formuleid

Formuleid is a proposed metadata construct and identifier system for mathematical formulas within digital documents and knowledge bases. It designates a specific symbolic expression, enabling unambiguous reference, version tracking, and provenance across documents, datasets, and proof archives. The term combines "formula" with "identifier" and is used in discussions of mathematical knowledge management and literate programming.

The concept emerged in the 2010s in the context of digital libraries and computer-assisted proof systems as a way to address formula-level referential integrity, especially when formulas are extracted, modified, or reorganized. A formuleid typically encodes a canonical form of the formula, a namespace, and a version tag, often as a compact alphanumeric string. Example formats vary, but common designs include a prefix identifying the source and a hash of the canonical representation, plus a version suffix, e.g., FML-abc123-v2.

Use cases include cross-document citation of formulas, dependency tracking in formal proofs, and reproducible research where calculating results depends on particular formulae. In proof assistants, formuleids can support indexing, search, and automatic recomputation when a formula is transformed. Challenges include achieving a robust canonicalization across algebraic domains, handling equivalent but rewritten expressions, and agreeing on standards among diverse communities. Some projects pursue formal ontologies or schemas to describe formula metadata (source, context, assumptions, dependencies) to improve interoperability.

Overall, formuleids aim to strengthen the traceability and reusability of mathematical content in digital ecosystems, supporting clearer provenance, improved collaboration, and more reproducible mathematical work.