Align jacobian math skill guidance after rebase

Co-authored-by: morluto <morluto@users.noreply.github.com>

Author: cursoragent

.agents/skills/jacobian-math/SKILL.md

@@ -10,18 +10,22 @@ description: Use Jacobian for specialized exact mathematics, including matrix de
 In Codex Code Mode, call the nested methods
 `tools.mcp__jacobian__math_find(...)` and
 `tools.mcp__jacobian__math_run(...)` directly. Do not enumerate, filter, or
-print `ALL_TOOLS` merely to locate them; that needlessly adds every matching
-tool description to the model context. Return only the typed projection when
-available, for example:
+print `ALL_TOOLS`; that loads matching tool descriptions into context. Return
+only the typed projection when available:
 
 ```js
 const r = await tools.mcp__jacobian__math_find({query: "...", limit: 3});
 text(r.structuredContent ?? r);
 ```
 
-Call `math.run` directly when the requested local outcome exactly matches one of
-these stable built-in contracts; replace the example values but preserve the
-shown JSON types:
+Use Jacobian for each requested exact mathematical outcome, even when small or
+shell-solvable. Route multiple requested outcomes separately. Prefer a
+capability matching the requested operation over a generic arithmetic substep
+that yields the same scalar; composing already-known supporting operations remains allowed when clearer.
+Do not call Jacobian for definitions, formatting, or non-execution tasks.
+
+Call `math.run` directly when the requested local outcome exactly matches these
+stable built-in contracts; replace examples but preserve JSON types:
 
 - `integer.compute.gcd`, `integer.compute.lcm`, or
   `integer.compute.extended_gcd` in `EXPLORE` mode:
@@ -36,26 +40,31 @@ shown JSON types:
   `{"determinant_uri":"<determinant_uri from compute output>"}`.
 
 For other outcomes or unfamiliar payloads, use `math.find` with a specific
-plain-language outcome and any domain or mode already implied by the task; a
-capability ID is not required. Request only as many matches as are useful
-because lower `limit` values reduce context. Inspect the `CONTRACT` view only
-when its typed schema is needed to construct the `math.run` payload. A discovery
-card's validated `invocation_example`, or its required top-level fields when no
-example is available, may already provide a sufficient payload shape.
+plain-language outcome and implied domain or mode; no capability ID is required.
+Use low `limit` values. Inspect `CONTRACT` only when the typed schema is needed.
+A card's `invocation_example`, or required top-level fields, may be enough.
+
+Do not add a discovery domain filter unless its exact installed spelling is
+known. When discovery exposes recovery paths, follow those fields (for example,
+`remove_unknown_domain_filter`, `remove_filters`, or `reformulate_query`) before
+treating absence as final. After invalid input, correct the reported constraint
+and retry within the task resource bounds as further errors appear. If one
+provider is unavailable, continue with other installed routes that can produce
+the outcome. Treat timeouts as non-conclusions. Accept only a completed result
+whose scope covers the input, and carry forward the smallest decisive value,
+witness, status, assurance, completeness, and open obligations; preserve artifact
+refs, including verification record URIs.
 
 Keep representation, decomposition, composition, iteration, verification
 timing, and stopping decisions agent-owned. Treat timeouts, errors, incomplete
 searches, and missing witnesses as non-conclusions.
 
-When independent checking is requested, calculations or programs authored by
-the same model are not independent checker evidence. Use an installed `VERIFY`
-capability when available. An artifact URI or checker-result summary is not a
-task-local verification-record file: never reconstruct or paraphrase such a
-record from the returned fields. Claim `VERIFIED` only when the result has
-assurance level `VERIFIED`, the exact record bytes are available, and any
-required task authorization and bindings are preserved. Otherwise use a lower
-assurance permitted by the task.
-
-Verification is bound to the exact checked claim. Do not transfer `VERIFIED` from an
-input, premise, factorization, or related artifact to a conclusion derived by the
-model; the final conclusion needs its own checker-bound verification record.
+When independent checking is requested, model-authored calculations or programs
+are not independent evidence. Use installed `VERIFY` when available. An artifact
+URI or checker summary is not a task-local verification-record file: never
+reconstruct or paraphrase such a record from returned fields. Claim `VERIFIED`
+only when the result has assurance level `VERIFIED`, exact record bytes, and
+required task authorization and bindings are preserved; otherwise use lower
+task-permitted assurance. Verification is bound to the exact checked claim: do
+not transfer `VERIFIED` from an input, premise, factorization, or related
+artifact to a model-derived conclusion, which needs its own checker-bound record.

npm/skills/jacobian-math/SKILL.md

@@ -10,18 +10,22 @@ description: Use Jacobian for specialized exact mathematics, including matrix de
 In Codex Code Mode, call the nested methods
 `tools.mcp__jacobian__math_find(...)` and
 `tools.mcp__jacobian__math_run(...)` directly. Do not enumerate, filter, or
-print `ALL_TOOLS` merely to locate them; that needlessly adds every matching
-tool description to the model context. Return only the typed projection when
-available, for example:
+print `ALL_TOOLS`; that loads matching tool descriptions into context. Return
+only the typed projection when available:
 
 ```js
 const r = await tools.mcp__jacobian__math_find({query: "...", limit: 3});
 text(r.structuredContent ?? r);
 ```
 
-Call `math.run` directly when the requested local outcome exactly matches one of
-these stable built-in contracts; replace the example values but preserve the
-shown JSON types:
+Use Jacobian for each requested exact mathematical outcome, even when small or
+shell-solvable. Route multiple requested outcomes separately. Prefer a
+capability matching the requested operation over a generic arithmetic substep
+that yields the same scalar; composing already-known supporting operations remains allowed when clearer.
+Do not call Jacobian for definitions, formatting, or non-execution tasks.
+
+Call `math.run` directly when the requested local outcome exactly matches these
+stable built-in contracts; replace examples but preserve JSON types:
 
 - `integer.compute.gcd`, `integer.compute.lcm`, or
   `integer.compute.extended_gcd` in `EXPLORE` mode:
@@ -36,26 +40,31 @@ shown JSON types:
   `{"determinant_uri":"<determinant_uri from compute output>"}`.
 
 For other outcomes or unfamiliar payloads, use `math.find` with a specific
-plain-language outcome and any domain or mode already implied by the task; a
-capability ID is not required. Request only as many matches as are useful
-because lower `limit` values reduce context. Inspect the `CONTRACT` view only
-when its typed schema is needed to construct the `math.run` payload. A discovery
-card's validated `invocation_example`, or its required top-level fields when no
-example is available, may already provide a sufficient payload shape.
+plain-language outcome and implied domain or mode; no capability ID is required.
+Use low `limit` values. Inspect `CONTRACT` only when the typed schema is needed.
+A card's `invocation_example`, or required top-level fields, may be enough.
+
+Do not add a discovery domain filter unless its exact installed spelling is
+known. When discovery exposes recovery paths, follow those fields (for example,
+`remove_unknown_domain_filter`, `remove_filters`, or `reformulate_query`) before
+treating absence as final. After invalid input, correct the reported constraint
+and retry within the task resource bounds as further errors appear. If one
+provider is unavailable, continue with other installed routes that can produce
+the outcome. Treat timeouts as non-conclusions. Accept only a completed result
+whose scope covers the input, and carry forward the smallest decisive value,
+witness, status, assurance, completeness, and open obligations; preserve artifact
+refs, including verification record URIs.
 
 Keep representation, decomposition, composition, iteration, verification
 timing, and stopping decisions agent-owned. Treat timeouts, errors, incomplete
 searches, and missing witnesses as non-conclusions.
 
-When independent checking is requested, calculations or programs authored by
-the same model are not independent checker evidence. Use an installed `VERIFY`
-capability when available. An artifact URI or checker-result summary is not a
-task-local verification-record file: never reconstruct or paraphrase such a
-record from the returned fields. Claim `VERIFIED` only when the result has
-assurance level `VERIFIED`, the exact record bytes are available, and any
-required task authorization and bindings are preserved. Otherwise use a lower
-assurance permitted by the task.
-
-Verification is bound to the exact checked claim. Do not transfer `VERIFIED` from an
-input, premise, factorization, or related artifact to a conclusion derived by the
-model; the final conclusion needs its own checker-bound verification record.
+When independent checking is requested, model-authored calculations or programs
+are not independent evidence. Use installed `VERIFY` when available. An artifact
+URI or checker summary is not a task-local verification-record file: never
+reconstruct or paraphrase such a record from returned fields. Claim `VERIFIED`
+only when the result has assurance level `VERIFIED`, exact record bytes, and
+required task authorization and bindings are preserved; otherwise use lower
+task-permitted assurance. Verification is bound to the exact checked claim: do
+not transfer `VERIFIED` from an input, premise, factorization, or related
+artifact to a model-derived conclusion, which needs its own checker-bound record.