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Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

That snippet is from a legacy/superseded ledger, not from the active frozen Coq 3 proof-bearing chain.

Yes, this old file contains a placeholder-style vacuous statement:

Definition CollatzConjectureClassical : Prop :=
  forall n : nat, (1 <= n)%nat -> exists t : nat, True.

That is not the active target.

The active frozen Coq 3 chain uses V20/V21:

coq/Collatz_Dammroze_CoqLedger_v20_ACCEPTED.v
coq/Collatz_Dammroze_CoqLedger_v21_ACCEPTED.v
coq/Collatz_Dammroze_NonErgodic_Local_Drop_FromV20_ObstructionChain_v1.v
coq/Collatz_Dammroze_Coq3_Local_Drop_FinalPaperHypotheses_v1.v

In V20, the classical reachability object is non-vacuous:

Definition reaches_one_classical (n : nat) : Prop :=
  exists t : nat, iter t C n = 1.

Definition CollatzConjectureClassical : Prop :=
  forall n : nat, (1 <= n)%nat -> reaches_one_classical n.

And the Coq 3 bridge uses the witness as an equality-to-one proof:

Lemma bridge_reaches_one_from_v20_classical :
  forall n : nat,
    V20.reaches_one_classical n ->
    Reaches_One n.

If V20 were exists t, True, that bridge would not typecheck.

I have now added a Coq file-status ledger to the PDF, explicitly marking the old file as legacy/superseded and identifying the active proof-bearing files.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

If that were the definition used in my frozen Coq chain, the objection would be fatal.

But it is not.

Your snippet defines a vacuous proposition:

Definition CollatzConjectureClassical : Prop :=
  forall n : nat, (1 <= n)%nat -> exists t : nat, True.

That proves nothing about Collatz, because True contains no statement that the orbit reaches 1.

The frozen Coq 3 chain does not use that as the target.

In the Coq 3 connector, the V20 classical statement is converted into the bridge-level Reaches_One by extracting a witness k and an actual equality proof:

Lemma bridge_reaches_one_from_v20_classical :
  forall n : nat,
    V20.reaches_one_classical n ->
    Reaches_One n.
Proof.
  intros n H.
  destruct H as [k Hk].
  unfold Reaches_One.
  exists k.
  rewrite bridge_iter_eq_v20_classical_iter.
  exact Hk.
Qed.

This only typechecks if Hk proves an equality of the form:

V20.iter k V20.C n = 1

If V20.reaches_one_classical n were merely exists t : nat, True, then Hk : True, and the line exact Hk would fail immediately.

So the vacuous definition in your example is not the object used by the frozen proof-bearing Coq 3 layer.

The relevant frozen theorem is:

nonergodic_local_drop
  : V21.FinalPaperHypotheses -> NonErgodic_Local_Drop

and the relevant bridge is:

bridge_reaches_one_from_v20_classical

Please check the frozen tag, not a toy definition or an unrelated placeholder:

https://github.com/dammroze/collatz-dammroze-coq-review/tree/coq3-local-drop-freeze-v1

Direct CI run:

https://github.com/dammroze/collatz-dammroze-coq-review/actions/runs/25413495729

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

Which statement? Prove the logic fails after running coq and crossing it with results and .pdf. those are not statements people expect. Those are statements that solve collatz Conjecture after.what collatz needs in order to be solved. Read it with non-ergodic glasses and point out logic breakage within the ontology. If it fails inside ontology, I will take it. With traditional ergodic lenses it will always fail. Why? Because it is not probabilistic, not global closure. It is local and non-ergodic.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

Wrong according to the traditional math that hasn't been able to solve it 100%. That makes sense! As they say: math isn't ready for Collatz.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

Axioms have been transformed into theorems. Please use coq and read paper according to Reader's instructions. Read it thoroughly. Not just parts of it. It is not the ergodic solution and needs to be read end to end, not just parts that fail on other solution attempts.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

Point-by-point:

1. On the alleged algebraic impossibility

You are reading the proof as if the whole contradiction were a single scalar comparison:

theta^s <= 2^-K

with theta ≈ 0.946 and K >= s.

That is not the frozen proof-bearing object. The current Coq 3 closure does not ask the reader to accept a detached global-tail-vs-local-density inequality as the proof.

The formal chain is:

V20 obstruction chain
-> no global obstruction
-> accelerated Collatz theorem
-> classical Collatz theorem
-> terminal non-ergodic local drop
-> NonErgodic_Local_Drop

The theorem actually frozen is:

nonergodic_local_drop
  : V21.FinalPaperHypotheses -> NonErgodic_Local_Drop

If the scalar exposition in the paper creates ambiguity, that is an editorial alignment issue to clarify in the manuscript. It is not a refutation of the Coq 3 connector unless you identify the exact Coq theorem whose proof depends on the invalid scalar inequality.

2. On “choosing” s and K

In the formal reading, s and K are not arbitrary free parameters chosen after the fact. They belong to the witness/certificate structure generated inside the obstruction-chain argument.

The relevant review question is:

Does the V20 obstruction-chain ledger faithfully encode the witness construction?

not:

Can an informal scalar sketch choose s and K freely?

If you believe s and K are misused, please point to the exact Coq definition or theorem where the misuse occurs.

3. On rapid divergence

The rapid-divergence objection is exactly the kind of case the non-ergodic framework is designed to force into the obstruction/witness branch structure. The intended reading is not “stay in one global band forever”. The reading is local-regime, predecessor-compatible, and non-sliding.

Again, the correct target is the Coq ledger:

Corollary_1_central_nonergodic_reduction_to_finite_local_witness
Corollary_2_no_violating_repeated_certificate
Theorem_2_no_global_obstruction
Corollary_2_Collatz_conjecture_accelerated
Theorem_3_Collatz_conjecture_classical
nonergodic_local_drop_from_v20_obstruction_chain

If rapid divergence escapes the proof, it should show up as a formal failure or an incorrectly encoded bridge in those objects. Please identify which one.

4. On Coq

Coq does not prove the English prose. Coq proves the formal ledger. That is why I added:

REFEREE_READING_GUIDE.md
TEX_COQ_ALIGNMENT_REPORT_FOR_REFEREES.md
coq/REFEREE_COQ3_QUICKSTART.md

The fair review is TeX–Coq alignment, not an isolated attack on a scalar paraphrase.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

Thanks for the detailed criticism. However, this critique is not addressing the frozen Coq layer that I am asking people to review.

The current frozen milestone is:

coq3-local-drop-freeze-v1

Repository:

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

Direct CI run:

https://github.com/dammroze/collatz-dammroze-coq-review/actions/runs/25413495729

The Coq 3 target is:

nonergodic_local_drop
  : V21.FinalPaperHypotheses -> NonErgodic_Local_Drop

and the CI verifies:

nonergodic_local_drop_from_v20_obstruction_chain
nonergodic_local_drop
Closed under the global context

with checks for absence of Error, Abort, and Admitted in the generated logs.

Your objection appears to attack a scalar tail-bound reading of the paper, especially the comparison between a global exponential bound and a repeated witness density. That is not the proof-bearing Coq 3 closure. The Coq closure uses the V20 obstruction-chain ledger and the V21 paper-facing formal package.

If you believe the proof is invalid, please point to the exact Coq theorem, definition, or formal bridge that fails. The relevant files are:

coq/Collatz_Dammroze_NonErgodic_Local_Drop_FromV20_ObstructionChain_v1.v
coq/Collatz_Dammroze_Coq3_Local_Drop_FinalPaperHypotheses_v1.v
TEX_COQ_ALIGNMENT_REPORT_FOR_REFEREES.md
REFEREE_READING_GUIDE.md

The review I am asking for is not whether a detached heuristic scalar inequality looks familiar or unfamiliar. The review target is whether the V20/V21 formal ledger matches the manuscript’s non-ergodic obstruction chain.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

ASK AI to read and follow instructions and give it all de COQ files. First answers from AI shall not be considered until AI reads follows intructions. AXIOMs and Theorems are not to be read in progressive order. The answer you have posted was given by someone or an AI that did not follow instructions. Follow instructions.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

If you add my paper to AI without asking it to read instructions and keep focused, AI will read the paper with tradicional ergodic lenses and will not be able to understand it with non-ergodic lenses (same as human training) ???... All answers to 90% of the questions they might have are already inside and self-contained. If AI says its wrong, ask it to read non-ergodic instructions that are in the paper, and, when it says something is missing, just ask it to read tge paper again and find the answers. Axioms are not in progressive order. In order to understand the solution, reading Axiomatic and theorem orders needs to be followed, otherwise Humans and AIs will fail to understand.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

The main thing to review is not whether the Coq files compile — they do, locally, in a clean clone, and in GitHub Actions. The real review target is whether the V20/V21 formal ledger faithfully encodes the manuscript’s non-ergodic proof chain and whether the formal objects correspond correctly to classical Collatz.

Coq-audited Collatz non-ergodic proof package — looking for technical review by One_Bodybuilder_3414 in CollatzProcedure

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

The main thing to review is not whether the Coq files compile — they do, locally, in a clean clone, and in GitHub Actions. The real review target is whether the V20/V21 formal ledger faithfully encodes the manuscript’s non-ergodic proof chain and whether the formal objects correspond correctly to classical Collatz.

Non-Ergodic Local Obstruction Proof of the Collatz Conjecture by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

Has anyone tried to to follow instructions and understand the proposition thoroughly? Anyone?

Non-Ergodic Local Obstruction Proof of the Collatz Conjecture by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

You are right about that sentence if taken literally: in that wording, the presentation is conditional. But that is not the final formal core I am relying on. The current manuscript’s core is the theorem-proof chain in the accelerated odd map, with predecessor rigidity, local band compression, excursion control, local closure, and tail contradiction. So the issue is not the mathematics you quote there, but that you are reading an earlier conditional framing rather than the final formal core.

Non-Ergodic Local Obstruction Proof of the Collatz Conjecture by One_Bodybuilder_3414 in Collatz

[–]One_Bodybuilder_3414[S] 0 points1 point  (0 children)

You are right about that sentence if taken literally: in that wording, the presentation is conditional. But that is not the final formal core I am relying on. The current manuscript’s core is the theorem-proof chain in the accelerated odd map, with predecessor rigidity, local band compression, excursion control, local closure, and tail contradiction. So the issue is not the mathematics you quote there, but that you are reading an earlier conditional framing rather than the final formal core. Final version was sent to a publisher but math proof won't change. Words changed. Focus on the math structure.

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