math.quadratic

≤4 ULP vs O3 applies only to the published tabulated vectors (two-real, repeated, complex, irrational, near-double-root, tiny-complex, tiny-real, tiny-scale, fraction-numeric, downward, large-scale, cancellation). It is not a guarantee over the entire coefficient space. Roots use a cancellation-safe q-form at the same ± order as x = (−b ± √Δ)/(2a).

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

12/12 passed

Oracle

O3 · mpmath 1.4.1

Reference table commitment (SHA-256)

6c8e67f2ed03b75a193e76be0cfa73781cd43587d0004503148223de0a9cbb8c

Generator commitment (SHA-256)

5a1157ecb5e8c163ca72f377c162c8501077f46d22cc32eba7a80a0855a83a36

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.