calculate

Calculate

Decide and route

• Do not load it for trivial, low-risk arithmetic the model can immediately verify.
• Treat fixed-width wrapping/saturating arithmetic as mandatory; do not classify them as trivial arithmetic.
• Always use it for fixed-width or IEEE-754 facts, exact/high-precision or symbolic work, matrices, units, statistics, probability, finance, verification, repeated calculations, or consequential results.
• Ask for a missing assumption when it changes the problem; a call must not hide ambiguity.
• The four tools are registered. Never call list_mcp_resources, inspect source, or use a shell to find them. Use math.run for a known operation; otherwise search, then describe only if needed.
• For an obligation DAG, failures-only checkpoint, or receipt replay, do not search the MCP catalog. When this installed Skill contains the Host-generated scripts/math-anchor launcher, invoke it relative to this Skill directory with check-obligations or replay-obligations; retain receipts outside model context. Never substitute an ambient command or source checkout. If the launcher is absent, report that this carrier has no obligation checkpoint.
• Every run uses the outer envelope {operation, arguments}. Put all operation-specific fields inside arguments; never flatten them beside operation.

Call these fully known routes directly; never search or describe these shapes first:

• Fixed-width arithmetic: {"operation":"integer.machine_arithmetic","arguments":{"action":"add","left":"255","right":"2","bitWidth":8,"signedness":"unsigned","inputMode":"value","overflowBehavior":"wrapping"}}
• Exact combinations/permutations: {"operation":"combinatorics.count","arguments":{"action":"binomial","n":52,"k":5}}
• Checkable polynomial identity: {"operation":"certificate.polynomial_identity","arguments":{"left":"(x+1)^2","right":"x^2+2*x+1","variables":["x"]}}

Execute economically

• Use one math.run, math.batch for 2–32 independent ordered calculations, or function.sample for one expression at many points. Batch is not a dependency graph.
• For bulky output, select resultMode and raise maxOutputBytes only when useful.
• Control digits with arguments.precision; precision is not a top-level math.run field. It counts significant digits. Exact fields stay exact. For decimal places, include integer digits plus at least two guard digits in the first call and round once for presentation.
• Supply answer-changing variables, bounds, units, conventions, and tolerances.