{
  "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": "combinatorics",
    "version": "1.0.0",
    "title": "Permutation and Combination Calculator",
    "formula_family": "combinatorics",
    "capability_id": "math.combinatorics",
    "verification_revision": "2026-09-22.discrete-algebra-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": "exact_integer",
    "os": "darwin"
  },
  "suite": {
    "id": "combinatorics",
    "version": "1.0.0",
    "uri": "https://www.calculatorx.com/evidence/math.combinatorics/1.0.0.json",
    "verification_revision": "2026-09-22.discrete-algebra-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-PROP-01",
    "CVP-XCAL-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "ISO 80000-2:2019 Quantities and units — Mathematics (combinatorial numbers)",
        "kind": "other"
      },
      {
        "label": "NIST / standard discrete-math identity P(n,k) = C(n,k)·k!",
        "kind": "other"
      }
    ]
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "P(n,k) and C(n,k) exact BigInt; O2 factorial-ratio dual-checked against multiplicative formula"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "0 ≤ k ≤ n ≤ 1000. Hub /permutation-combination. Not n!, not Pascal’s triangle. Declared partitions are the 2 published modes plus invalid-domain."
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "dimensionless integer"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O2 expected_values/numerical_behavior (factorial-ratio dual-checked against multiplicative; exact_equality; same_runtime_as_iut)"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "2/2 legacy golden; 5/5 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "2/2 numeric-edge Evidence + 2/2 near-singularity numeric; illegal enum/system is Invalid only"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3 Evidence illegal-input + 4/4 oracle-backed error-code (exact_error_match, not ULP)"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "exact_integer · BigInt · exact_equality (actual exact decimal string === independent oracle exact decimal string); mismatches=0; ULP not applicable"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 declared partitions (combination, permutation, invalid-domain) · 2 legacy golden / 4 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 combinatorics; exact_integer BigInt (IUT/O2). Node is a runtime dependency, not the numeric model"
    },
    "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 @ 2026-09-22T04:01:09.113Z (19 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 (19 capabilities; 170 remain CURRENT) @ 2026-09-22T04:01:09.113Z · 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 · 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=2026-09-22T02:48:32.771Z · evidence_attested_at=2026-09-22T02:48:32.771Z · last_confirmed_current_at=2026-09-22T04:01:06.903Z · rendered_at=2026-09-22T04:01:09.161Z · binds=cvp_core_sha256",
      "check_result": "PASS",
      "production_state": "CURRENT",
      "binding_current": true
    },
    "CVP-DIM-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "Unitless core calculator — no physical dimension algebra"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 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": "2/2 cross-calculator · xcal-p-nn-factorial PASS vs math.factorial; xcal-c-times-kfact PASS vs math.factorial"
    },
    "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": "73cc35cb9be890432c8dbc741367b7fc7883b25115159a3e0ac7a5287e440c96",
    "evidence_digest": "423bc06f604d12964439d290b70c65eeff9c8c354546f30f594b40d41c80ef5e",
    "production_sha256": "ab66486c562fc7c8f16c9af1e1fa18208ecc7410ff0a33a12be34f8ad968b22b",
    "attested_catalog_sha256": "e00979a0a41218268bfef843cbca86f27d9855fac81f401e5f9defefca4b39ef",
    "production_checks": [
      {
        "id": "math.combinatorics:output-const",
        "status": "pass",
        "detail": "output const 1.0.0 vs capability 1.0.0",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:evidence-sha256",
        "status": "pass",
        "detail": "06d5dfbde9ac",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:semantic-contract",
        "status": "pass",
        "detail": "11/11",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.0 vs origin 1.0.0",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.combinatorics/1.0.0/2026-09-22.discrete-algebra-cvp/core/423bc06f604d",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z",
        "projection_compared": false
      },
      {
        "id": "math.combinatorics:cvp-latest-alias-agrees",
        "status": "pass",
        "detail": "math.combinatorics/1.0.0/2026-09-22.discrete-algebra-cvp/core/423bc06f604d",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z",
        "projection_compared": false
      },
      {
        "id": "math.combinatorics:cvp-immutable-manifest-fetch",
        "status": "pass",
        "detail": "public=200 origin=200",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:cvp-immutable-manifest-sha256",
        "status": "pass",
        "detail": "423bc06f604d",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:cvp-latest-alias-matches-immutable",
        "status": "pass",
        "detail": "math.combinatorics/1.0.0/2026-09-22.discrete-algebra-cvp/core/423bc06f604d",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z",
        "projection_compared": false
      },
      {
        "id": "math.combinatorics:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      },
      {
        "id": "math.combinatorics:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-22T02:48:32.771Z"
      }
    ],
    "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": "423bc06f604d12964439d290b70c65eeff9c8c354546f30f594b40d41c80ef5e",
          "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": "423bc06f604d12964439d290b70c65eeff9c8c354546f30f594b40d41c80ef5e",
          "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": "06d5dfbde9ac940d52af37eb680cb1d3540b45ef31c53e4048d1db28eb7c77b5",
          "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": "423bc06f604d12964439d290b70c65eeff9c8c354546f30f594b40d41c80ef5e"
  },
  "dependencies": [
    {
      "name": "combinatorics-engine",
      "version": "1.0.0"
    },
    {
      "name": "combinatorics-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "math.factorial",
      "version": "1.0.2",
      "role": "cross_calculator_peer",
      "capability_id": "math.factorial",
      "evidence_digest": "b7065c58307c3477dc76583b92ad80a0fffcbe5c4ed3ec567d0cd56fa6edf1a6",
      "evidence": "https://www.calculatorx.com/evidence/math.factorial/1.0.2.cvp.json"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "2215e43bd5546922b9b7142484b40765c775fc3ae5e41ddad6f42d09a93ba13b",
    "attested_at": "2026-09-22T02:48:32.771Z",
    "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": "2026-09-22T04:01:09.113Z",
    "bound_snapshot": {
      "status": "pass",
      "attested_at": "2026-09-22T04:01:06.903Z",
      "site_stale_count": 19
    },
    "live_site_status": {
      "href": "/.well-known/calculatorx-production-attestation.json"
    },
    "bound_snapshot_site_stale_count": 19,
    "site_stale_capability_count": 19,
    "evidence_attested_at": "2026-09-22T02:48:32.771Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.0",
    "external_third_party": false,
    "note": "Named expert review not performed"
  },
  "timestamps": {
    "verified_at": "2026-09-22T02:48:32.771Z",
    "generated_at": "2026-09-22T02:48:32.771Z",
    "rendered_at": "2026-09-22T04:01:09.161Z",
    "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": 4,
      "total": 4,
      "failed": 0
    },
    "invalid": {
      "passed": 7,
      "total": 7,
      "failed": 0,
      "comparison": "exact_error_match"
    },
    "property": {
      "passed": 3,
      "total": 3,
      "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": 3,
      "total": 3,
      "failed": 0
    },
    "cross_calculator": {
      "passed": 2,
      "total": 2,
      "failed": 0
    }
  },
  "numerical": {
    "representation": "exact_integer",
    "tolerance": {
      "type": "exact",
      "value": 0,
      "declared_before_evaluation": true,
      "rationale": "P(n,k) and C(n,k) are exact integers. Acceptance is exact decimal-string identity vs an O2 factorial-ratio dual-checked against the multiplicative formula. Comparison is exact_equality; ULP is not applicable. Node/V8 is a runtime dependency, not the numeric model. Declared a priori."
    },
    "profile": "exact_integer",
    "arithmetic": "BigInt",
    "comparison": "exact_equality",
    "criterion": "actual exact decimal string === independent oracle exact decimal string",
    "exact_policy": true,
    "ulp_applicable": false,
    "exact_mismatches": 0
  },
  "coverage": {
    "partitions": [
      {
        "id": "combination",
        "description": "combination",
        "exercised": true,
        "case_count": 15
      },
      {
        "id": "permutation",
        "description": "permutation",
        "exercised": true,
        "case_count": 5
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 7
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "P(n,k) = n!/(n−k)! and C(n,k) = n!/(k!(n−k)!)"
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module combinatorics oracle — n!/(n−k)! and n!/(k!(n−k)!) dual-checked against the multiplicative formula (same runtime as IUT; not IUT transcription)",
        "engine": {
          "name": "combinatorics-reference",
          "numeric_model": "exact_integer",
          "criterion": "actual exact decimal string === independent oracle exact decimal string",
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs exact decimal-string identity vs IUT — exact_equality, ULP not applicable",
        "engine": {
          "name": "combinatorics-reference",
          "numeric_model": "exact_integer",
          "criterion": "actual exact decimal string === independent oracle exact decimal string",
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      }
    ]
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/math.combinatorics/1.0.0.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.combinatorics/1.0.0",
    "calculator": "https://www.calculatorx.com/calc/math/permutation-combination",
    "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.combinatorics/1.0.0.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/math.combinatorics/1.0.0/2026-09-22.discrete-algebra-cvp.cvp.json",
    "manifest_core": "https://www.calculatorx.com/evidence/math.combinatorics/1.0.0/2026-09-22.discrete-algebra-cvp.423bc06f604d.cvp.json"
  },
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}