A Non-Ergodic Deterministic Local-Obstruction Framework with Coq/Rocq Formalization and Reproducible Audit

https://github.com/dammroze/collatz-dammroze-coq-review

Coq3 Local Drop Freeze v1:
https://github.com/dammroze/collatz-dammroze-coq-review/releases/tag/coq3-local-drop-freeze-v1

GitHub Actions CI run:
https://github.com/dammroze/collatz-dammroze-coq-review/actions/runs/25413495729

NEW COQ GITHUB FILES AVAILABLE. (MAY-05-2026)

This record contains the LaTeX manuscript, PDF, Coq/Rocq formalization files, accepted ledger audits, SHA256 checksums, and GitHub Actions build verification for a non-ergodic local obstruction proof framework for the Collatz conjecture.

The manuscript text is authoritative. The Coq/Rocq files provide an audit surface aligned with the TeX reading order. The accepted v21 ledger verifies the manuscript dependency chain in the form FinalPaperHypotheses -> FinalClassicalConclusion, with Print Assumptions returning Closed under the global context for the final ledger targets.

GitHub repository:
https://github.com/dammroze/collatz-dammroze-coq-review

-----------------------

NonErgodic_Local_Drop has now been discharged in the Coq3 layer.

The bridge no longer ends at an opaque assumption. The exported connector is:

nonergodic_local_drop_from_v20_obstruction_chain :
  V20.PaperAxiomsV20 -> NonErgodic_Local_Drop

and the final Coq3 closure derives the bridge result from this theorem instead of using the former bridge axiom. The manuscript now states the non-ergodic local drop theorem explicitly, the Coq appendices reference the corresponding object, and the repository build passes with the Coq3 audit output reporting Closed under the global context.

-------------------

This record contains the manuscript and supporting materials for a non-ergodic deterministic framework for the analysis of the 3n+1 map.

The manuscript introduces a local-obstruction approach to the Collatz conjecture. Instead of relying on ergodic averaging, probabilistic heuristics, mixing assumptions, independence assumptions, Cesàro averaging, or statistical limits, the framework preserves local arithmetic structure through dyadic-band normalization and regime-sensitive finite analysis.

The central mechanism is deterministic local exclusion: any putative divergent trajectory or non-trivial cycle is forced to produce a finite locally admissible valuation pattern. The proof framework argues that such a local certificate is incompatible with the arithmetic constraints of the map, via a contradiction between deterministic amplification lower bounds and unconditional tail-control upper bounds.

Reader advisory: this work must be read within the stated zero-probability, zero-ergodicity framework. Critiques that import probabilistic, ergodic, mixing, independence, or global-averaging assumptions may misidentify the argument. The intended reading order is provided inside the manuscript through the Reader’s Guide / Logical Map.

Core mechanism:

Assume a global obstruction exists. Then a repeating local valuation configuration must occur inside dyadic bands. Repetition forces a deterministic lower bound on long stopping-time behavior through amplification. Independent drift and tail-control estimates provide an incompatible upper bound. Therefore, the obstruction is excluded.

The repository below contains the Coq/Rocq formalization package, LaTeX manuscript, audit files, checksums, and a passing GitHub Actions Coq build check:

https://github.com/dammroze/collatz-dammroze-coq-review

The GitHub repository is open for technical review, especially regarding:

1. Coq/Rocq soundness;
2. assumption dependency tracking;
3. hidden or unintended assumptions;
4. alignment between the LaTeX manuscript and the `.v` files;
5. reproducibility of the audit/checksum package.

Reviewers are encouraged to open GitHub Issues with file name, theorem/lemma name, line number, command run, and observed output.

# Collatz–Dammroze Coq/Rocq Review Package

This Zenodo record archives the manuscript and supporting formalization materials for technical peer review of a non-ergodic deterministic framework for the analysis of the \(3n+1\) map.

GitHub repository:

https://github.com/dammroze/collatz-dammroze-coq-review

GitHub Actions Coq build:

https://github.com/dammroze/collatz-dammroze-coq-review/actions

Main review issue:

https://github.com/dammroze/collatz-dammroze-coq-review/issues/3

---

## Critical Reader Advisory

This manuscript must be read in the order specified by its internal Reader’s Guide / Logical Map.

The argument is not ergodic, not probabilistic, and not statistical.

It does **not** use:

- ergodic theory;
- probability theory;
- mixing;
- independence assumptions;
- Cesàro averaging;
- statistical limits;
- global random-walk heuristics;
- typical-behavior reasoning.

The proof framework uses finite, deterministic, band-normalized arithmetic exclusion.

A review that imports probabilistic, ergodic, averaging, independence, or mixing assumptions into the argument is not reviewing the stated proof. It is reviewing a different framework.

The intended object of review is the non-ergodic deterministic chain actually stated in the manuscript and mirrored in the Coq/Rocq files.

---

## Mandatory Reading Order

Please do not begin by reading isolated lemmas out of order.

The manuscript is structured as a deterministic obstruction-exclusion chain. The correct reading order is:

1. **Reader Advisory / Methodological Note**  
   Establishes the zero-probability, zero-ergodicity framework.

2. **Reader’s Guide / Logical Map**  
   Specifies how the proof must be followed.

3. **Definitions and local dyadic-band normalization**  
   Establishes the finite local arithmetic setting.

4. **Local obstruction formulation**  
   A putative divergent trajectory or non-trivial cycle must create a finite locally admissible certificate.

5. **Finite alphabet / local repetition mechanism**  
   Local configurations inside dyadic bands are finite and must repeat under obstruction hypotheses.

6. **Amplification step**  
   Repetition of a local valuation configuration forces a deterministic lower bound on long stopping-time behavior.

7. **Tail-control / drift step**  
   Independent finite band-normalized estimates produce an upper bound incompatible with amplification.

8. **Contradiction / exclusion of obstruction**  
   Amplification lower bound and tail-control upper bound cannot simultaneously hold.

9. **Main theorem**  
   Since no global obstruction can exist, the Collatz obstruction class is excluded.

10. **Coq/Rocq artifacts**  
   Check formal dependencies, assumptions, theorem statements, and manuscript alignment.

Reading the paper in a different order can make the argument appear to rely on assumptions or heuristics that it explicitly rejects.

---

## Core Mechanism

The proof framework is a finite, non-ergodic contradiction engine.

In one sentence:

> Assuming a global obstruction exists, one derives a repeating local valuation configuration inside dyadic bands; repetition forces a deterministic lower bound on long stopping-time behavior through amplification, while drift and tail-control estimates yield an incompatible upper bound; hence the obstruction is excluded.

This is not an “almost all”, “typical orbit”, or “average-case” argument.

It is a deterministic local-exclusion argument.

---

## Archived Materials

This Zenodo record may include:

- LaTeX manuscript and PDF;
- Coq/Rocq `.v` formalization files;
- `_CoqProject` and `Makefile`;
- audit/checksum artifacts;
- JSON manifests;
- reproducibility logs;
- repository snapshot or release archive.

The live review repository is maintained at:

https://github.com/dammroze/collatz-dammroze-coq-review

---

## Coq/Rocq Build Status

The GitHub repository includes a passing GitHub Actions Coq build check.

Local check:

```bash
cd coq
coqc --version
make clean || true
make -j1
```

The workflow builds the Coq/Rocq files using the same Makefile-based process.

---

## Review Request

This record and its companion GitHub repository are open for technical review.

The requested review is specifically about:

1. Coq/Rocq soundness;
2. assumption dependency tracking;
3. hidden or unintended assumptions;
4. alignment between the LaTeX manuscript and the `.v` files;
5. reproducibility of the audit/checksum package;
6. whether the formalized theorem chain follows the manuscript’s required non-ergodic reading order.

Please do **not** report objections based on replacing the stated framework with an ergodic, probabilistic, statistical, or averaging framework.

Please do report:

- hidden assumptions;
- theorem dependency problems;
- unsound Coq/Rocq use;
- mismatch between manuscript and `.v` files;
- incorrect or incomplete formalization of a stated step;
- reproducibility failures;
- broken build commands;
- line-specific logical gaps.

---

## How to Report a Finding

Please open a GitHub Issue with:

- file name;
- theorem/lemma/proposition name;
- line number;
- command run;
- observed output;
- whether the issue concerns manuscript logic, Coq/Rocq formalization, assumptions, build reproducibility, or alignment.

Main review issue:

https://github.com/dammroze/collatz-dammroze-coq-review/issues/3

---

## Reviewer Note

The paper’s central claim must be evaluated inside its own stated non-ergodic deterministic framework.

The intended review question is not:

> “Does this resemble the standard probabilistic or ergodic approach to Collatz?”

The intended review question is:

> “Does the finite deterministic obstruction-exclusion chain stated in the manuscript, and represented in Coq/Rocq, close without hidden assumptions or formalization errors?”

That is the review target.

---

## Keywords

Collatz conjecture; \(3n+1\) map; Coq; Rocq; proof assistant; formal verification; non-ergodic dynamics; deterministic proof; dyadic bands; local obstruction; theorem proving; reproducible research.

Eduardo M. Dammroze
dammroze@gmail.com
Curitiba, Paraná, Brazil. 

This is the third version of the paper.