The Corrected Primon-Gas Dictionary: Zeta Partition Functions and the Discipline of Arithmetic Interpretations

In the paper's words

The primon gas has connected quantum statistical mechanics with multiplicative number theory since the early 1990s and remains in active use. This paper consolidates the correspondence into a single audited reference: a corrected, verified dictionary; a five-level ladder separating mathematical isomorphism from physical realization claims; and a negative list of what the correspondence does not license. The premises end where a physical temperature would be identified at a p-adic place, and no such identification is asserted.

The abstract, verbatim; every line below is quoted from the text.

What it claims

They stratify into five levels.

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. The draft's "Theorem 2" bundled the specific-heat signature with the small-spacing exclusion.

   from 3. The Correction Ledger

2. A claim about a laboratory system, held to the same protocol discipline that the finite-distinction reading of quantum mechanics applies to its own claims.

   from 4. The Five-Level Interpretive Ladder

3. Second, a scope statement that decides, before an experiment, what a realization claim may consist of: by the ladder's rules, a claim that a device realizes the arithmetic partition function must state the spectrum, the counting rule, the null model, and the test in advance — an engineering-relevant discipline that separates a physical signature from a simulation.

   from 5. What the Correspondence Licenses, and What It Does Not

4. The completeness of the correction ledger is an audit-level statement, not a proof: a twelfth error found by an independent reader would be a corrigendum, not a collapse, and that status is asserted rather than concealed.

   from 7. Premise Boundaries

What would falsify it

1. A falsifiable distributional claim, requiring a pre-registered null.

   from 4. The Five-Level Interpretive Ladder

2. Second, L3 is the only admissible bridge : a physical claim must be stated as a distributional prediction with a pre-registered null.

   from 4. The Five-Level Interpretive Ladder

3. The rules are methodological discipline, not a discovery: the L2-to-L4 inference they forbid is an inference that informal drafts of this very correspondence made, so the rules are non-vacuous as self-correction, and as external guidance they are a pre-commitment — "admissible inference" is defined by the protocol above, and the ladder's falsifiability is precisely that an exhibited admissible L2-to-L4 inference would break its central rule.

   from 4. The Five-Level Interpretive Ladder

Where the claim stops

1. This paper does not claim the correspondence as new.

   from 1. Introduction

2. Its contribution is a consolidation with discipline: a corrected, audited dictionary in which every entry is stated exactly and every formula is verified by deposited deterministic computations; a five-level ladder that separates what the correspondence is (an exact mathematical isomorphism) from what it is not (a physical realization claim); a ledger of corrections to errors that have circulated in informal drafts of the dictionary; and a negative list stating what the correspondence does not imply.

   from 1. Introduction

3. They do not define the statistics and they do not define the leading thermodynamics.

   from 2. The Correspondence

Where to read

1. 1. Introduction313 words · 1 min
2. 2. The Correspondence646 words · 3 min
3. 3. The Correction Ledger422 words · 2 min
4. 4. The Five-Level Interpretive Ladder398 words · 2 min
5. 5. What the Correspondence Licenses, and What It Does Not259 words · 1 min
6. 6. Verification678 words · 3 min
7. 7. Premise Boundaries101 words · 1 min
8. 8. Term Crosswalk109 words · 1 min
9. Changelog7 words · 1 min