle. **Main message (reduction):** the remaining arithmetic bottlenecks are isolated into a *single auditable base-scale certificate packet* at \((k_,L)\). Once that packet exists (and passes a public mechanical audit), the paper’s internal operator/absorption implications close the “Gate B absorption step” and yield deterministic convergence. Optional speculative addenda (ARH/QBI and quantum-assisted heuristics) are segregated and disabled by default. --- ## What is proved internally (closed proof engine)Sections 1–8 and the core appendices provide the *internal* implication chain:- Dirichlet/absorption framework on \(M_C\);- comparison/transfer lemmas from the reversible kernel to the deterministic Collatz flow;- “large numbers first” absorption mechanism, conditional only on externally supplied certificate objects at a base scale. In particular, the paper formalizes the following **EB-only consumption interface**:given an auditable finite closure packet at \((k_,L)\) consisting of1) **TwGap**: certified spectral contraction for a finite family of twisted operators,2) **Corr\(_δ\)**: residue-class correlation/dispersion certificate derived from TwGap,3) **Budget bounds**: certified carry/composition leakage bounds ensuring an effective margin\[κeff := κ_ - ηlift > 0,\]then the deterministic absorption chain closes. All remaining arithmetic requirements are stated explicitly as **Target Theorems / Interface Statements**. --- ## What this record provides (artifacts)This Zenodo record ships:1) The PDF manuscript: `Collatz_Final_Gate_v5.7.pdf`.2) A minimal **Level-2B tiny demo closure packet**: `demo_closure_packet_Level2B_tiny_v5.7_auditpass.zip`. ### Important note (demo vs. theorem)The tiny Level-2B packet is provided as a **smoke test of the reproducibility/audit interface only**. It demonstrates that:- the packet schema is complete,- hashes/manifests bind all files,- `thresholds.json` enforcement is applied mechanically (missing/violated cutoffs → FAIL),- `audit_gateb.py` validates the Gate B witness bundle format at the interface level. **It does not contribute any floating-point evidence to the mathematical claims.**“Closed (demo)” means an interface instance exists and passes mechanical audit; it is not an unconditional theorem about the true Collatz dynamics at all scales. --- ## Reproducibility / mechanical auditUnzip the packet and run the audit entrypoint inside `closure_packet/`: ```bashcd closure_packetPYTHONDONTWRITEBYTECODE=1 python -B scripts/audit_all.py --packet_dir . ========================= Author: Lee Byoungwoo leeclinic@protonmail.com