feat(skills): add public operation contract audit

Author: morluto

.agents/skills/audit-public-operation-contracts/SKILL.md

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+---
+name: audit-public-operation-contracts
+description: Audit new or materially changed Jacobian mathematical operations for public-domain mismatches, hidden work expansion, lossy exact results, source-unbound conclusions, and producer-consumer incompatibility. Use for operation-contract reviews and adjacent-domain searches; do not use for general repository, CI, MCP-discovery, or security audits.
+---
+
+# Audit Public Operation Contracts
+
+Audit whether a Jacobian operation is a bounded, truthful, composable
+mathematical instrument. Treat the request model, native value, kernel or
+backend adapter, result model, declaration, examples, and downstream consumers
+as one contract.
+
+Before auditing, read the current relevant sections of:
+
+- `AGENTS.md`;
+- `docs/reference/domain-operation-library.md`;
+- `docs/reference/testing-strategy.md`; and
+- `docs/reference/mathematical-backends.md` when a backend is involved.
+
+Use those files as the policy authority. Do not copy their general rules into
+the report.
+
+## Establish the audit boundary
+
+Record the revision, operation IDs, owner domain, changed paths, backend and
+version when relevant, and whether the request is audit-only or also authorizes
+implementation. Local investigation never authorizes commits, pushes, issue or
+PR changes, comments, or thread resolution.
+
+Map each operation end to end:
+
+```text
+public request model
+  -> canonical domain value and admission
+  -> native kernel or private backend adapter
+  -> exact result conversion and invariant validation
+  -> canonical result and downstream consumers
+```
+
+Inspect generated schema, declaration text, examples, and MCP-visible errors
+when the public projection is in scope. Do not infer the public contract from
+the implementation alone.
+
+## Complete the contract preflight
+
+Fill the review artifact from `domain-operation-library.md`. For every produced
+mathematical value, additionally answer:
+
+- What owner-defined canonical type is returned?
+- Which downstream operations consume it?
+- Can its serialized value enter those consumers unchanged?
+- Does it retain parent, presentation, ordered axes, ambient dimension, and
+  normalization where meaningful?
+- What context survives empty, zero, identity, and other degenerate values?
+- Is a decision or certificate bound to the exact source value it concerns?
+- Can validation replay its defining relation within the admitted work bound?
+
+Classify each output as a canonical value, source-bound result, or display
+projection. A display projection must not masquerade as a composable value.
+
+## Probe the recurrent failure classes
+
+Use small deterministic reproductions before broad mutation. Check for:
+
+- a request accepted beyond the kernel or backend's mathematical domain;
+- input, intermediate, algorithmic-work, or exact-result growth omitted from
+  admission, especially exponentiation, dense products, closure, and replay;
+- backend units, multiplicities, generators, witnesses, parents, or axes lost
+  during conversion;
+- exact properties inferred from the shape of lossy output;
+- a result model that accepts a forged conclusion, certificate, or derived
+  value independently of its source;
+- parallel producer and consumer representations that require caller-side
+  reconstruction;
+- empty or singular values that lose their ambient mathematical context;
+- implicit coercion across rings, fields, parents, presentations, or axes;
+- implementation semantics that disagree with title, description, scope,
+  method, examples, or result field names; and
+- a private backend imported or exposed at the public namespace boundary.
+
+When a finding depends on a maintained library, verify its current documented
+domain and semantics against official documentation and the pinned version.
+Generated documentation summaries are discovery aids; confirm consequential
+claims in source, tests, or release documentation.
+
+## Search for the shared mechanism
+
+After proving a defect, search the owner domain, shared helper, and every caller
+of that helper for the same mechanism. Keep the search causal: do not turn one
+finding into an unbounded repository audit. Report each adjacent candidate as
+confirmed, disproved, or untested.
+
+Prefer a root repair at the owning layer:
+
+- admission for unsupported or excessive requests;
+- canonical value ownership for composition failures;
+- adapter conversion for backend information loss;
+- result validation for source authenticity and reconstruction; or
+- declaration/schema text for a public semantic mismatch.
+
+Do not use result validation to compensate for overbroad admission, and do not
+add source-text lint rules for mathematical properties.
+
+## Require discriminating evidence
+
+For a confirmed bug, first preserve a focused behavioral regression that fails
+on the base for the intended reason when feasible. Then use the smallest
+relevant evidence:
+
+- accepted and immediately rejected boundary cases;
+- reconstruction or defining-identity properties;
+- producer -> serialization -> consumer closure, including a degenerate value;
+- independent mutation of source and conclusion fields;
+- a bounded independent oracle or metamorphic property for mathematical logic;
+- catalog invocation for public projection changes; and
+- the owner lane named in `CONTRIBUTING.md`.
+
+Examples are necessary evidence for discoverability, not proof of mathematical
+correctness. Generic fuzzing can expose validation gaps but cannot replace a
+domain invariant or independent oracle.
+
+## Report the audit
+
+Lead with the conclusion. For every confirmed finding include the affected
+operation, public claim, minimal reproduction, observed result, mathematical or
+architectural invariant violated, shared root mechanism, affected siblings,
+smallest repair, and regression evidence. Separate confirmed facts from
+hypotheses and list meaningful proof gaps.
+
+If implementation was authorized, preserve unrelated work, make focused
+changes with their tests, run the owning validation, and report only evidence
+that actually ran. Do not perform external mutations without explicit
+authorization.

.agents/skills/audit-public-operation-contracts/agents/openai.yaml

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+interface:
+  display_name: "Audit Public Operation Contracts"
+  short_description: "Audit Jacobian mathematical operation contracts"
+  default_prompt: "Use $audit-public-operation-contracts to audit these Jacobian operations and search their owner domains for the same root mechanism."