Audit a bounded mathematical slice for missing or unusable Jacobian capabilities, beyond a single-operation review.
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Diagnose malformed calls, retries, and unusable results after an agent selects an MCP tool.
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Audit whether an agent that has chosen a tool can form a valid request, recover from a failure, and use the returned value. This is a public-contract audit, not a call-count target and not a test of model willingness to use a tool.
Record the tool, revision, client, task or trace, and public inputs inspected. Keep these questions separate:
Do not call a successful Python fallback evidence that a tool contract is easy to use. Do not call a single malformed request a product defect without checking what the public contract exposed beforehand.
For each relevant operation, inspect the generated MCP input and output schemas, tool description, discovery/inspection result, operation examples, and error messages. Trace every non-obvious requirement to its owner:
| Contract element | Check |
|---|---|
| Input expression | Required values, units, encodings, ordering, and bounds are visible before the call. |
| Schema projection | Constraints representable in JSON Schema appear there with useful field descriptions and examples. |
| Semantic validation | Rules enforced only by a model validator have an explicit description and minimal valid example. |
| Recovery | Errors identify the field and state the smallest concrete correction. |
| Result use | Result shape, exactness, limits, and reconstruction information let the caller continue without guessing. |
Pydantic does not infer JSON-Schema descriptions or examples from custom model
validators. Add Field(description=..., examples=...) or appropriate
json_schema_extra when a semantic invariant cannot be encoded as a standard
JSON-Schema constraint. Keep canonical output rules when they support stable
composition; improve the input guidance before weakening the invariant.
Capture the exact operation ID, first payload, typed result or error, retry, and final use of the value. Classify the first failure narrowly:
Compare a direct known-valid execution separately from the trace. A direct pass proves the operation works; it does not erase caller friction. A trace with no call is out of scope unless availability or adoption is under review.
For comparable runs, freeze task, image, server revision, model, client, budget, and MCP configuration. Report final verifier outcome separately from:
Use repeated tasks or attempts before claiming a stable rate. A successful answer after retries is evidence of recoverability, not evidence of a frictionless interface.
Prefer, in order: clearer field metadata and examples; actionable errors; schema-level constraints; a narrowly scoped adapter or helper. Normalize input only when it preserves the documented mathematical meaning and does not hide ambiguity, duplicate terms, or caller mistakes. Preserve bounded operation semantics and return values directly.
Report confirmed behavior, the exact public evidence, the affected stage, proportionate repair, and what remains untested. State when the evidence only supports an agent slip rather than a tool-design finding.
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Audit a bounded mathematical slice for missing or unusable Jacobian capabilities, beyond a single-operation review.
中文简介正在准备中。当前显示原文说明。
Design or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition.
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Extract reusable Jacobian capabilities from a mathematical solution corpus, rather than one agent trajectory.
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Investigate MCP tool availability, discovery, and selection, including controlled adoption evaluations.
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Author, package, validate, or run mathematical evaluations as Jacobian Harbor datasets.
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Use Jacobian's MCP operations for nontrivial mathematical computation, finite search, structural analysis, formal checking, probability, or optimization.
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