Datasets:

PureOne
/

VELORYN-Boundary-Kernel-Entropy

# Reading VELORYN accurately

This guide identifies the research's authoritative files and the limits that should accompany summaries and citations. It adds no mathematical theorem and does not replace the manuscript.

1. Read `STATUS.json` and `docs/CLAIM_LEDGER.md` for the scope of each claim.
2. Read `manuscript/VELORYN_Manuscript.tex` or the PDF for definitions, hypotheses, and proofs. Sections 1–3 contain the factor model and boundary-kernel theorem; Section 4 covers Shannon order and mixtures; Sections 5–7 cover arithmetic geometry, replicas, and certification.
3. Use `RESEARCH_METADATA.json` and `data/research_index.jsonl` as finding aids. Their summaries are secondary to the complete statements.
4. Read `docs/PRIOR_ART.md` before describing novelty. The combination is a proposed contribution, not established world-first priority.
5. Distinguish original recorded evidence under `evidence/` from the packaging audit under `evidence/hf_release/`.

## Claims that need their hypotheses

The non-Shannon rate enclosure requires a finite labelled Markov source, a full-support initial law, a first-block factor bound uniform over the second block length, and subexponential factor growth. The error is order-independent; this does not provide a numerical compiler for arbitrary real orders.

The Shannon interval implementation requires an exactly stationary initial law. Statistical coverage assumes independent exact draws as stated in the research README; a deterministic seed is a reproducibility feature, not a proof of coverage. Shannon continuity is confined to the stated irreducible finite-source factor model. Reducible stationary mixtures have a different selection rule.

The full variable-clock output is `(total_clock, numerator)`. Distinct clocks must not be merged because numerators coincide. Entropy per branch is not automatically entropy per contraction time or a geometric dimension formula.

## Implementation versus theory

Executable replicas support fixed integer orders `q >= 2`, the listed arithmetic fields, and finite sources with positive integer clocks. Generic noninteger kernels, endpoint optimizers, a general algebraic-field parser, and a generic Jordan-matrix compiler are not implemented. Fixed-geometry polynomial complexity is not a uniform claim in all input parameters.

## Status when citing

- The fair-Salem equality `h_1 = log(beta)` is not proved.
- Written proofs are supplied and internally audited; external peer review and proof-assistant verification are absent.
- Finite test counts verify stated computational cases, not all theorem hypotheses or conclusions.
- World-first priority and major-breakthrough status are not established.
- Release completion percentages describe a deliverable checklist, not mathematical certainty or problem completion.
- The research is not a trained model, an AI performance benchmark, or evidence of improved neural-network performance.
- No outbound license has been selected. Inspect `RIGHTS_AND_ATTRIBUTION.md` before reuse.

Use `CITATION.cff` or `CITATION.bib`; retain the exact supplied author line. Do not invent a DOI, publication URL, acceptance, or affiliation.

	# Reading VELORYN accurately

	This guide identifies the research's authoritative files and the limits that should accompany summaries and citations. It adds no mathematical theorem and does not replace the manuscript.

	1. Read `STATUS.json` and `docs/CLAIM_LEDGER.md` for the scope of each claim.
	2. Read `manuscript/VELORYN_Manuscript.tex` or the PDF for definitions, hypotheses, and proofs. Sections 1–3 contain the factor model and boundary-kernel theorem; Section 4 covers Shannon order and mixtures; Sections 5–7 cover arithmetic geometry, replicas, and certification.
	3. Use `RESEARCH_METADATA.json` and `data/research_index.jsonl` as finding aids. Their summaries are secondary to the complete statements.
	4. Read `docs/PRIOR_ART.md` before describing novelty. The combination is a proposed contribution, not established world-first priority.
	5. Distinguish original recorded evidence under `evidence/` from the packaging audit under `evidence/hf_release/`.

	## Claims that need their hypotheses

	The non-Shannon rate enclosure requires a finite labelled Markov source, a full-support initial law, a first-block factor bound uniform over the second block length, and subexponential factor growth. The error is order-independent; this does not provide a numerical compiler for arbitrary real orders.

	The Shannon interval implementation requires an exactly stationary initial law. Statistical coverage assumes independent exact draws as stated in the research README; a deterministic seed is a reproducibility feature, not a proof of coverage. Shannon continuity is confined to the stated irreducible finite-source factor model. Reducible stationary mixtures have a different selection rule.

	The full variable-clock output is `(total_clock, numerator)`. Distinct clocks must not be merged because numerators coincide. Entropy per branch is not automatically entropy per contraction time or a geometric dimension formula.

	## Implementation versus theory

	Executable replicas support fixed integer orders `q >= 2`, the listed arithmetic fields, and finite sources with positive integer clocks. Generic noninteger kernels, endpoint optimizers, a general algebraic-field parser, and a generic Jordan-matrix compiler are not implemented. Fixed-geometry polynomial complexity is not a uniform claim in all input parameters.

	## Status when citing

	- The fair-Salem equality `h_1 = log(beta)` is not proved.
	- Written proofs are supplied and internally audited; external peer review and proof-assistant verification are absent.
	- Finite test counts verify stated computational cases, not all theorem hypotheses or conclusions.
	- World-first priority and major-breakthrough status are not established.
	- Release completion percentages describe a deliverable checklist, not mathematical certainty or problem completion.
	- The research is not a trained model, an AI performance benchmark, or evidence of improved neural-network performance.
	- No outbound license has been selected. Inspect `RIGHTS_AND_ATTRIBUTION.md` before reuse.

	Use `CITATION.cff` or `CITATION.bib`; retain the exact supplied author line. Do not invent a DOI, publication URL, acceptance, or affiliation.