{ "protocol": { "name": "CVP", "version": "1.0.0-proposed" }, "document_status": "proposed", "calculator": { "id": "factorial", "version": "1.0.2", "title": "Factorial Calculator", "formula_family": "factorial", "capability_id": "math.factorial", "verification_revision": "2026-09-08.exact-integer-profile" }, "profile": "core", "status": "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": "factorial", "version": "1.0.2", "uri": "https://www.calculatorx.com/evidence/math.factorial/1.0.2.json", "verification_revision": "2026-09-08.exact-integer-profile" }, "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-META-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "NIST Digital Library of Mathematical Functions, Chapter 5", "kind": "other", "reference": "Gamma Function", "url": "https://dlmf.nist.gov/5" }, { "label": "NIST DLMF §5.4", "kind": "other", "reference": "Special values and extrema", "url": "https://dlmf.nist.gov/5.4" }, { "label": "CalculatorX mathematical conventions", "kind": "other", "reference": "Domain 0 ≤ n ≤ 5000; exact BigInt n!" } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Ordinary nonnegative integer factorial" }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Precomputed Python math.factorial table — CPython arbitrary-precision int, not Node BigInt and not IEEE-754 binary64", "engine": { "name": "factorial-python-math-o3", "independent_of_iut": true, "same_runtime_as_iut": false, "library": "Python 3.13.5 math.factorial", "generator_version": "1.0.0", "generator_sha256": "de8c1b59ea29ed21ee36376627208b80872710dfa87b27bb367a39fdc609a782", "table_sha256": "f96ef604c13d8e4da222c3e1e5347cb80273ab2b4b5f794c5a23cb956ba4a9a6", "seed": "20260908", "source": "https://www.calculatorx.com/developers/cvp/reproduce/factorial-o3-tables.json", "public_table": "/developers/cvp/reproduce/factorial-o3-tables.json", "public_generator": "/developers/cvp/reproduce/generate-factorial-o3.py", "public_checker": "/developers/cvp/reproduce/check-factorial-o3-rest.py", "runtime": "python3", "numeric_model": "CPython arbitrary-precision int — not IEEE-754 binary64", "representation": "exact unbounded integer (CPython int)", "criterion": "actual exact decimal string === independent oracle exact decimal string" } }, { "class": "O3", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O3 table vs IUT exact decimal string; identity match (not ULP). 5000! is the published domain maximum.", "engine": { "name": "factorial-python-math-o3", "independent_of_iut": true, "same_runtime_as_iut": false, "library": "Python 3.13.5 math.factorial", "generator_version": "1.0.0", "generator_sha256": "de8c1b59ea29ed21ee36376627208b80872710dfa87b27bb367a39fdc609a782", "table_sha256": "f96ef604c13d8e4da222c3e1e5347cb80273ab2b4b5f794c5a23cb956ba4a9a6", "seed": "20260908", "source": "https://www.calculatorx.com/developers/cvp/reproduce/factorial-o3-tables.json", "public_table": "/developers/cvp/reproduce/factorial-o3-tables.json", "public_generator": "/developers/cvp/reproduce/generate-factorial-o3.py", "public_checker": "/developers/cvp/reproduce/check-factorial-o3-rest.py", "runtime": "python3", "numeric_model": "CPython arbitrary-precision int — not IEEE-754 binary64", "representation": "exact unbounded integer (CPython int)", "criterion": "actual exact decimal string === independent oracle exact decimal string" } }, { "class": "O2", "reference_scope": "expected_values", "scope": "expected_values", "label": "Separate-module factorial oracle — independent Node BigInt product (same runtime as IUT)", "engine": { "name": "factorial-reference", "independent_of_iut": true, "same_runtime_as_iut": true, "runtime": "node", "numeric_model": "exact_integer", "representation": "exact_integer", "criterion": "actual exact decimal string === independent oracle exact decimal string", "algorithms": [ "bigint-product" ], "arithmetic": "BigInt", "comparison": "exact_equality" } }, { "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": "factorial-reference", "independent_of_iut": true, "same_runtime_as_iut": true, "runtime": "node", "numeric_model": "exact_integer", "representation": "exact_integer", "criterion": "actual exact decimal string === independent oracle exact decimal string", "algorithms": [ "bigint-product" ], "arithmetic": "BigInt", "comparison": "exact_equality" } } ], "notes": "Golden expected values prefer O3 Python math.factorial (heterogeneous runtime). O2 is a live Node BigInt product that shares V8 with the IUT (same_runtime_as_iut). IUT numeric model is exact_integer with BigInt arithmetic and exact_equality. Node is a runtime dependency, not IEEE-754 binary64. ULP is not applicable." }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "n! exact BigInt product; acceptance is exact decimal-string identity" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "0 ≤ n ≤ 5000 ordinary factorial" }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless integer" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O3 Python math.factorial expected_values/numerical_behavior (exact decimal identity) + O2 Node BigInt live oracle (same_runtime_as_iut)" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "8/8 legacy golden; 6/6 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "7/7 boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "6 invalid-domain cases" }, "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": "2/2 declared partitions (factorial, invalid-domain) · 8 golden / 7 boundary unique cases · 6 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "1/1 contract checks" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine factorial; exact_integer BigInt (IUT/O2) · CPython int (O3). Node is a runtime dependency, not the numeric model" }, "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 1.0.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.2 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20" }, "CVP-DIM-01": { "result": "SKIP", "applicability": "not_applicable", "notes": "Unitless core calculator — no physical dimension algebra" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "19/19 property" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "5/5 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." }, "CVP-ORACLE-01": { "result": "PASS", "applicability": "higher_assurance", "notes": "O3 23/23 tabulated vectors vs IUT · Exact decimal-string identity vs Python math.factorial on the 23 published tabulated vectors (named 0,1,5,10,20,100,5000 plus 16 seeded n in 0–4999). 5000! is verified as the full 16,326-digit value and as SHA-256 of those ASCII digits. This is not a whole-domain proof beyond the published table." }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "expert_reviewed=false" } }, "tests": { "golden": { "passed": 6, "total": 6, "failed": 0, "case_ids": [ "g-0", "g-1", "g-5", "g-20", "g-100", "g-5000" ] }, "boundary": { "passed": 7, "total": 7, "failed": 0, "case_ids": [ "negative", "fraction", "above-max", "empty", "boundary-alias-nInput", "boundary-non-numeric", "boundary-half-integer" ] }, "invalid": { "passed": 6, "total": 6, "failed": 0, "case_ids": [ "negative", "fraction", "above-max", "empty", "boundary-non-numeric", "boundary-half-integer" ] }, "property": { "passed": 19, "total": 19, "failed": 0, "case_ids": [ "prop-0", "prop-1", "prop-5", "prop-gen-00", "prop-gen-01", "prop-gen-02", "prop-gen-03", "prop-gen-04", "prop-gen-05", "prop-gen-06", "prop-gen-07", "prop-gen-08", "prop-gen-09", "prop-gen-10", "prop-gen-11", "prop-gen-12", "prop-gen-13", "prop-gen-14", "prop-gen-15" ], "definition_ids": [ "zero-factorial", "one-factorial", "five-factorial", "seeded-recurrence-digits" ] }, "round_trip": { "passed": 0, "total": 0, "failed": 0, "case_ids": [] }, "metamorphic": { "passed": 5, "total": 5, "failed": 0, "case_ids": [ "meta-recurrence-5", "meta-recurrence-7", "meta-recurrence-20", "meta-recurrence-100", "meta-recurrence-seeded" ], "definition_ids": [ "n-plus-one" ] }, "contract": { "passed": 1, "total": 1, "failed": 0 }, "cross_interface": { "passed": 1, "total": 1, "failed": 0, "case_ids": [ "iface-5" ] }, "o3": { "passed": 23, "total": 23, "failed": 0, "case_ids": [ "o3-fact-0", "o3-fact-1", "o3-fact-5", "o3-fact-10", "o3-fact-20", "o3-fact-100", "o3-fact-5000", "o3-fact-rand-00", "o3-fact-rand-01", "o3-fact-rand-02", "o3-fact-rand-03", "o3-fact-rand-04", "o3-fact-rand-05", "o3-fact-rand-06", "o3-fact-rand-07", "o3-fact-rand-08", "o3-fact-rand-09", "o3-fact-rand-10", "o3-fact-rand-11", "o3-fact-rand-12", "o3-fact-rand-13", "o3-fact-rand-14", "o3-fact-rand-15" ], "generator_id": "factorial-python-math-o3", "seed": "20260908", "table_sha256": "f96ef604c13d8e4da222c3e1e5347cb80273ab2b4b5f794c5a23cb956ba4a9a6", "criterion": "actual exact decimal string === independent oracle exact decimal string", "exact_mismatches": 0, "reproduce": "python3 generate-factorial-o3.py", "table_url": "/developers/cvp/reproduce/factorial-o3-tables.json", "generator_url": "/developers/cvp/reproduce/generate-factorial-o3.py", "checker_url": "/developers/cvp/reproduce/check-factorial-o3-rest.py", "claim_scope": "Exact decimal-string identity vs Python math.factorial on the 23 published tabulated vectors (named 0,1,5,10,20,100,5000 plus 16 seeded n in 0–4999). 5000! is verified as the full 16,326-digit value and as SHA-256 of those ASCII digits. 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