- Status: Active direction
- Planning model: Rolling goals, pursued in parallel
- Related records: Product model and architecture
Jacobian is building a broad toolbox of composable mathematical capabilities for AI agents. The project does not follow a linear sequence in which search, claim transformation, retrieval, or formal proof must mature before another area can be explored. Useful capabilities may be added, evaluated, revised, or removed independently.
Current reference documents and the installed catalog describe supported behavior. They do not prescribe research order, block experimental capabilities, or promise that an idea will become a stable interface.
Expose useful operations from maintained proof assistants, computer algebra systems, solvers, optimization systems, databases, and domain libraries. Prefer capabilities with one clear, agent-visible mathematical outcome. Experimental adapters may change without compatibility guarantees.
Help agents find relevant capabilities without loading every schema into their initial context. Improve descriptors, examples, catalog search, ranking, and value and artifact relationships from observed agent behavior. Keep research strategy with the agent rather than encoding one preferred proof workflow in the runtime.
Add independent checkers for exact claims and evidence where they close real trust gaps. Bind verification to the exact claim, semantics, candidate, scope, certificate format, and checker identity. Computation, search, retrieval, and model judgment never verify themselves.
Use held-out datasets, hidden oracles, real transcripts, and paired ablations to measure complete capability portfolios as well as individual operations. Track correctness, false certification, runtime, tokens, tool calls, and parameter errors. Use the evidence to improve discovery, defaults, consolidation, and retirement—not to gate experimentation.
Keep important intermediate objects, failed attempts, transformations, relationships, and proof obligations inspectable. Retain them durably when identity, replay, resumability, evidence binding, or size requires it. Optional workflows may coordinate several operations, but must not erase their evidence or independent verification boundaries.
Expose mathematical breadth through namespaced capabilities behind
math.find and math.run, not through a growing set of
top-level MCP tools. Remove compatibility wrappers and duplicate interfaces
when they no longer serve a supported contract. Reuse maintained mathematical
backends rather than accumulating custom infrastructure.
Work may advance on any goal when a dataset, transcript, backend, or trust gap provides a useful test. Concrete implementation work belongs in focused GitHub issues with observable success criteria. Current reference documents record supported contracts; benchmarks and evaluation reports record evidence.
The direction is working when better agents can discover and compose the same portfolio more effectively, exact conclusions remain independently checkable, and adding a mathematical backend does not require redesigning the runtime or MCP surface.