{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed",
    "revision": "2026-09-13",
    "spec_sha256": "f62725968356c92930531cd6085db76e216da06e95be53d636b0d2cf3218b148",
    "spec": "https://www.calculatorx.com/developers/cvp/spec/1.0"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "bending-stress",
    "version": "1.0.0",
    "title": "Bending Stress",
    "formula_family": "bending_stress",
    "capability_id": "mechanical.statics.bending_stress",
    "verification_revision": "2026-09-27.o2-o3"
  },
  "profile": "engineering",
  "verified_scope": "σ = M/S on one centroidal axis; S given or S = Ix/c; + O3 mpmath tabulated σ.",
  "deferred_scope": "Not plastic modulus, not a rectangle from b·h, and not beam deflection.",
  "status": "STALE",
  "verification_status": "VERIFIED",
  "production_freshness": "STALE",
  "overall_trust": "VERIFIED_STALE",
  "runner": {
    "name": "cvp-runner",
    "version": "1.0.0"
  },
  "environment": {
    "runtime": "node",
    "runtime_version": "20.19.2",
    "numeric_model": "IEEE-754 binary64",
    "os": "darwin"
  },
  "suite": {
    "id": "bending-stress",
    "version": "1.0.0",
    "uri": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/1.0.0.json",
    "verification_revision": "2026-09-27.o2-o3"
  },
  "obligation_set": [
    "CVP-PROV-01",
    "CVP-MODEL-01",
    "CVP-SCOPE-01",
    "CVP-UNIT-01",
    "CVP-REF-01",
    "CVP-GOLD-01",
    "CVP-BND-01",
    "CVP-INV-01",
    "CVP-NUM-01",
    "CVP-COV-01",
    "CVP-CONTRACT-01",
    "CVP-DEP-01",
    "CVP-ART-01",
    "CVP-PROD-01",
    "CVP-DIM-01",
    "CVP-PROP-01",
    "CVP-META-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "Hibbeler, Mechanics of Materials",
        "kind": "other",
        "reference": "Bending — flexure formula"
      },
      {
        "label": "Gere and Goodno, Mechanics of Materials",
        "kind": "other",
        "reference": "Bending — flexure formula"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Elastic flexure σ = M/S"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath bending stress (80 dps)",
        "engine": {
          "name": "bending-stress-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "same_runtime_as_iut": false,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "generator_version": "1.0.0",
          "generator_sha256": "d24b69105fccd6d0af23c0799a1b1b3970fcc6c557a4bdf2601383613f05eef6",
          "table_sha256": "bb73a9f80d63e57442a213862a889e711ff060ca0f8ae6df9512b6c7bd729bed",
          "seed": "20260927.bending-stress-o3",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/bending-stress-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/bending-stress-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-bending-stress-o3.py"
        }
      },
      {
        "class": "O3",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O3 table vs IUT flow; ≤2 ULP on tabulated vectors only",
        "engine": {
          "name": "bending-stress-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "same_runtime_as_iut": false,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "generator_version": "1.0.0",
          "generator_sha256": "d24b69105fccd6d0af23c0799a1b1b3970fcc6c557a4bdf2601383613f05eef6",
          "table_sha256": "bb73a9f80d63e57442a213862a889e711ff060ca0f8ae6df9512b6c7bd729bed",
          "seed": "20260927.bending-stress-o3",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/bending-stress-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/bending-stress-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-bending-stress-o3.py"
        }
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module bending-stress oracle",
        "engine": {
          "name": "bending-stress-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP σ comparison",
        "engine": {
          "name": "bending-stress-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ],
    "notes": "Golden expected values use a separate O2 module (not IUT transcription). O2 shares Node/V8 binary64 with the IUT unless noted otherwise."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "σ = M/S; O3 tabulated σ"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Not plastic modulus. O3 tabulated vectors only."
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "M is N·m. S is m³. σ is Pa (N/m²)."
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 + O2 + O3"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 legacy golden; 4/4 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 CVP boundary · 3/3 legacy Evidence boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3 Evidence illegal-input + 2/2 oracle-backed error-code (exact_error_match, not ULP)"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "max_error_observed_ulp=1; policy declared a priori"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "5/5 partitions"
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "6/6 CVP contract · release-artifacts-aligned=PASS · schema-output-required-declared=PASS · schema-valid-input-executes=PASS · engine-success-output-validates-schema=PASS · schema-rejects-incomplete-input=PASS · rest-success-payload-validates-schema=PASS"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine bending-stress; Node binary64"
    },
    "CVP-ART-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "release_integrity.status=verified · digests: artifact_evidence_sha256=Evidence core (Trust freshness) · cvp_evidence_digest=artifacts.evidence_digest (fingerprint v2) · evidence_bundle_sha256=legacy Evidence JSON bytes · evidence_catalog_digest=attested_catalog_sha256 · production_sha256=bound production report · see artifacts.digest_registry"
    },
    "CVP-PROD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Capability production binding: STALE · Site report: stale · STALE (freshness / digest drift after last PASS snapshot) · site report stale · local checks pass · local production checks PASS; capability production binding is not CURRENT — final status must stay STALE, not VERIFIED · attestation_id=5f26825d06766888502f8c66b8e774f1d2c117d79d35add8eac32756335ab114 · previous live site report said CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-09-24T10:09:46.472Z · Live production status STALE (198 capabilities; 237 remain CURRENT) @ 2026-09-27T00:32:31.861Z · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.0 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-latest-alias-agrees=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=36b20a13ec97ef1e6a76802f1f86b4d6a2b04374a7d11e4f0d3d10a2308804fa · verified_at=2026-09-27T00:33:16.800Z · evidence_attested_at=2026-09-27T00:33:16.800Z · last_confirmed_current_at=2026-09-27T00:33:16.800Z · rendered_at=2026-09-27T00:33:16.800Z · binds=cvp_core_sha256 · attestation snapshot core 45bf7b58ef79 ≠ live cvp_core_sha256 2dc6e2ca9a7c (2026-09-27.o2-o3)",
      "check_result": "PASS",
      "production_state": "STALE",
      "binding_current": false
    },
    "CVP-DIM-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "Bending stress"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "1/1 property · enumerated fixed assertions (not generated; no seed)"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "1/1 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "No inverse / round-trip vectors in pack — control not in obligation set"
    },
    "CVP-XCAL-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "No related calculator in the same formula family / no related-identity peers declared — control not in obligation set"
    },
    "CVP-IFACE-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only."
    },
    "CVP-ORACLE-01": {
      "result": "PASS",
      "applicability": "higher_assurance",
      "notes": "O3 8/8 tabulated vectors vs IUT · O2: σ = M/S vs a separate-module identity (≤2 ULP). Not plastic modulus, not a rectangle from b·h, and not beam deflection. ≤2 ULP vs O3 applies only to the published tabulated bending-stress vectors. Not plastic modulus."
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "named expert review not performed"
    }
  },
  "tests": {
    "golden": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "g-MS",
        "g-Ix",
        "g-neg",
        "g-I"
      ]
    },
    "boundary": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "boundary-modulus",
        "boundary-moment",
        "boundary-missing"
      ]
    },
    "invalid": {
      "passed": 5,
      "total": 5,
      "failed": 0,
      "case_ids": [
        "boundary-modulus",
        "boundary-moment",
        "boundary-missing",
        "inv-S",
        "inv-Ix"
      ],
      "comparison": "exact_error_match",
      "records": [
        {
          "id": "inv-S",
          "comparison": "exact_error_match",
          "expected": {
            "code": "VALUE_MUST_BE_POSITIVE"
          },
          "actual": {
            "code": "VALUE_MUST_BE_POSITIVE"
          },
          "match": true
        },
        {
          "id": "inv-Ix",
          "comparison": "exact_error_match",
          "expected": {
            "code": "INVALID_INPUT"
          },
          "actual": {
            "code": "INVALID_INPUT"
          },
          "match": true
        }
      ]
    },
    "property": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "prop-check"
      ],
      "kind": "fixed",
      "claim_scope": "Enumerated identity: M = 12, S = 4 gives σ = 3.",
      "definition_ids": [
        "M-12-S-4"
      ]
    },
    "round_trip": {
      "passed": 0,
      "total": 0,
      "failed": 0,
      "case_ids": []
    },
    "metamorphic": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "meta-M"
      ],
      "definition_ids": [
        "double-M-doubles-sigma"
      ]
    },
    "contract": {
      "passed": 6,
      "total": 6,
      "failed": 0
    },
    "cross_interface": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "iface-MS",
        "iface-S"
      ]
    },
    "o3": {
      "passed": 8,
      "total": 8,
      "failed": 0,
      "case_ids": [
        "o3-MS",
        "o3-Ix",
        "o3-alias",
        "o3-awkward",
        "o3-I-alias",
        "o3-neg-M",
        "o3-small",
        "o3-large"
      ],
      "generator_id": "bending-stress-mpmath-o3",
      "seed": "20260927.bending-stress-o3",
      "table_sha256": "bb73a9f80d63e57442a213862a889e711ff060ca0f8ae6df9512b6c7bd729bed",
      "max_error_ulp": 1,
      "reproduce": "python3 generate-bending-stress-o3.py",
      "table_url": "/developers/cvp/reproduce/bending-stress-o3-tables.json",
      "generator_url": "/developers/cvp/reproduce/generate-bending-stress-o3.py",
      "claim_scope": "O2: σ = M/S vs a separate-module identity (≤2 ULP). Not plastic modulus, not a rectangle from b·h, and not beam deflection. ≤2 ULP vs O3 applies only to the published tabulated bending-stress vectors. Not plastic modulus.",
      "reproduce_url": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/reproduce"
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "S",
        "description": "given S",
        "exercised": true,
        "case_count": 12
      },
      {
        "id": "Ix",
        "description": "S from Ix/c",
        "exercised": true,
        "case_count": 5
      },
      {
        "id": "alias",
        "description": "moment/section_modulus aliases",
        "exercised": true,
        "case_count": 1
      },
      {
        "id": "awkward",
        "description": "non-integer M/S",
        "exercised": true,
        "case_count": 1
      },
      {
        "id": "invalid-domain",
        "description": "non-positive S or negative Ix",
        "exercised": true,
        "case_count": 5
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64",
    "claim_scope": "O2: σ = M/S vs a separate-module identity (≤2 ULP). Not plastic modulus, not a rectangle from b·h, and not beam deflection. ≤2 ULP vs O3 applies only to the published tabulated bending-stress vectors. Not plastic modulus.",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Independent bending-stress identity vs IUT. ≤2 ULP declared a priori.",
      "declared_before_evaluation": true
    },
    "max_error_observed": 1,
    "records": [
      {
        "id": "g-MS",
        "reference": {
          "model": "bending_stress",
          "M": 12,
          "S": 4,
          "sigma": 3,
          "solver": "elastic flexure"
        },
        "actual": {
          "model": "bending_stress",
          "M": 12,
          "S": 4,
          "sigma": 3,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-Ix",
        "reference": {
          "model": "bending_stress",
          "M": 100,
          "S": 25,
          "Ix": 50,
          "c": 2,
          "sigma": 4,
          "solver": "section modulus"
        },
        "actual": {
          "model": "bending_stress",
          "M": 100,
          "S": 25,
          "Ix": 50,
          "c": 2,
          "sigma": 4,
          "solver": "section modulus",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-neg",
        "reference": {
          "model": "bending_stress",
          "M": -18,
          "S": 6,
          "sigma": -3,
          "solver": "elastic flexure"
        },
        "actual": {
          "model": "bending_stress",
          "M": -18,
          "S": 6,
          "sigma": -3,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-I",
        "reference": {
          "model": "bending_stress",
          "M": 40,
          "S": 10,
          "Ix": 20,
          "c": 2,
          "sigma": 4,
          "solver": "section modulus"
        },
        "actual": {
          "model": "bending_stress",
          "M": 40,
          "S": 10,
          "Ix": 20,
          "c": 2,
          "sigma": 4,
          "solver": "section modulus",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "meta-M",
        "reference": 2,
        "actual": 2,
        "error_ulp": 0,
        "threshold_ulp": 2,
        "suite": "metamorphic",
        "hops": {
          "base": {
            "reference": {
              "model": "bending_stress",
              "M": 12,
              "S": 4,
              "sigma": 3,
              "solver": "elastic flexure"
            },
            "actual": {
              "model": "bending_stress",
              "M": 12,
              "S": 4,
              "sigma": 3,
              "solver": "elastic flexure",
              "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
            },
            "error_ulp": 0
          },
          "follow": {
            "reference": {
              "model": "bending_stress",
              "M": 24,
              "S": 4,
              "sigma": 6,
              "solver": "elastic flexure"
            },
            "actual": {
              "model": "bending_stress",
              "M": 24,
              "S": 4,
              "sigma": 6,
              "solver": "elastic flexure",
              "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
            },
            "error_ulp": 0
          },
          "relation": {
            "reference": 2,
            "actual": 2,
            "error_ulp": 0
          }
        }
      },
      {
        "id": "o3-MS",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 3,
          "M": 12,
          "S": 4
        },
        "actual": {
          "model": "bending_stress",
          "M": 12,
          "S": 4,
          "sigma": 3,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-Ix",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 4,
          "M": 100,
          "S": 25
        },
        "actual": {
          "model": "bending_stress",
          "M": 100,
          "S": 25,
          "Ix": 50,
          "c": 2,
          "sigma": 4,
          "solver": "section modulus",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-alias",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 3,
          "M": 24,
          "S": 8
        },
        "actual": {
          "model": "bending_stress",
          "M": 24,
          "S": 8,
          "sigma": 3,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-awkward",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 3.3783783783783785,
          "M": 12.5,
          "S": 3.7
        },
        "actual": {
          "model": "bending_stress",
          "M": 12.5,
          "S": 3.7,
          "sigma": 3.378378378378378,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 1,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 1
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-I-alias",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 4,
          "M": 40,
          "S": 10
        },
        "actual": {
          "model": "bending_stress",
          "M": 40,
          "S": 10,
          "Ix": 20,
          "c": 2,
          "sigma": 4,
          "solver": "section modulus",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-neg-M",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": -3,
          "M": -18,
          "S": 6
        },
        "actual": {
          "model": "bending_stress",
          "M": -18,
          "S": 6,
          "sigma": -3,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-small",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 4,
          "M": 0.08,
          "S": 0.02
        },
        "actual": {
          "model": "bending_stress",
          "M": 0.08,
          "S": 0.02,
          "sigma": 4,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-large",
        "reference": {
          "oracle_layer": "analytic",
          "sigma": 400,
          "M": 1000000,
          "S": 2500
        },
        "actual": {
          "model": "bending_stress",
          "M": 1000000,
          "S": 2500,
          "sigma": 400,
          "solver": "elastic flexure",
          "convention": "σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page."
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "sigma": {
            "ok": true,
            "error_ulp": 0
          },
          "M": {
            "ok": true,
            "error_ulp": 0
          },
          "S": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      }
    ]
  },
  "interfaces": {
    "compared": [
      "ui-ssr",
      "rest",
      "mcp"
    ],
    "result": "PASS",
    "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only."
  },
  "artifacts": {
    "evidence_bundle_sha256": "b252c0b9f23c2825a6619f78b184a77c0a0c9c161b7f893a00ac7b6b92aab76a",
    "evidence_digest": "2dc6e2ca9a7c1cf5cc5f2146b4c4d86cb69efd7c750073f9313e88e3b615dbd1",
    "production_sha256": "36b20a13ec97ef1e6a76802f1f86b4d6a2b04374a7d11e4f0d3d10a2308804fa",
    "attested_catalog_sha256": "416608b7efe51524f7de1157d0db4f6847e390a8419dd0f8de74156eb915f129",
    "production_checks": [
      {
        "id": "mechanical.statics.bending_stress:output-const",
        "status": "pass",
        "detail": "output const 1.0.0 vs capability 1.0.0",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core"
      },
      {
        "id": "mechanical.statics.bending_stress:evidence-sha256",
        "status": "pass",
        "detail": "a776506cf4cd",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core"
      },
      {
        "id": "mechanical.statics.bending_stress:semantic-contract",
        "status": "pass",
        "detail": "6/6",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core"
      },
      {
        "id": "mechanical.statics.bending_stress:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.0 vs origin 1.0.0",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core"
      },
      {
        "id": "mechanical.statics.bending_stress:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "mechanical.statics.bending_stress/1.0.0/2026-09-27.o2-o3/engineering/2dc6e2ca9a7c",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core",
        "projection_compared": false
      },
      {
        "id": "mechanical.statics.bending_stress:cvp-latest-alias-agrees",
        "status": "pass",
        "detail": "mechanical.statics.bending_stress/1.0.0/2026-09-27.o2-o3/engineering/2dc6e2ca9a7c",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core",
        "projection_compared": false
      },
      {
        "id": "mechanical.statics.bending_stress:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core"
      },
      {
        "id": "mechanical.statics.bending_stress:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": false,
        "attestation_binding_current": false,
        "attested_at": "2026-09-27T00:33:16.800Z",
        "attestation_revision": "core"
      }
    ],
    "digest_registry": {
      "digest_algorithm": "sha256",
      "canonicalization": "json-sorted-keys-utf8",
      "entries": [
        {
          "name": "cvp_core_sha256",
          "field": "artifacts.cvp_core_sha256",
          "digest_scope": "cvp_verification_fingerprint_v2",
          "value": "2dc6e2ca9a7c1cf5cc5f2146b4c4d86cb69efd7c750073f9313e88e3b615dbd1",
          "note": "Immutable verification core; excludes attestation/live-status and Evidence contract counts"
        },
        {
          "name": "cvp_evidence_digest",
          "field": "artifacts.evidence_digest",
          "digest_scope": "cvp_verification_fingerprint_v2",
          "value": "2dc6e2ca9a7c1cf5cc5f2146b4c4d86cb69efd7c750073f9313e88e3b615dbd1",
          "note": "Alias of cvp_core_sha256 (historical field name)"
        },
        {
          "name": "artifact_evidence_sha256",
          "field": "release_integrity.digests.evidence_core_sha256",
          "digest_scope": "evidence_artifact_core",
          "value": "a776506cf4cd7524be7aae09e3cb0f59ff464fdd9c71047aa02b02860e51ec7b",
          "note": "Published Evidence JSON core — Trust freshness / production bind subject"
        },
        {
          "name": "evidence_catalog_digest",
          "field": "artifacts.attested_catalog_sha256",
          "digest_scope": "capability_catalog",
          "value": "416608b7efe51524f7de1157d0db4f6847e390a8419dd0f8de74156eb915f129",
          "note": "Capability catalog integrity; site-wide, not per-suite fingerprint"
        }
      ]
    },
    "cvp_core_sha256": "2dc6e2ca9a7c1cf5cc5f2146b4c4d86cb69efd7c750073f9313e88e3b615dbd1"
  },
  "dependencies": [
    {
      "name": "bending-stress-engine",
      "version": "1.0.0"
    },
    {
      "name": "bending-stress-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "bending-stress-mpmath-o3-table",
      "version": "bending-stress-mpmath-o3"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "STALE",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "5f26825d06766888502f8c66b8e774f1d2c117d79d35add8eac32756335ab114",
    "attested_at": "2026-09-27T00:33:16.800Z",
    "last_confirmed_current_at": "2026-09-27T00:33:16.800Z",
    "site_attestation_current": false,
    "capability_attestation_current": false,
    "bound_snapshot_status": "pass",
    "live_report_status": "stale",
    "bound_attested_at": "2026-09-24T10:09:46.472Z",
    "live_updated_at": "2026-09-27T00:32:31.861Z",
    "bound_snapshot": {
      "status": "pass",
      "attested_at": "2026-09-24T10:09:46.472Z",
      "site_stale_count": 198
    },
    "live_site_status": {
      "href": "/.well-known/calculatorx-production-attestation.json"
    },
    "bound_snapshot_site_stale_count": 198,
    "site_stale_capability_count": 198,
    "evidence_attested_at": "2026-09-27T00:33:16.800Z",
    "stale_reason": "attestation snapshot core 45bf7b58ef79 ≠ live cvp_core_sha256 2dc6e2ca9a7c (2026-09-27.o2-o3)"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.0",
    "external_third_party": false,
    "note": "Named expert review not performed"
  },
  "timestamps": {
    "verified_at": "2026-09-27T00:33:16.800Z",
    "generated_at": "2026-09-27T00:33:16.800Z",
    "rendered_at": "2026-09-27T00:33:16.800Z",
    "notes": "verified_at/generated_at mark the first publication of this cvp_core_sha256 (artifacts.evidence_digest alias) for suite verification. evidence_attested_at/attested_at is the first production bind of that core digest. last_confirmed_current_at is the latest site-wide report that still confirms CURRENT. rendered_at is this JSON serialization and is not part of cvp_core_sha256 / evidence_digest. Production attestation binds cvp_core_sha256 (binds evidence_digest). Causal order: verified_at ≤ evidence_attested_at ≤ last_confirmed_current_at. attestation.bound_snapshot.site_stale_count is the site-wide stale capability count at Manifest bind time — not a live value. Fetch attestation.live_site_status.href for the current site report."
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/1.0.0.json",
    "evidence_page": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/1.0.0",
    "calculator": "https://www.calculatorx.com/calc/physics/bending-stress",
    "schema": "https://www.calculatorx.com/developers/cvp/schema/cvp-evidence-1.0.json",
    "protocol": "https://www.calculatorx.com/developers/cvp/spec/1.0",
    "manifest": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/1.0.0.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/1.0.0/2026-09-27.o2-o3.cvp.json",
    "reproduce": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/reproduce",
    "o3_table": "https://www.calculatorx.com/developers/cvp/reproduce/bending-stress-o3-tables.json",
    "o3_generator": "https://www.calculatorx.com/developers/cvp/reproduce/generate-bending-stress-o3.py",
    "manifest_core": "https://www.calculatorx.com/evidence/mechanical.statics.bending_stress/1.0.0/2026-09-27.o2-o3.2dc6e2ca9a7c.cvp.json"
  }
}