{
  "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": "discrete-fourier-transform",
    "version": "1.2.0",
    "title": "Discrete Fourier Transform Calculator",
    "formula_family": "dft",
    "capability_id": "math.transform.dft",
    "verification_revision": "2026-09-22.special-transform-cvp"
  },
  "profile": "core",
  "verified_scope": "all published modes",
  "status": "VERIFIED",
  "verification_status": "VERIFIED",
  "production_freshness": "CURRENT",
  "overall_trust": "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": "discrete-fourier-transform",
    "version": "1.2.0",
    "uri": "https://www.calculatorx.com/evidence/math.transform.dft/1.2.0.json",
    "verification_revision": "2026-09-22.special-transform-cvp"
  },
  "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-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "ISO 80000-2:2019 Quantities and units — Mathematics",
        "kind": "standard",
        "reference": "Discrete Fourier transform of a finite sequence"
      },
      {
        "label": "Oppenheim & Schafer, Discrete-Time Signal Processing — DFT / radix-2 FFT, Numpy backward normalization",
        "kind": "other",
        "reference": "X[k]=Σ x[n] e^{−2πi kn/N}; inverse 1/N; radix-2 Cooley–Tukey when N=2^k"
      }
    ]
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Unrounded O2 naive DFT definition vs IUT roundSmart / radix-2 FFT"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "N≤64. FFT requires N=2^k. Numpy backward. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS."
    },
    "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": "6/6 legacy golden; 5/5 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "2/2 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 + 2/2 oracle-backed error-code (exact_error_match, not ULP)"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "max_error_observed_ulp=4851932361532738000; policy declared a priori"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "5/5 declared partitions (dft, idft, fft, ifft, invalid-domain) · 6 legacy golden / 3 CVP boundary unique cases · 3 Evidence invalid-input (may overlap boundary)"
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "5/5 CVP contract · release-artifacts-aligned=PASS · schema-output-required-declared=PASS · schema-valid-input-executes=PASS · engine-success-output-validates-schema=PASS · rest-success-payload-validates-schema=PASS"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine discrete-fourier-transform; 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 @ 2026-09-22T04:01:06.903Z · live site-wide report stale @ 2026-09-22T04:01:10.986Z (3 other capabilities) · local checks pass · attestation_id=2215e43bd5546922b9b7142484b40765c775fc3ae5e41ddad6f42d09a93ba13b · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-09-22T04:01:06.903Z · Live production status STALE (3 capabilities; 186 remain CURRENT) @ 2026-09-22T04:01:10.986Z · Public schema 1.2.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.2.0 · 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 · 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=ab66486c562fc7c8f16c9af1e1fa18208ecc7410ff0a33a12be34f8ad968b22b · verified_at=2026-09-22T03:44:41.289Z · evidence_attested_at=2026-09-22T03:44:41.289Z · last_confirmed_current_at=2026-09-22T04:01:06.903Z · rendered_at=2026-09-22T04:01:11.036Z · binds=cvp_core_sha256",
      "check_result": "PASS",
      "production_state": "CURRENT",
      "binding_current": true
    },
    "CVP-DIM-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "length-N complex bins"
    },
    "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": "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": "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 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": "ae8db004235a38b1b7d19542680625cadd4f10cb80aa30d7affae347bf9b15bd",
    "evidence_digest": "01fbb8a62b65f89f1c85631cc77cdb5d8a8e0a6831bb4bfa8300c9be5a800e49",
    "production_sha256": "ab66486c562fc7c8f16c9af1e1fa18208ecc7410ff0a33a12be34f8ad968b22b",
    "attested_catalog_sha256": "e00979a0a41218268bfef843cbca86f27d9855fac81f401e5f9defefca4b39ef",
    "production_checks": [
      {
        "id": "math.transform.dft:output-const",
        "status": "pass",
        "detail": "output const 1.2.0 vs capability 1.2.0",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:evidence-sha256",
        "status": "pass",
        "detail": "430d626a3d6e",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:semantic-contract",
        "status": "pass",
        "detail": "17/17",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.2.0 vs origin 1.2.0",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.transform.dft/1.2.0/2026-09-22.special-transform-cvp/core/01fbb8a62b65",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z",
        "projection_compared": false
      },
      {
        "id": "math.transform.dft:cvp-latest-alias-agrees",
        "status": "pass",
        "detail": "math.transform.dft/1.2.0/2026-09-22.special-transform-cvp/core/01fbb8a62b65",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z",
        "projection_compared": false
      },
      {
        "id": "math.transform.dft:cvp-immutable-manifest-fetch",
        "status": "pass",
        "detail": "public=200 origin=200",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:cvp-immutable-manifest-sha256",
        "status": "pass",
        "detail": "01fbb8a62b65",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:cvp-latest-alias-matches-immutable",
        "status": "pass",
        "detail": "math.transform.dft/1.2.0/2026-09-22.special-transform-cvp/core/01fbb8a62b65",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z",
        "projection_compared": false
      },
      {
        "id": "math.transform.dft:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      },
      {
        "id": "math.transform.dft:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T03:44:41.289Z"
      }
    ],
    "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": "01fbb8a62b65f89f1c85631cc77cdb5d8a8e0a6831bb4bfa8300c9be5a800e49",
          "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": "01fbb8a62b65f89f1c85631cc77cdb5d8a8e0a6831bb4bfa8300c9be5a800e49",
          "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": "430d626a3d6ec67e7ebac4b9ebd66bbe341196a0f4bbde2dba47ac5e8cd66f49",
          "note": "Published Evidence JSON core — Trust freshness / production bind subject"
        },
        {
          "name": "evidence_catalog_digest",
          "field": "artifacts.attested_catalog_sha256",
          "digest_scope": "capability_catalog",
          "value": "e00979a0a41218268bfef843cbca86f27d9855fac81f401e5f9defefca4b39ef",
          "note": "Capability catalog integrity; site-wide, not per-suite fingerprint"
        }
      ]
    },
    "cvp_core_sha256": "01fbb8a62b65f89f1c85631cc77cdb5d8a8e0a6831bb4bfa8300c9be5a800e49"
  },
  "dependencies": [
    {
      "name": "discrete-fourier-transform-engine",
      "version": "1.2.0"
    },
    {
      "name": "discrete-fourier-transform-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "2215e43bd5546922b9b7142484b40765c775fc3ae5e41ddad6f42d09a93ba13b",
    "attested_at": "2026-09-22T03:44:41.289Z",
    "last_confirmed_current_at": "2026-09-22T04:01:06.903Z",
    "site_attestation_current": false,
    "capability_attestation_current": true,
    "bound_snapshot_status": "pass",
    "live_report_status": "stale",
    "bound_attested_at": "2026-09-22T04:01:06.903Z",
    "live_updated_at": "2026-09-22T04:01:10.986Z",
    "bound_snapshot": {
      "status": "pass",
      "attested_at": "2026-09-22T04:01:06.903Z",
      "site_stale_count": 3
    },
    "live_site_status": {
      "href": "/.well-known/calculatorx-production-attestation.json"
    },
    "bound_snapshot_site_stale_count": 3,
    "site_stale_capability_count": 3,
    "evidence_attested_at": "2026-09-22T03:44:41.289Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.2.0",
    "external_third_party": false,
    "note": "Named expert review not performed"
  },
  "timestamps": {
    "verified_at": "2026-09-22T03:44:41.289Z",
    "generated_at": "2026-09-22T03:44:41.289Z",
    "rendered_at": "2026-09-22T04:01:11.036Z",
    "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": 5,
      "total": 5,
      "failed": 0
    },
    "boundary": {
      "passed": 3,
      "total": 3,
      "failed": 0
    },
    "invalid": {
      "passed": 5,
      "total": 5,
      "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": 5,
      "total": 5,
      "failed": 0
    },
    "cross_interface": {
      "passed": 4,
      "total": 4,
      "failed": 0
    }
  },
  "numerical": {
    "representation": "IEEE-754 binary64; IUT publishes toPrecision(12) / roundSmart",
    "tolerance": {
      "type": "relative",
      "value": 1e-8,
      "rationale": "O2 is unrounded closed-form identities (antiderivative, quadratic formula, vertex, y0 e^{kΔt}, Lagrange/lerp). IUT is iterative/quadrature with 12-digit publication. Relative 1e-8 covers truncation on well-posed goldens plus roundSmart; |expected|<1e-8 uses absolute 1e-6 because golden/brent stop at default tol 1e-8. Declared a priori.",
      "declared_before_evaluation": true
    },
    "max_error_observed": 4851932361532738000
  },
  "coverage": {
    "partitions": [
      {
        "id": "dft",
        "description": "dft",
        "exercised": true,
        "case_count": 14
      },
      {
        "id": "idft",
        "description": "idft",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "fft",
        "description": "fft",
        "exercised": true,
        "case_count": 3
      },
      {
        "id": "ifft",
        "description": "ifft",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 5
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "X[k]=Σ x[n] e^{−2πi kn/N}; DFT and radix-2 FFT are methods of one capability"
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module DFT oracle — unnormalized X[k]=Σ x[n] e^{−2πi kn/N} (Numpy backward 1/N on inverse); always direct sum, never radix-2",
        "engine": {
          "name": "dft-reference",
          "precision_bits": 53,
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs unrounded naive DFT vs IUT roundSmart / radix-2 FFT — relative 1e-8 / abs 1e-6 near 0",
        "engine": {
          "name": "dft-reference",
          "precision_bits": 53,
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      }
    ]
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/math.transform.dft/1.2.0.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.transform.dft/1.2.0",
    "calculator": "https://www.calculatorx.com/calc/math/discrete-fourier-transform",
    "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.transform.dft/1.2.0.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/math.transform.dft/1.2.0/2026-09-22.special-transform-cvp.cvp.json",
    "manifest_core": "https://www.calculatorx.com/evidence/math.transform.dft/1.2.0/2026-09-22.special-transform-cvp.01fbb8a62b65.cvp.json"
  },
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}