CVP verified calculation capability
Arithmetic and geometric sequences, Fibonacci (F_0=0), and linear recurrences. Exact BigInt. Discovery pages share this capability. Not Pascal, not partition, not n!. Engine id is sequence — never arithmetic.
Math Capability ID math.sequences version 1.0.3 CVP VERIFIED CURRENT Core
Arithmetic
a_n = a + (n−1)da_n = a r^{n−1}F_n = F_{n−1} + F_{n−2}Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
n | — | — | input / output |
nInput | — | — | input / output |
a | — | — | input / output |
first | — | — | input / output |
a1 | — | — | input / output |
aInput | — | — | input / output |
d | — | — | input |
difference | — | — | input |
common_difference | — | — | input |
dInput | — | — | input |
r | — | — | input |
ratio | — | — | input |
common_ratio | — | — | input |
rInput | — | — | input |
p | — | — | input |
pInput | — | — | input |
q | — | — | input |
qInput | — | — | input |
a0 | — | — | input |
u0 | — | — | input |
a0Input | — | — | input |
u1 | — | — | input |
a1Input | — | — | input |
review | — | — | output |
api_version | — | — | output |
api_contract_version | — | — | output |
spec_version | — | — | output |
page | Canonical calculator page URL | — | output |
links | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | integer |
exactness | exact |
algorithm | BigInt AP/GP closed forms; iterative Fibonacci and second-order recurrence |
valid_domain | AP/GP n1..1000,Fibonacci/recurrence n0..1000; signed integer coefficients<=48digits, rawtokens<=512chars,index<=4digits; strict agreeing aliases andactive fields |
singularity_policy | Reject invalid/missing/unknown/conflicting/inactive inputs; no approximate arithmetic. Safe JSON integers or exactdecimalstrings; explicit graph omission outside safe coordinates. |
branch_policy | not applicable — integer domain |
tolerance | not applicable — exact integer identity |
convergence | not applicable — non-iterative Euclidean / combinatorial |
conditioning | not applicable — not a floating matrix |
rounding | none — BigInt / exact integer |
overflow | coded error or stringified BigInt when exceeding JSON number |
reproducibility | deterministic exact integer + Capability@Version |
independent_oracle | 37 independent CPython integer enumeration/matrix-power complete packs; exact complete keys/types/values/metadata; old1.0.1 pins retained |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
mode=arithmetic a=2 d=3 n=5 → 14
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · four integer sequence modes andfour entries. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/sequence' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"arithmetic","a":2,"d":3,"n":5},"calculation_version":"1.0.3"}'{
"inputs": {
"mode": "arithmetic",
"a": 2,
"d": 3,
"n": 5
},
"calculation_version": "1.0.3"
}POST /api/v1/calc/sequence. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Declared calculation modes for this capability.
arithmeticgeometricfibonaccilinear_recurrenceHuman-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior
Inspect, then execute. Same engine as REST and the human calculator.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.sequences"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: execute_calculation' \
-d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.sequences","inputs":{"mode":"arithmetic","a":2,"d":3,"n":5},"calculation_version":"1.0.3"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.0.3) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.