docs/DATA_SCHEMA.md

Data schema and provenance

The machine-readable data are a small research index, not a measured dataset about human behavior, a trained model, or a validated machine-learning benchmark. There are two JSON Lines files with one object per line. The original images are not included.

claims

Every theorem, proposition, lemma, corollary, and conjecture environment in the supplied manuscript is extracted once, in source order. Definitions, unnumbered calculations, audit prose, and open questions outside those environments are not separate rows. Proofs are copied without rewriting; source macros and cross-references are retained. This deliberate extraction boundary prevents treating the index as the full paper.

Field	Type	Meaning
claim_id	string	Original unique LaTeX label.
title	string	Original environment title.
environment	string	theorem, proposition, lemma, corollary, or conjecture.
component	string	Main area-feedback construction, algebraic alternative, or spectral appendix.
status	string	manuscript_proved or conjecture.
statement_latex	string	Complete environment body, including its label.
proof_latex	string	Immediately associated manuscript proof, or empty for the conjecture.
references_in_statement_or_proof	list of strings	Syntactic ref and eqref targets, not a certified logical dependency graph.
source_file	string	Repository-relative standalone LaTeX path.
proof_audit_file	string	Repository-relative original audit path.
priority_status	string	Priority is not certified at the record level.
verification_limit	string	Meaning and limits of the manuscript proof label.

manuscript_proved means a proof is supplied in the paper. It does not assert acceptance by a journal, a human expert, or a proof assistant. Many constituent ideas are established; the index makes no novelty claim for every row.

worked_examples

Eight curated finite calculations are serialized using exact rational numbers. Matrices and control lists are stored as JSON strings so all dimensions, including zero, share one simple tabular schema. Parse them with json.loads and exact fractions, never by eval.

Field	Type	Meaning
example_id	string	Stable descriptive ID.
dimension	integer	Ambient dimension.
initial_state_json	string	JSON object with x and A, with rational-string entries.
controls_json	string	JSON list of displacement vectors with rational-string entries.
all_controls_legal	boolean	Whether every proposed input is legal.
first_illegal_step	integer	One-based index of the first illegal input; zero if none.
final_legal_prefix_state_json	string	State after the legal prefix only.
final_rank	integer	Rank of the final legal-prefix operator.
final_rho_squared	string	Exact rational squared projection radius.
note	string	Calculation context and interpretation.
source_file	string	Manuscript containing the underlying construction and examples.

Two examples use the same finite controls with different explanatory roles; this is not an independent sampling claim. The illegal rectangle record intentionally stops before its illegal input. It does not apply an illegal update to reach its reported state.

Splits and appropriate use

Each configuration uses the conventional train split solely for simple Hub loading. There is no training/validation/test partition. These examples are deliberately curated, small, and dependent on the defining construction. They should not be used to claim out-of-distribution reasoning performance, unbiased coverage, or statistical superiority.

Natural uses are claim retrieval, proof auditing, exact-example reproduction, comparison with related mathematics, and extension experiments. If used for model training or evaluation, first resolve reuse permission and record this narrow provenance. See the license notice.