math.root

Path-specific ULP vs O3 applies only to the 19 published tabulated vectors: identity n=1 (0 ULP); Math.sqrt including tiny/huge (≤2); Math.cbrt including odd-negative and tiny/huge (≤2); moderate Math.pow including odd-negative, ⁸√15, and max safe n (≤2); extreme Math.pow at |a|=1e±300 (≤64). It is not a whole-domain guarantee. Even roots of a<0 and illegal n are contract errors (NOT_REAL / INVALID_INDEX), not ULP claims.

This summary records the outcome of the verification run. The full test corpus, oracle implementations, reference tables and generators are retained privately. Their digests identify those artifacts; a digest alone does not let a reader independently reproduce the full verification run.

Recorded result

19/19 passed

Oracle

O3 · mpmath 1.4.1

Reference table commitment (SHA-256)

d0c85277acd014046ec073aca6650c34eedfa2ec3a205af9af4a7ecb6506f324

Generator commitment (SHA-256)

3a38d49784974fade813298be4a21a1c1c5c91d288c1773b2802c300a069e93c

Check a calculation

Use the capability's public input schema and examples to call the versioned REST API or MCP. These interfaces remain available without downloading the validation infrastructure. A successful example checks that example; it does not establish that the complete private suite has been independently reproduced.