{
  "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": "numerical-derivative",
    "version": "1.1.4",
    "title": "Numerical Derivative Calculator",
    "formula_family": "numerical_derivative",
    "capability_id": "math.numerical.derivative",
    "verification_revision": "2026-10-18.derivative-input-stencil-contract-v3"
  },
  "profile": "core",
  "verified_scope": "all published methods",
  "status": "VERIFIED",
  "verification_status": "VERIFIED",
  "production_freshness": "CURRENT",
  "overall_trust": "VERIFIED",
  "runner": {
    "name": "cvp-runner",
    "version": "1.0.0"
  },
  "environment": {
    "runtime": "node",
    "runtime_version": "22.20.0",
    "numeric_model": "IEEE-754 binary64",
    "os": "darwin"
  },
  "suite": {
    "id": "numerical-derivative",
    "version": "1.1.4",
    "uri": "https://www.calculatorx.com/evidence/math.numerical.derivative/1.1.4.json",
    "verification_revision": "2026-10-18.derivative-input-stencil-contract-v3"
  },
  "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-XCAL-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "ISO 80000-2:2019 Quantities and units — Mathematics",
        "kind": "standard",
        "reference": "Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.",
        "url": "https://www.iso.org/standard/64973.html"
      },
      {
        "label": "CRC Standard Mathematical Tables — forward, backward, and central differences",
        "kind": "other",
        "reference": "Forward (f(x+h)−f(x))/h; backward; central (f(x+h)−f(x−h))/(2h); two-sided probe of f"
      },
      {
        "label": "NIST DLMF §3.4 — Differentiation",
        "kind": "other",
        "reference": "§3.4",
        "url": "https://dlmf.nist.gov/3.4"
      },
      {
        "label": "Gilbert Strang, Calculus — Chapter 2: Derivatives (MIT OpenCourseWare)",
        "kind": "other",
        "reference": "§§2.6–2.7 Limits and Continuous Functions",
        "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch02.pdf"
      }
    ]
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Independent Fraction polynomial and mpmath600/800dps finite-step values plus analytic baselines; legacy independent analytic vectors; bounded binary64 publication"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "FD of poly/sin/exp, plus method=limit. Discovery /two-sided-limit. Not symbolic d/dx, not one-sided, not L’Hôpital."
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "dimensionless"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O2 expected_values + O2 numerical_behavior"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "4/4 legacy golden; 255/255 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "1/1 numeric-edge Evidence + 1/1 near-singularity numeric; illegal enum/system is Invalid only"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3 Evidence illegal-input + 13/13 oracle-backed error-code (exact_error_match, not ULP)"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "max_error_observed_ulp=0; policy declared a priori"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "7/7 declared partitions (tiny-step, subnormal-exp, central, forward, backward, limit, invalid-domain) · 4 legacy golden / 2 CVP boundary unique cases · 3 Evidence invalid-input (may overlap boundary)"
    },
    "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 numerical-derivative; 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": "this calculator CURRENT · bound snapshot pass @ 2026-10-19T07:58:46.038Z · live site-wide report stale @ 2026-10-19T07:58:57.899Z (7 other capabilities) · local checks pass · attestation_id=c64cc612dc6c3a945c8f29b84029807be91aeb07eee35eea41b94b1b8594e211 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-10-19T07:58:46.038Z · Live production status STALE (7 capabilities; 369 remain CURRENT) @ 2026-10-19T07:58:57.899Z · Public schema 1.1.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.1.4 · 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 · cvp-immutable-manifest-fetch=pass · cvp-immutable-manifest-sha256=pass · cvp-latest-alias-matches-immutable=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=589b90803730d03fdb921029dbc9e570b3d8a9047e839174126db3b72f2cd1c6 · verified_at=2026-10-18T01:19:25.052Z · evidence_attested_at=2026-10-18T01:19:25.052Z · last_confirmed_current_at=2026-10-19T07:58:46.038Z · rendered_at=2026-10-19T07:58:58.175Z · binds=cvp_core_sha256",
      "check_result": "PASS",
      "production_state": "CURRENT",
      "binding_current": true
    },
    "CVP-DIM-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "scalar derivative"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "1/1 property · enumerated fixed assertions (not generated; no seed)"
    },
    "CVP-META-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "No input→output transformation vectors in pack — control not in obligation set"
    },
    "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": "PASS",
      "applicability": "applicable",
      "notes": "1/1 cross-calculator · xcal-sin-cos PASS vs math.cos"
    },
    "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 3/3 (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. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity."
    },
    "CVP-ORACLE-01": {
      "result": "SKIP",
      "applicability": "higher_assurance",
      "notes": "O2 present; O3 not required this wave"
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "named expert review not performed"
    }
  },
  "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 3/3 (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. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity."
  },
  "artifacts": {
    "evidence_bundle_sha256": "d04e4ad20a2a916f5dc10e111d6eae794f3e374692cab53b6f55c58782ed9c54",
    "evidence_digest": "940d2da6a91a9c7e979828232a7de7c4b1071a8f39752c03337d627ce52e7d4b",
    "production_sha256": "589b90803730d03fdb921029dbc9e570b3d8a9047e839174126db3b72f2cd1c6",
    "attested_catalog_sha256": "93b711f8b5b8d602c9f2ecfb852b561e5cd33585603555116fdf45f0bd4f1957",
    "production_checks": [
      {
        "id": "math.numerical.derivative:output-const",
        "status": "pass",
        "detail": "output const 1.1.4 vs capability 1.1.4",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:evidence-sha256",
        "status": "pass",
        "detail": "271f39561e96",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:semantic-contract",
        "status": "pass",
        "detail": "14/14",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.1.4 vs origin 1.1.4",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.numerical.derivative/1.1.4/2026-10-18.derivative-input-stencil-contract-v3/core/940d2da6a91a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z",
        "projection_compared": false
      },
      {
        "id": "math.numerical.derivative:cvp-latest-alias-agrees",
        "status": "pass",
        "detail": "math.numerical.derivative/1.1.4/2026-10-18.derivative-input-stencil-contract-v3/core/940d2da6a91a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z",
        "projection_compared": false
      },
      {
        "id": "math.numerical.derivative:cvp-immutable-manifest-fetch",
        "status": "pass",
        "detail": "public=200 origin=200",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:cvp-immutable-manifest-sha256",
        "status": "pass",
        "detail": "940d2da6a91a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:cvp-latest-alias-matches-immutable",
        "status": "pass",
        "detail": "math.numerical.derivative/1.1.4/2026-10-18.derivative-input-stencil-contract-v3/core/940d2da6a91a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z",
        "projection_compared": false
      },
      {
        "id": "math.numerical.derivative:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      },
      {
        "id": "math.numerical.derivative:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-10-18T01:19:25.052Z"
      }
    ],
    "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": "940d2da6a91a9c7e979828232a7de7c4b1071a8f39752c03337d627ce52e7d4b",
          "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": "940d2da6a91a9c7e979828232a7de7c4b1071a8f39752c03337d627ce52e7d4b",
          "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": "271f39561e963d3303008d9ce56c9a577f5ac779cb86580e0988bdd07f938a01",
          "note": "Published Evidence JSON core — Trust freshness / production bind subject"
        },
        {
          "name": "evidence_catalog_digest",
          "field": "artifacts.attested_catalog_sha256",
          "digest_scope": "capability_catalog",
          "value": "93b711f8b5b8d602c9f2ecfb852b561e5cd33585603555116fdf45f0bd4f1957",
          "note": "Capability catalog integrity; site-wide, not per-suite fingerprint"
        }
      ]
    },
    "cvp_core_sha256": "940d2da6a91a9c7e979828232a7de7c4b1071a8f39752c03337d627ce52e7d4b"
  },
  "dependencies": [
    {
      "name": "numerical-derivative-engine",
      "version": "1.1.4"
    },
    {
      "name": "numerical-derivative-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "math.cos",
      "version": "1.0.5",
      "role": "cross_calculator_peer",
      "capability_id": "math.cos",
      "evidence_digest": "ece0bdda8ca9515cd122d2544c9f69ccbc9c211a3294389127b1204dd18fcdae",
      "evidence": "https://www.calculatorx.com/evidence/math.cos/1.0.5.cvp.json"
    },
    {
      "name": "node",
      "version": "22.20.0"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "c64cc612dc6c3a945c8f29b84029807be91aeb07eee35eea41b94b1b8594e211",
    "attested_at": "2026-10-18T01:19:25.052Z",
    "last_confirmed_current_at": "2026-10-19T07:58:46.038Z",
    "site_attestation_current": false,
    "capability_attestation_current": true,
    "bound_snapshot_status": "pass",
    "live_report_status": "stale",
    "bound_attested_at": "2026-10-19T07:58:46.038Z",
    "live_updated_at": "2026-10-19T07:58:57.899Z",
    "bound_snapshot": {
      "status": "pass",
      "attested_at": "2026-10-19T07:58:46.038Z",
      "site_stale_count": 7
    },
    "live_site_status": {
      "href": "/.well-known/calculatorx-production-attestation.json"
    },
    "bound_snapshot_site_stale_count": 7,
    "site_stale_capability_count": 7,
    "evidence_attested_at": "2026-10-18T01:19:25.052Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.1.4",
    "external_third_party": false,
    "note": "Named expert review not performed"
  },
  "timestamps": {
    "verified_at": "2026-10-18T01:19:25.052Z",
    "generated_at": "2026-10-18T01:19:25.052Z",
    "rendered_at": "2026-10-19T07:58:58.175Z",
    "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."
  },
  "tests": {
    "golden": {
      "passed": 255,
      "total": 255,
      "failed": 0
    },
    "boundary": {
      "passed": 2,
      "total": 2,
      "failed": 0
    },
    "invalid": {
      "passed": 16,
      "total": 16,
      "failed": 0,
      "comparison": "exact_error_match"
    },
    "property": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "kind": "fixed"
    },
    "round_trip": {
      "passed": 0,
      "total": 0,
      "failed": 0
    },
    "metamorphic": {
      "passed": 0,
      "total": 0,
      "failed": 0
    },
    "contract": {
      "passed": 6,
      "total": 6,
      "failed": 0
    },
    "cross_interface": {
      "passed": 16,
      "total": 16,
      "failed": 0
    },
    "cross_calculator": {
      "passed": 1,
      "total": 1,
      "failed": 0
    }
  },
  "numerical": {
    "representation": "IEEE-754 binary64; 12 significant digits, nonzero values retained",
    "tolerance": {
      "type": "relative",
      "value": 2e-10,
      "declared_before_evaluation": true,
      "rationale": "Independent exact/high-precision finite-step and analytic golden values use relative2e-10 plus4 smallest subnormals; true zero is exact and nonzero cannot become zero. Vectors use well-posed default stencils; this is not an arbitrary-h accuracy guarantee."
    },
    "max_error_observed": 0
  },
  "coverage": {
    "partitions": [
      {
        "id": "tiny-step",
        "description": "Elementary stencils with h below x resolution",
        "exercised": true,
        "case_count": 65
      },
      {
        "id": "subnormal-exp",
        "description": "Positive subnormal exp stencils and limit",
        "exercised": true,
        "case_count": 16
      },
      {
        "id": "central",
        "description": "central",
        "exercised": true,
        "case_count": 79
      },
      {
        "id": "forward",
        "description": "forward",
        "exercised": true,
        "case_count": 64
      },
      {
        "id": "backward",
        "description": "backward",
        "exercised": true,
        "case_count": 64
      },
      {
        "id": "limit",
        "description": "limit",
        "exercised": true,
        "case_count": 62
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 16
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "forward / backward / central difference; two-sided numeric limit"
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Independent Python Fraction polynomial and mpmath600/800dps elementary finite-step fixtures; separate analytic references for legacy default-step vectors; no IUT imports",
        "engine": {
          "name": "numerical-derivative-reference",
          "precision_bits": 53,
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Independent finite-step value and analytic baseline; relative2e-10 plus4 smallest subnormals; exact true zero and no false zero for nonzero primary values",
        "engine": {
          "name": "numerical-derivative-reference",
          "precision_bits": 53,
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      }
    ]
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/math.numerical.derivative/1.1.4.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.numerical.derivative/1.1.4",
    "calculator": "https://www.calculatorx.com/calc/math/numerical-derivative",
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