{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "exponential-growth",
    "version": "1.0.7",
    "title": "Exponential Growth Calculator",
    "formula_family": "exponential_growth",
    "capability_id": "math.exponential_growth"
  },
  "profile": "engineering",
  "status": "VERIFIED",
  "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": "exponential-growth",
    "version": "1.0.7",
    "uri": "https://www.calculatorx.com/evidence/math.exponential_growth/1.0.7.json"
  },
  "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-ROUND-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "NIST DLMF §4.2(i) The Logarithm",
        "kind": "other",
        "reference": "Principal logarithm ln z",
        "url": "https://dlmf.nist.gov/4.2"
      },
      {
        "label": "NIST DLMF §4.2(iii) The Exponential Function",
        "kind": "other",
        "reference": "exp z and the real exponential",
        "url": "https://dlmf.nist.gov/4.2"
      },
      {
        "label": "NIST DLMF §4.2(iv) Powers",
        "kind": "other",
        "reference": "Principal value z^a = exp(a ln z)",
        "url": "https://dlmf.nist.gov/4.2"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Exponential growth and decay"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath 1.4.1 exp_growth (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*",
        "engine": {
          "name": "exp_growth-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "rounding": "round-to-nearest-binary64",
          "backend": "python",
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
          "seed": "20260907",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/math-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-math-o3.py",
          "public_checker": "/developers/cvp/reproduce/check-math-o3-rest.py"
        }
      },
      {
        "class": "O3",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O3 table vs IUT x(t)/solved variable; ≤32 ULP for iterated pow/log-ratio. Distinct from legacy Evidence case-level tol.",
        "engine": {
          "name": "exp_growth-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "rounding": "round-to-nearest-binary64",
          "backend": "python",
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
          "seed": "20260907",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/math-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-math-o3.py",
          "public_checker": "/developers/cvp/reproduce/check-math-o3-rest.py"
        }
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module exponential-growth oracle",
        "engine": {
          "name": "exponential-growth-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤32 ULP scalar comparison vs IUT (iterated pow/log-ratio)",
        "engine": {
          "name": "exponential-growth-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ],
    "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node ** / Math.exp). O2 is a live oracle for identities and shares V8 binary64 with the IUT. Profile stays engineering: constant-rate model, consistent time units."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "x₀(1+r/100)^t or x₀e^(kt)"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "periodic r > −100%; continuous uses k=ratePct; inverse solves any missing field among x₀, r, t given x(t)"
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "consistent time"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O3 mpmath table + O2 live identities"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "14/14 legacy golden; 5/5 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "6/6 boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "6 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "CVP ≤32 ULP vs O3 when tabulated (iterated pow/log-ratio, not a correctly-rounded libm); legacy Evidence `tol` is not this policy. Evidence `tol_type` is absolute where declared."
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "7/7 declared partitions (forward-periodic, forward-continuous, inverse-time, inverse-x0, inverse-rate, verify, invalid-domain) · 14 golden / 6 boundary unique cases · 6 Evidence invalid-input (may overlap boundary)"
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "24/24 contract checks"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine exponential-growth; Node binary64"
    },
    "CVP-ART-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "release_integrity.status=verified · evidence_digest=CVP verification fingerprint v2 (canonical inputs, expected/actual/status, policy, versions; independent of generated_at) · evidence_bundle_sha256=legacy Evidence JSON bytes · production_sha256=bound production attestation report"
    },
    "CVP-PROD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "CURRENT · site report pass · local checks pass · attestation_id=00c818a77ba026c2d6aa3f7402680cd2dac2a40a816209600bc3c3fcd0b8921c · CURRENT · Public schema 1.0.7 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.7 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20"
    },
    "CVP-DIM-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "Engineering constant-rate model — consistent time units, not a unitless core identity"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 property"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "1/1 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 round-trips"
    },
    "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). Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session."
    },
    "CVP-ORACLE-01": {
      "result": "PASS",
      "applicability": "higher_assurance",
      "notes": "O3 13/13 tabulated vectors vs IUT"
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "expert_reviewed=false"
    }
  },
  "tests": {
    "golden": {
      "passed": 5,
      "total": 5,
      "failed": 0,
      "case_ids": [
        "g-eg-100-5-2",
        "g-eg-50-4-90",
        "g-eg-decay",
        "g-eg-cont",
        "g-eg-cont-neg"
      ]
    },
    "boundary": {
      "passed": 6,
      "total": 6,
      "failed": 0,
      "case_ids": [
        "r-minus-100",
        "r-below-minus-100",
        "solve-t-nonpositive",
        "solve-t-zero-rate",
        "solve-rate-zero-t",
        "boundary-eg-rate"
      ]
    },
    "invalid": {
      "passed": 6,
      "total": 6,
      "failed": 0,
      "case_ids": [
        "r-minus-100",
        "r-below-minus-100",
        "solve-t-nonpositive",
        "solve-t-zero-rate",
        "solve-rate-zero-t",
        "boundary-eg-rate"
      ]
    },
    "property": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "prop-t0",
        "prop-r0",
        "prop-double"
      ],
      "definition_ids": [
        "identity-at-t0",
        "identity-at-r0",
        "double-at-100pct"
      ]
    },
    "round_trip": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "rt-time",
        "rt-x0",
        "rt-rate"
      ]
    },
    "metamorphic": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "meta-time-split"
      ],
      "definition_ids": [
        "compose-time"
      ]
    },
    "contract": {
      "passed": 24,
      "total": 24,
      "failed": 0
    },
    "cross_interface": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "iface-eg"
      ]
    },
    "ui_integration": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "ui-eg-100-5-2",
        "ui-eg-pop90",
        "ui-eg-decay",
        "ui-eg-outside"
      ]
    },
    "o3": {
      "passed": 13,
      "total": 13,
      "failed": 0,
      "case_ids": [
        "o3-eg-100m5m2",
        "o3-eg-50m4m90",
        "o3-eg-100mm10m10",
        "o3-eg-100m5mm10",
        "o3-eg-0m4m90",
        "o3-eg-16m100m1",
        "o3-eg-10000m5m11",
        "o3-eg-cont-50-0p04-10",
        "o3-eg-cont-50-m0p04-10",
        "o3-eg-solve-t",
        "o3-eg-solve-x0",
        "o3-eg-solve-rate",
        "o3-eg-half-life-50pct"
      ],
      "generator_id": "math-mpmath-o3",
      "seed": "20260907",
      "max_error_ulp": 23
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "forward-periodic",
        "description": "Forward periodic x₀(1+r/100)^t",
        "exercised": true,
        "case_count": 27
      },
      {
        "id": "forward-continuous",
        "description": "Forward continuous x₀e^(kt)",
        "exercised": true,
        "case_count": 6
      },
      {
        "id": "inverse-time",
        "description": "Solve t from x₀, r, x(t)",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "inverse-x0",
        "description": "Solve x₀ from r, t, x(t)",
        "exercised": true,
        "case_count": 1
      },
      {
        "id": "inverse-rate",
        "description": "Solve r from x₀, t, x(t)",
        "exercised": true,
        "case_count": 1
      },
      {
        "id": "verify",
        "description": "Four-field displayed-precision verify",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 6
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64 (1+r/100)^t / Math.exp",
    "tolerance": {
      "type": "ulp",
      "value": 32,
      "rationale": "Iterated binary64 pow/log-ratio vs MPFR rounded to nearest f64 is not a correctly-rounded libm. A priori ≤32 ULP covers the published 90-period vector and inverse t = ln(xt/x0)/ln(1+r/100). Declared before evaluation.",
      "declared_before_evaluation": true
    },
    "legacy_regression_notes": "Legacy Evidence JSON may record case-level `tol` (e.g. 1e-8). That is a regression epsilon, not the CVP numerical acceptance policy (this calculator: ≤32 ULP vs O3). CVP records list reference, actual, error_ulp, and the a-priori ULP threshold.",
    "max_error_observed": 23,
    "records": [
      {
        "id": "g-eg-100-5-2",
        "reference": 110.25,
        "actual": 110.25,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "g-eg-50-4-90",
        "reference": 1705.9666670848003,
        "actual": 1705.9666670848055,
        "error_ulp": 23,
        "threshold_ulp": 32
      },
      {
        "id": "g-eg-decay",
        "reference": 34.86784401,
        "actual": 34.86784401000001,
        "error_ulp": 2,
        "threshold_ulp": 32
      },
      {
        "id": "g-eg-cont",
        "reference": 74.59123488206352,
        "actual": 74.59123488206352,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "g-eg-cont-neg",
        "reference": 33.51600230178197,
        "actual": 33.51600230178197,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-100m5m2",
        "reference": 110.25,
        "actual": 110.25,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-50m4m90",
        "reference": 1705.9666670848003,
        "actual": 1705.9666670848055,
        "error_ulp": 23,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-100mm10m10",
        "reference": 34.86784401,
        "actual": 34.86784401000001,
        "error_ulp": 2,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-100m5mm10",
        "reference": 61.39132535407594,
        "actual": 61.39132535407591,
        "error_ulp": 4,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-0m4m90",
        "reference": 0,
        "actual": 0,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-16m100m1",
        "reference": 32,
        "actual": 32,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-10000m5m11",
        "reference": 17103.393581163135,
        "actual": 17103.39358116314,
        "error_ulp": 2,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-cont-50-0p04-10",
        "reference": 74.59123488206352,
        "actual": 74.59123488206352,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-cont-50-m0p04-10",
        "reference": 33.51600230178197,
        "actual": 33.51600230178197,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-solve-t",
        "reference": 22.51708530541104,
        "actual": 22.51708530541102,
        "error_ulp": 6,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-solve-x0",
        "reference": 16,
        "actual": 16,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-solve-rate",
        "reference": 100,
        "actual": 100,
        "error_ulp": 0,
        "threshold_ulp": 32
      },
      {
        "id": "o3-eg-half-life-50pct",
        "reference": 1,
        "actual": 1,
        "error_ulp": 0,
        "threshold_ulp": 32
      }
    ]
  },
  "interfaces": {
    "compared": [
      "ui-ssr",
      "rest",
      "mcp",
      "ui-url-result-graph"
    ],
    "result": "PASS",
    "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session."
  },
  "artifacts": {
    "evidence_bundle_sha256": "6255e5afc5f6bc91807257983715eb19d839dcfc3a63a0c9903d179d2b2db86e",
    "evidence_digest": "4da3d88a831dece4fd9f1150a90d26c0527e616065945d7e70999dae5e828110",
    "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20",
    "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb",
    "production_checks": [
      {
        "id": "math.exponential_growth:output-const",
        "status": "pass",
        "detail": "output const 1.0.7 vs capability 1.0.7",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponential_growth:evidence-sha256",
        "status": "pass",
        "detail": "79f46371a72e",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponential_growth:semantic-contract",
        "status": "pass",
        "detail": "20/20",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponential_growth:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.7 vs origin 1.0.7",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponential_growth:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.exponential_growth/1.0.7/-/engineering/4da3d88a831d",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z",
        "projection_compared": false,
        "observed_live_projection_at_attestation": "VERIFIED"
      },
      {
        "id": "math.exponential_growth:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Manifest",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.exponential_growth:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Manifest",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      }
    ]
  },
  "dependencies": [
    {
      "name": "exponential-growth-engine",
      "version": "1.0.7"
    },
    {
      "name": "exponential-growth-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "exponential-growth-o3-mpmath-table",
      "version": "math-mpmath-o3"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "00c818a77ba026c2d6aa3f7402680cd2dac2a40a816209600bc3c3fcd0b8921c",
    "attested_at": "2026-09-10T02:52:51.379Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.7"
  },
  "timestamps": {
    "verified_at": "2026-09-10T03:41:50.209Z",
    "generated_at": "2026-09-10T03:41:50.209Z"
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/math.exponential_growth/1.0.7.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.exponential_growth/1.0.7",
    "calculator": "https://www.calculatorx.com/calc/math/exponential-growth",
    "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/math.exponential_growth/1.0.7.cvp.json"
  }
}