Reference and source-use standard

Standard

A skeptical reader should be able to identify each source, find the exact passage or artifact used, and see which statement it supports. References should read like the bibliography of a careful mathematical paper. A bare URL, search-result page, unexplained paper list, or citation copied from another bibliography fails this standard.

When in doubt, cite. Extra relevant citations are preferable to an unsupported claim. Repeated references to one source should share one bibliography row while preserving every distinct locator and relevance note.

What needs a citation

Give a claim-level citation for:

• a theorem, lemma, construction, bound, classification, computation, or counterexample taken from earlier work;
• a historical, priority, attribution, novelty, or open-status statement;
• a nonstandard definition, convention, or equivalence imported from a source;
• a proof step that invokes a named result or a substantial method developed elsewhere;
• an external dataset, program, formalization, table, figure, or benchmark;
• a reported failed approach or negative result whose value depends on prior work.

Common mathematical facts may stand without a citation. A complete proof still cites the nontrivial results and constructions it imports. An independently written proof records the sources that supplied its ideas, even when its exposition and details are new.

The citation appears at the point of use and links to the corresponding References row. Placing a work in the bibliography without connecting it to a claim does not establish what the work supports.

Checked Markdown proof files use [@key] at the sentence that invokes a source and define the key with [@key]: <stable URL> in the proof’s references section. The URL matches the DOI, versioned preprint, or other stable identity in the selected record’s structured bibliography. Public HTML turns the marker into a linked [n] and gives the proof a short source map. Generated Markdown uses the same number and link. The full publication-style entry remains in References. An undefined key or a key with no matching structured row is a release failure.

Source selection

Prefer the primary source for a theorem, construction, computation, or priority claim. Add a secondary source when it supplied the exposition or terminology actually followed. Record the version that was read. Include relevant corrections, errata, later revisions, and independent checks.

Trace discovery tools to the underlying work. Search snippets, generated answers, citation indexes, and unsourced database summaries are leads. They do not serve as evidence for a mathematical claim.

A closed-access paper may be cited. When a lawful open version exists, record it beside the stable publisher or DOI link. Access and reuse are separate questions.

Structured reference row

New and materially changed packets use explicit structured reference rows. Each row records:

• citation, a publication-style citation containing the authors or responsible organization, title, publication venue or publisher, and year when those facts exist;
• source_kind, such as journal_article, proceedings_article, book, thesis, preprint, dataset, software, website, forum, or reference_database;
• source_role, chosen from primary, secondary, reference, discovery, independent_check, software, or dataset;
• a stable identity, preferably a DOI, versioned arXiv identifier, ISBN, repository release or commit, dataset release, or archival URL;
• locator, naming the theorem, page, section, equation, table, declaration, file and line range, commit, or dataset slice used;
• relevance, stating in one sentence what the source supports here;
• checked_on, in YYYY-MM-DD form, for mutable web pages, repositories, databases, and living documents;
• open_url when a lawful open copy is available in addition to the canonical landing page;
• use.mode, described under Source use and rights.

A whole-work locator is acceptable only when the whole work is genuinely the cited object, as with a short note or a software release. Literature searches record their date, sources and databases, queries or equivalent formulations, strongest nearby result, and remaining uncertainty.

When a packet or record also carries source_url, that URL matches one structured row. An unrelated bibliography cannot satisfy the source field.

Source use and rights

Citation and reproduction are separate acts.

citation_only identifies and links to a work. original_summary adds TheoremDB’s own account of facts, ideas, methods, or results. These modes do not require the cited work to carry an open license. The summary must be independently written. Publisher abstracts and close paraphrases count as source material.

A resolution proof that draws on earlier work records metadata.authorship_mode as original_derivation, independent_reconstruction, source_adapted, or verbatim. The latter two modes trigger the reused-text checks below.

The following uses place source material inside TheoremDB and require a recorded rights basis:

• short_quotation;
• reproduced_text or adapted_text, including copied or closely adapted proof prose;
• code_used, data_used, or figure_used;
• a copied table, scan, screenshot, diagram, or automatic link-preview image.

For those modes, record the exact material, rights_basis, rights holder, required attribution, the license and its version when licensed, a link to the governing terms or permission, and who checked it on what date. Accepted bases are licensed, public_domain, permission, and fair_use_reviewed. Fair use is a reviewed exception whose facts are recorded. Agents cannot approve it for themselves.

Free access and open access do not by themselves grant reuse rights. Check the license on the particular work and confirm that it covers the material used. A source-code repository without an explicit license remains citation-only. Third-party figures or datasets inside an openly licensed paper receive their own check.

When the rights basis is unclear, retain the citation and replace the source material with an original account. A packet’s license covers the packet author’s contribution. It does not extend to cited or separately marked third-party material.

A replay may require a user-supplied local copy of a cited dataset when redistribution rights are unclear. In that case, the packet stores no source bytes. The artifact names the lawful source, tells the user how to supply the local path, checks a pinned digest before computing, and keeps only independently derived results and hashes. The reference row may remain citation_only or original_summary because TheoremDB is not reproducing the input.

The legal background for this conservative project rule is summarized by the U.S. Copyright Office’s Copyright Basics and Fair Use Index. License-specific checks should use the publisher’s terms or the applicable Creative Commons license. This rule is an editorial and release policy. It is not legal advice.

Public presentation

References contains external scholarship and separately identified reused material. Internal replay paths, hashes, agent traces, and repository provenance stay with their research records unless they identify a publicly citable software or data release.

The renderer deduplicates DOI and canonical URL identities. It preserves every distinct locator, relevance note, source version, and lawful open-copy link. HTML, print, and generated Markdown show the same bibliography and in-text links.

Legacy free-form source metadata may remain visible during migration. It is provisional. New or materially changed work cannot rely on renderer recovery from arbitrary metadata. When normalizing an immutable published object would change its content ID, keep that object frozen and add the reviewed row to dataset.references. The fixed 2026-07 launch corpus may instead use the reviewed web migration registry when changing a fixture would invalidate its publication-authority hash. That registry binds each covered problem to the SHA-256 digest of its canonical parsed fixture, its review file, and its review date. A changed fixture stops the build until its references have been reviewed again and the digest has been updated. The registry applies only to stable source identities already present in the reviewed packet. It records corrected publication citations and source-specific relevance notes where a legacy row needs them, and rejects placeholder explanations. It supplies only missing bibliography fields and leaves every source visible. The validator permits this only for the exact historical slugs named in code and admits no later submissions.

Review

Machine checks cover required fields, URL and DOI shape, duplicate identities, date shape, and the presence of a resolved rights basis for reused material. A reviewer still checks:

• that the cited passage supports the exact sentence;
• that names, title, venue, year, version, and locator are accurate;
• that primary and later relevant sources were included;
• that mathematical conventions and indexing match;
• that copied or adapted material stays within the recorded rights basis.

A packet fails reference review when a substantive external claim lacks a linked source, when a bibliography row cannot identify the work or cited passage, when relevant prior work found during review is omitted, or when reused material lacks a resolved rights basis.