Data model and identifiers

The catalogue is a network of typed mathematical records. Groups, algebras, real forms, families, maps, spaces, representations, and constructions have different required fields.

Stable identities

Identifiers use a type prefix and immutable slug, for example group:su-3 or map:su-2-to-su-3-principal. Canonical routes do not depend on the collection through which a visitor arrived. Exceptional aliases resolve to that identity.

Required evidence

Every definition has source evidence. Every property and explanatory paragraph has source locators or an explicit derivation. Claim identifiers combine the record ID and an assertion key. Definition, property, paragraph, and relationship namespaces are checked for collisions.

Typed relationships

A group’s Lie-algebra link resolves to a real algebra. Real-form complexification links resolve to complex algebras, and integrating-group links to Lie groups. A group homomorphism has group endpoints, an image, a kernel, and explicit injectivity/surjectivity data. A quotient space points to its acting group, subgroup, and defining map where supplied.

Exact values and serialization

Finite orders are decimal strings so large integers survive JSON readers without precision loss. Mathematical workbench outputs preserve exact normalized rationals within their declared bounds. A dimension or order in a structured payload must agree with its sourced display assertion.

Download the entity schema, source schema, and catalogue snapshot. JSON Schema describes the structural contract; cross-record reference and mathematical consistency checks are enforced by the repository validator.

Versioning

Physical setups are separately versioned input records. The setup schema fixes spacetime, gauge group, field species, flavor multiplicities, a monomial, and its equivalence convention. The setup reference explains why these records are distinct from group identities and from cached calculation results.

Schema, dataset, application, and algorithm versions are separate. A UI change need not claim a mathematical-engine change. Read reproducibility for exported results and review fingerprints.