Cards & schema

A card is the unit of meaning in Lemma: a typed, schema-validated specification of one scientific principle. Cards live in cards/<domain>/<id>.json and every card validates against schema/card.v0.1.json.

A real card

This is a shipping principle card from the corpus, verbatim:

{
  "kind": "principle",
  "id": "density-of-states",
  "version": "1.3.0",
  "name": "Electronic density of states",
  "domain": "physics-condensed-matter",
  "principles": [
    "Bloch theorem",
    "k-point Brillouin-zone sampling",
    "spectral function"
  ],
  "formulaTeX": "g(\\varepsilon) = \\sum_{n,\\mathbf{k}} w_{\\mathbf{k}} \\, \\delta(\\varepsilon - \\varepsilon_{n\\mathbf{k}})",
  "conventions": [
    "g(epsilon) >= 0",
    "spin factor 2 absorbed (non-magnetic)"
  ],
  "expectedLimits": [
    "metallic systems: g(epsilon_F) > 0",
    "smooth under k-mesh refinement (Methfessel-Paxton or Gaussian smearing)"
  ],
  "references": [
    "Ashcroft & Mermin, Solid State Physics, ch.8",
    "Methfessel & Paxton 1989"
  ]
}

The fields

A principle card requires kind, id, version, name, principles, formulaTeX, conventions, expectedLimits, and references. domain and validationEnvelopes are optional.

Field	Meaning
`kind`	The structural discriminator: `principle`, `ops`, `hypothesis`, or `unidentified`. The kind is structural, not subject-area.
`id`	Stable, lowercase, hyphen-separated (`^[a-z][a-z0-9-]*$`). Part of the URL once published; never reused.
`version`	Semver. MAJOR for a breaking convention change, MINOR for added limits, PATCH for refs/typos.
`name`	Human-readable name.
`domain`	Subject area, hyphenated — e.g. `physics-condensed-matter`, `chemistry-thermodynamics`, `numerical-methods`. Must match the folder path.
`principles`	The named principles the card rests on.
`formulaTeX`	The canonical equation in LaTeX (KaTeX-renderable).
`conventions`	Sign / normalisation / unit conventions the output must follow.
`expectedLimits`	Asymptotic and boundary cases the output must respect.
`references`	Primary-source citations (not blog posts).
`validationEnvelopes` (optional)	Numerical bounds the engine asserts at runtime — an object of `{ key: [min, max] }` tuples in conventional units (e.g. `{ "gEarth_m_per_s2": [9.79, 9.83] }`).

Licensing

The schema is MIT; the cards corpus is CC-BY 4.0. Anyone can read, fork the schema, and contribute a card — attribution is the only requirement.

One schema, many domains

kind is the structural discriminator — PrincipleCard covers physics, chemistry, biology, climate, mathematics, and engineering because the verification operations are universal. The subject area lives in domain. A card in optics, fluid dynamics, climate, or pure mathematics has the same shape.