Public evidence

math.sequences

Machine-checked verification for calculation version 1.0.1 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP status

Engine id is sequence — never the add/sub arithmetic engine. n ≤ 1000. Discovery arithmetic-sequence / geometric-sequence / fibonacci. Not Pascal, not partition, not n!.

Declared partition coverage: PASS · 5/5 declared partitions (arithmetic, geometric, fibonacci, linear-recurrence, invalid-domain)
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-10-07.signed-bigint-publication
Verification revision: 2026-10-07.signed-bigint-publication · 3/3 property · digest 0c1fda7d6011

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 1.0.1 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 2026-10-07.signed-bigint-publication. Calculation version 1.0.1. CVP 1.0.0-proposed. 8/8 golden · 3/3 CVP boundary · 6/6 invalid · 3/3 property · 5/5 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest 0c1fda7d6011.

Golden (oracle-backed) 8 / 8
CVP boundary 3 / 3
Invalid input 6 / 6
Property 3 / 3
Cross-interface 5 / 5
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 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.
Verified scope all published modes
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:a75114e8f89a3f9390866ea7fa12bc62febab7be1a21cf0fc6e095ec8301a9af

Input schema sha256:fcdc6ee697b0ceb428ca8d2892c673530fca04d26462e279d100ed7f9cc92bde · Output schema sha256:2d281f0c109a5d3f45e5bf4bf1023ead53d185e0eb84a992258cb006c5775916 · 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: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-23T01:27:11.633Z
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

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

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.