index.md

Jacobian documentation

Jacobian provides a native mathematical library and a catalog of published operations. Through MCP, math.find matches operations or reads one exact contract, math.run executes it, and the caller composes the returned values. Native Python callers can use domain functions without a catalog or server.

Choose a path

Use Jacobian

• Discover and invoke operations — the agent workflow: find, inspect, run, and compose one bounded result.

• Tool surface — exact MCP contracts and result/error boundaries.

• Native Python API — supported jacobian.math functions and canonical values.

• Reduce ordered-simplex LPs — chain differences before exact basis-work admission.

Understand the model

• Executable mathematical vocabulary — why operations are semantically atomic and how vocabulary gaps are discovered.
• Product model — caller/server ownership and public contract boundaries.
• Architecture — the responsibility map for library, publication, and delivery; values versus requests; trust and limit ownership; package organization; and a worked operation path.
• Classical matrix groups — which classical families are deferred and what each one would require.

Deploy or contribute

• Backend requirements — maintained Python backends.
• Remote deployment — serve Jacobian over MCP.
• Domain operation library — design rules for public mathematical operations.
• Public operation admission — what belongs in the agent-visible catalog.

Reference

• Mathematical backends — adapter, conversion, and external-process contracts.
• Known backend defects — upstream defects that adapters compensate for, with guard tests.
• Operation references — external-boundary notes that are not captured by the live schema.
• Proper hypergeometric terms — exact factorial-ratio carriers and their support semantics.
• Schemas and value interoperability — canonical ownership, explicit conversions, and serialized trust boundaries.
• Graph deck values — source-bound deletion families versus anonymous graph-card multisets and their canonical form.
• Finite basis matroids — the bounded complete-basis carrier and exact basis-exchange contract.
• Rational Bernstein coordinates — exact polynomial basis conversion on boxes, admission bounds, and evidence.
• Berry--Esseen operation — the i.i.d. finite-sum constant 14/25 with its exact error form.
• Berry--Esseen operation — the i.i.d. finite-sum constant 14/25 with its exact error form.
• Testing strategy — validation ownership and focused test lanes.

The live math.find tool is authoritative for available operations and their current schemas.

Contributing

Use the relevant section of CONTRIBUTING.md for validation, documentation changes, releases, or pull requests.