A universal, atomic library of mathematics and tools for agents to compose them.
Skill Claude CodeCodex
Audit one bounded Jacobian mathematical slice for missing or unusable executable vocabulary using source demand, catalog composition, contract evidence, and maintained-backend feasibility. Use for proactive gap audits that are broader than one operation but narrower than a repository-wide inventory; do not use for…
Skill Claude CodeCodex
Audit existing MCP tools for execution friction after an agent has reached the tool. Use when reviewing public JSON Schemas, Pydantic validation, operation examples, error recovery, completed agent traces, or benchmark runs to explain malformed calls, retries, or unusable results. Do not use to measure whether agents…
Skill Claude CodeCodex
Audit new or existing Jacobian mathematical operations for public-domain mismatches, hidden work expansion, evidence-backed scale or backend improvements, lossy exact results, source-unbound conclusions, and producer-consumer incompatibility. Use for operation-contract reviews, mathematical performance investigations…
Skill Claude CodeCodex
Decompose a bounded corpus of mathematical proofs, formalizations, scripts, and certificates into recurring solution techniques and the smallest reusable Jacobian postconditions. Use for repository- or corpus-level “what can Jacobian learn?” audits; do not use for one operation contract or one agent trajectory.
Skill Claude CodeCodex
Diagnose whether agents can see, discover, select, and correctly execute MCP tools without conflating those stages. Use when investigating why agents did or did not use an MCP tool, evaluating MCP server instructions or tool descriptions, testing natural-language discovery, or designing a frozen control/treatment…
Skill Claude CodeCodex
Build, validate, and run Jacobian evaluations packaged as Harbor datasets. Use when authoring or changing Harbor tasks, independent verifiers, Oracle jobs, workflow fixtures, task digests, or evaluation handoffs.
Skill Claude CodeCodex
Use when solving nontrivial mathematical problems or investigating conjectures that may benefit from Jacobian's local library of typed operations for exact computation, finite search, structural analysis, formal reasoning, probability, or optimization.
Skill Claude CodeCodex
Review completed or paused mathematical agent transcripts, visible reasoning, code, searches, tool calls, corrections, and final claims to extract evidence-backed lessons for Jacobian operations, discovery, contracts, skills, evaluations, and documentation. Use for mathematical workflow retrospectives and "what should…
Skill Claude CodeCodex
Run source-grounded Jacobian reliability evaluations using recently resolved conjectures as held-out probes. Use for source selection and deduplication, exact input-bound oracles, current-main math.find/math.run contract audits, frozen control/treatment comparisons, observable trajectory scoring, failure attribution…
Skill Claude CodeCodex
Design, audit, and repair fail-closed mathematical verifiers and evaluation contracts, including public schemas, frozen-input binding, task-specific witnesses, diagnostic scoring, adversarial fixtures, and Oracle validation. Use when a verifier can crash, accept malformed claims, reject equivalent witnesses, leak…