Discover installed mathematical outcomes or inspect one exact capability contract.

Use this first when a task may benefit from exact computation, structural analysis, transformation, bounded search, counterexample generation, formal-environment inspection, or independent checking. You do not need to know a capability ID.

Discovery:

• Pass query to rank compact installed outcomes by mathematical intent.

• Optionally filter with domain and mode; limit is between 1 and 20 and defaults to 5.

• Omit all arguments to browse a compact installed catalog.

• When next_cursor is present, pass it back with the same filters and limit to continue without loading the complete catalog.

• Ranking is deterministic retrieval over published IDs, titles, descriptions, and tags. Match fields and terms are returned; results are candidates, not recommendations.

• Once a domain-owned match fits the required outcome, inspect only the strongest one or two candidates. Search again when none fits. Invoke a producer before looking for its checker, then follow the checker, certificate, and verification fields in the producer result instead of guessing a generic verifier.

• Compose capabilities as the investigation requires; Jacobian does not prescribe a mathematical workflow.

Exact inspection:

• Pass capability_id for the small default SUMMARY projection when judging fit.

• Request view="CONTRACT" once a capability fits and before invoking it. CONTRACT adds the validation-equivalent input schema, runtime identity, related operations, and validated invocation examples.

• Add view="FULL" only when complete output schema, provider configuration, licensing, or audit metadata is needed.

• Every exact response states the scope rule: repeated bounded invocations remain finite evidence and do not establish an all-orders or all-parameters conclusion.

Examples:

• {"query":"find a counterexample to associativity","domain":"universal_algebra","mode":"EXPLORE","limit":5}

• {"query":"verify a polynomial identity","mode":"VERIFY","limit":5}

• {"capability_id":"polynomial.compute.gcd"}

• {"capability_id":"polynomial.compute.gcd","view":"CONTRACT"}

• {"capability_id":"polynomial.compute.gcd","view":"FULL"}

Execute one installed mathematical capability after inspecting its exact descriptor.

Call capability.describe first; do not guess payload fields or aliases. Use EXPLORE for proposed, heuristic, or computed evidence and VERIFY only for an installed checker-backed contract. After invocation, inspect execution, scope, completeness, relationships, open obligations, assurance, diagnostics, and artifact URIs independently. COMPLETED does not by itself establish a mathematical conclusion. One invocation covers only its exact supplied input or claim. Repeating finite or bounded instances does not widen that scope to an all-orders or all-parameters claim. The default view="STANDARD" keeps the canonical result in MCP structured content while bounding large model-visible output fields. Its mcp_projection reports exact logical and model-visible byte counts, digests every omission, and points to the durable full result episode. Use view="SUMMARY" only when output fields are not needed, or view="FULL" when the complete result must also appear in text. Synchronous SAT and SMT requests are capped at 150 seconds so structured TIMEOUT or CANCELLED diagnostics can arrive before remote transport deadlines. Partition larger searches; retrying a cancelled call starts a new computation.

Examples:

• {"capability_id":"integer.compute.gcd","mode":"EXPLORE","payload":{"left":"84","right":"30"}}

• {"capability_id":"integer.compute.gcd","mode":"EXPLORE","view":"SUMMARY","payload":{"left":"84","right":"30"}}

• {"capability_id":"polynomial.identity.verify","mode":"VERIFY","payload":{"variables":["x"],"left":{"terms":[]},"right":{"terms":[]}}}

These demonstrate valid envelopes, not a required sequence or research strategy.

Direct tool; do not call capability.describe. Create a durable epistemic workspace with one canonical problem, a main branch, and an immutable initial revision. Workspace content is agent-authored and UNVERIFIED.

Direct tool. Do not call capability.describe. Arguments are flat: send base_revision (never revision_id) and top-level findings, attempts, marks, scratch, or focus (never a batch wrapper). Every draft uses client_ref, never ref. Append at an exact base revision. Finding fields are client_ref, kind, title, body; optional links are dependency_refs and assumption_refs (never depends_on_refs). Attempt fields are client_ref, target_ref, method, outcome, summary. Margin marks append an explicit ACTIVE, CLOSED, RETRACTED, SUPERSEDED, or ARCHIVED state; only SUPERSEDED carries superseded_by_ref. References may use a client_ref from the same batch. PROBLEM is reserved for workspace.open. A RETRACTED or SUPERSEDED card must receive an ACTIVE mark before CLOSED or ARCHIVED. Set focus with active_ref/pinned_refs, clear it with clear=true, or omit it; focus references finding cards, never attempts, marks, or scratch. Never send verification/assertion/stale fields: all workspace assertions remain AGENT_RECORDED and UNVERIFIED. Canonical batch example: findings=[{"client_ref":"C1","kind":"CLAIM","title":"...","body":"..."}], attempts=[{"client_ref":"T1","target_ref":"C1","method":"...","outcome":"COMPLETED","summary":"..."}], focus={"active_ref":"C1","pinned_refs":["C1"]}.

Direct tool; do not call capability.describe. Read a compact deterministic RESUME, FRONTIER, ATTEMPTS, CONTEXT, or STALE view from agent-authored workspace state. CONTEXT requires target_card_id and follows only explicit dependency/assumption links. Derived staleness is a paper-like warning, not a mathematical conclusion. Retrieval preserves UNVERIFIED status.