Containment and Finite-Quotient Structure in Bad-State Lifting for the Odd Collatz Map

This repository contains a computational number theory manuscript and its accompanying reproducibility record, investigating the dynamics of the odd Collatz map. Approaching the problem from a computer science and engineering perspective, this work does not claim a global analytic proof of the Collatz conjecture. Instead, it provides a highly structured, certified finite map of the non-contractive "bad-state" sector under 2-adic refinement.Through row-level exact per-state CSV certificates across the 2²¹ → 2²² and 2²² → 2²³ transitions, this study establishes three robust computational laws: Child Refinement Certificate: Every audited bad source state has exactly two bad child lifts, uniquely preserving the parent's refined type.Exact-Image Certificate: The bad-image count follows a strict 0 or 2 law, and positive images always occupy a unique refined target type.Fine Selector Certificate: The fine selection of the image target is highly stable across consecutive refinements, with the q64 quotient coordinate dominating the selection in 21 out of 22 refined source types.To bridge the gap between empirical data science and rigorous mathematical certification, this package includes an independent finite certifier. This Python verifier reads the large per-state CSVs directly from the preserved ZIP input to validate the row-level claims without invoking the exploratory scripts, effectively removing instrumental bias.This work aims to provide the pure mathematics community with a rigorously audited, noise-free topological map of finite obstructions, serving as a structured foundation for future analytical proofs of uniform lifting.Files included in this repository:The referee-hardened arXiv-style manuscript and LaTeX source.Original ZIP inputs and CSV support tables.The original exploratory scripts.An independent finite certifier and checksum verifier for absolute reproducibility.