{
  "capability_id": "math.sequences",
  "tool_id": "sequence",
  "engine": "sequence",
  "calculation_version": "1.0.1",
  "generated_at": "2026-10-23T01:27:11.633Z",
  "engine_build": "2026-10-14",
  "test_count": 12,
  "passed": 12,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 4,
      "total": 4
    },
    "boundary": {
      "passed": 2,
      "total": 2
    },
    "property": {
      "passed": 6,
      "total": 6
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/math/sequence",
  "api": "https://www.calculatorx.com/api/v1/calc/sequence",
  "schema_input": "https://www.calculatorx.com/schemas/math.sequences.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.sequences.output.json",
  "assumptions": [
    "The Result Card includes an engine-linked stem figure of a_k (marker is published term; at most 16 indices, window ending at n). Same closed form / recurrence as REST/MCP. Terms array is not a REST field. Huge BigInt terms omit the figure.",
    "Integers",
    "n ≤ 1000",
    "Not Pascal / partition / n!"
  ],
  "limitations": [
    "Not Pascal’s triangle and not integer partition",
    "Not /calc/math/factorial and not /calc/math/permutation-combination",
    "Integers only — no Binet float Fibonacci",
    "Engine id is sequence; never alias the add/sub engine id arithmetic",
    "n=0 on AP/GP → VALUE_MUST_BE_POSITIVE",
    "n>1000 → VALUE_ABOVE_MAX",
    "unknown mode → INVALID_MODE"
  ],
  "boundary_conditions": [
    "unknown mode (including pascal) → INVALID_MODE",
    "n=0 on AP/GP → VALUE_MUST_BE_POSITIVE",
    "n>1000 → VALUE_ABOVE_MAX"
  ],
  "sources": [
    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "url": "https://www.iso.org/standard/64973.html",
      "supports": "Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.",
      "kind": "standard",
      "publisher": "International Organization for Standardization",
      "reference_scope": "all"
    },
    {
      "title": "Knuth, The Art of Computer Programming, Fibonacci F₀=0 F₁=1 and linear recurrences",
      "supports": "F_n = F_{n-1}+F_{n-2} with F_0=0; u_n = p u_{n-1} + q u_{n-2}",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
    },
    {
      "title": "Margaret Stevens — The Maths Workbook (University of Oxford)",
      "section": "Chapter 3, §2: Arithmetic and Geometric Sequences and Series",
      "url": "https://www.some.ox.ac.uk/wp-content/uploads/2024/08/Maths-Workbook.pdf",
      "supports": "Arithmetic terms and sums from first term and common difference, geometric terms and finite sums from first term and common ratio, including derivations. At ratio 1 the finite geometric sum is n times the first term; it is the removable special case of the quoted expression. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.",
      "kind": "reference",
      "publisher": "University of Oxford, Department of Economics; hosted by Somerville College"
    },
    {
      "title": "MIT Mathematics for Computer Science — Fibonacci Recurrences",
      "section": "§15.4 Solving Linear Recurrences",
      "url": "https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/mit6_042js15_textbook.pdf",
      "supports": "The Fibonacci recurrence with F₀=0 and F₁=1, its generating function and Binet expression. The recurrence identifies the mathematical sequence; it does not independently test a fast-doubling implementation. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.",
      "kind": "reference",
      "publisher": "Massachusetts Institute of Technology"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:a75114e8f89a3f9390866ea7fa12bc62febab7be1a21cf0fc6e095ec8301a9af",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 12,
      "total": 12,
      "golden": 4,
      "boundary": 2,
      "property": 6
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-10-14T05:05:51.930Z",
  "rendered_at": "2026-10-23T01:27:11.633Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.1",
    "artifacts": {
      "engine": "1.0.1",
      "page": "1.0.1",
      "capability": "1.0.1",
      "evidence": "1.0.1",
      "input_schema": "1.0.1",
      "output_schema": "1.0.1",
      "mcp_contract": "1.0.1"
    },
    "digests": {
      "input_schema_sha256": "fcdc6ee697b0ceb428ca8d2892c673530fca04d26462e279d100ed7f9cc92bde",
      "output_schema_sha256": "2d281f0c109a5d3f45e5bf4bf1023ead53d185e0eb84a992258cb006c5775916",
      "evidence_sha256": "c371a220db3f20db093f231dac001682cc181b52d60f1aa013a6d4488a55e354",
      "evidence_core_sha256": "c371a220db3f20db093f231dac001682cc181b52d60f1aa013a6d4488a55e354",
      "capability_sha256": "2f41b23c307554cd590ec232336f3d59b2194cd2d7245034cc5d8add33526b96",
      "engine_sha256": "a664ae25cd2134de7de43a99352933043215473589aec38c9416508150cb1008",
      "mcp_contract_sha256": "8defa770ea0b34118e3444b698842353896edfffa88b4ef1c34898f3f5378790"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.1"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}
