Public evidence

math.sequences

Machine-checked verification for calculation version 1.0.3 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

n<=1000;coefficients48digits/raw512chars;old1.0.1 immutable pins retained.

Declared partition coverage: PASS · 5/5 declared partitions (arithmetic, geometric, fibonacci, linear_recurrence, invalid)
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-10-28.meta-metrics-v2
Verification revision: 2026-10-28.meta-metrics-v2 · 2/2 property · digest 862921453e34

Verification

Legacy regression suite: 12/12 calculation tests · Production surface contract 6/6

Three distinct suites: educational examples on the calculator page, this legacy regression count (12/12 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.3 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-28.meta-metrics-v2. Calculation version 1.0.3. CVP 1.0.0-proposed. 37/37 golden · 1/1 CVP boundary · 31/31 invalid · 2/2 property · 2/2 metamorphic · 69/69 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest 862921453e34.

Golden (oracle-backed) 37 / 37
CVP boundary 1 / 1
Invalid input 31 / 31
Property 2 / 2
Metamorphic 2 / 2
Cross-interface 69 / 69
Cross-calculator 1 / 1
CVP contract 6 / 6
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 29/29 (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.
Verified scope four integer sequence modes andfour entries
Assurance Core

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

Fingerprint sha256:51c1f0a9ba93bff9483e62b6e9090528371aa0b73d253b3477634c9385c6f7e9

Input schema sha256:70b976f827b6b541f52ad47483d655ac1e3685da8de9c790728b520f6a64e89c · Output schema sha256:004ebd84d52e458b1f969a092fc8b7b15c53d373238546a617675f7be7955d1d · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: sequence
Engine: sequence
Engine build: 2026-10-27
Evidence core: 2026-10-27T11:17:37.580Z
Rendered: 2026-10-29T17:04:55.745Z
Last reviewed: —

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

Exact integer arithmetic for four modes;AP/GP n=1..1000,Fibonacci/recurrence n=0..1000. Coefficients at most48 digits,rawtokens at most512 characters,index at most4 digits.
Digit strings only;unsafe JSON numbers rejected. Aliases must agree;unknown andinactive inputs rejected. Results use JSON numbers only within safe integers, otherwise exact decimal strings.
37 independent Python integer-enumeration/matrix-power full packs;exact complete structure/type/metadata comparison,notthird-party certification.
Large orindistinguishable exact terms omit graph explicitly;fullintegers remain inresult/work/nativeexports. Continuousreal-valued ornonintegersequences unsupported.

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

ISO 80000-2:2019 Quantities and units — Mathematics
Supports: Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.
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}
Margaret Stevens — The Maths Workbook (University of Oxford) — Chapter 3, §2: Arithmetic and Geometric Sequences and Series
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.
MIT Mathematics for Computer Science — Fibonacci Recurrences — §15.4 Solving Linear Recurrences
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.

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.