CVP verified calculation capability

Coordinate geometry Calculation Capability

Distance, midpoint, slope, two-point line, point-line distance, line intersection, and angle in the plane. Slope is not share-key m. Discovery /line-equation, /point-line-distance, /line-intersection, /angle-between-lines. Not Pythagorean, not CAS.

Math · Geometry Capability ID math.geometry.coordinate version 1.8.0 CVP VERIFIED CURRENT Core

Model

Coordinate geometry primitives

Coordinate geometry primitives: Distance, midpoint, slope, two-point line, point-line distance, line intersection, and principal angle between lines
Distance: d = √((x₂−x₁)²+(y₂−y₁)²)
Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)
Slope: slope = (y₂−y₁)/(x₂−x₁)
Two-point line: A = y₂ − y₁, B = x₁ − x₂, C = x₂ y₁ − y₂ x₁
Point-line distance: |Ax₀ + By₀ + C| / √(A² + B²)
Line intersection: A₁x + B₁y + C₁ = 0 ∩ A₂x + B₂y + C₂ = 0
Angle between lines: θ = arccos(|A₁A₂ + B₁B₂| / (√(A₁²+B₁²) √(A₂²+B₂²))), 0° ≤ θ ≤ 90°

Modes: angle · angle-between · angle-between-lines · angle between · angle between lines · dist · dist-to-line · dist to line · distance · distance-to-line · distance to line · equation · gradient · intersect · intersection · length · line · line-angle · line-equation · line-intersect · line-intersection · line angle · line equation · line intersect · line intersection · mid · midpoint · point-line · point-line-distance · point-to-line · point line · point line distance · point to line · slope · two-line · two-line-angle · two-line-intersection · two-lines · two-point · two-point-line · two line · two line angle · two line intersection · two lines · two point · two point line

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit policy	Role
`x1`	length	consistent length unit	input / output
`y1`	length	consistent length unit	input / output
`x2`	length	consistent length unit	input / output
`y2`	length	consistent length unit	input / output
`x0`	length	consistent length unit	input / output
`y0`	length	consistent length unit	input / output
`x3`	length	consistent length unit	input / output
`y3`	length	consistent length unit	input / output
`x4`	length	consistent length unit	input / output
`y4`	length	consistent length unit	input / output
`px`	length	consistent length unit	input
`py`	length	consistent length unit	input
`distance`	length	consistent length unit	output
`mx`	length	consistent length unit	output
`my`	length	consistent length unit	output
`slope`	—	—	output
`vertical`	—	—	output
`intercept`	length	consistent length unit	output
`equation`	—	—	output
`standard`	—	—	output
`A`	—	—	output
`B`	—	—	output
`C`	—	—	output
`signed`	length	consistent length unit	output
`foot_x`	length	consistent length unit	output
`foot_y`	length	consistent length unit	output
`x`	length	consistent length unit	output
`y`	length	consistent length unit	output
`A1`	—	—	output
`B1`	—	—	output
`C1`	—	—	output
`A2`	—	—	output
`B2`	—	—	output
`C2`	—	—	output
`standard1`	—	—	output
`standard2`	—	—	output
`angle_deg`	scalar plane angle	—	output
`angle_rad`	scalar plane angle	—	output
`supplement_deg`	scalar plane angle	—	output
`dx`	—	—	output
`dy`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	real
`exactness`	float64
`algorithm`	exact dyadic predicates and rational intermediates on normalized binary64; scaled norm and atan2(abs cross,abs dot); full binary64 presentation
`valid_domain`	finite normal nonzero binary64 coordinates or zero; strict decimal inputs; all published numeric results normal or zero; coincident points invalid for slope and all line operations
`singularity_policy`	INVALID_INPUT on coincident defining points; exact predicates code parallel/coincident; NUMERIC_RANGE on unrepresentable nonzero outputs; near-parallel results are input-sensitive
`branch_policy`	not applicable — real principal value only
`tolerance`	type: relative; value: 2e-12; note: Exact zero/discrete fields; well-conditioned reference comparisons, not an input perturbation bound
`convergence`	not applicable — non-iterative
`conditioning`	exact predicates apply to normalized binary64; decimal rounding can change near-parallel classification/positions; no input perturbation bound; display equations rounded by binary64
`rounding`	ieee754_round_ties_to_even
`overflow`	NUMERIC_RANGE on nonzero output outside normal binary64; raw decimal nonzero-to-zero NUMERIC_UNDERFLOW
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	cvp:math.geometry.coordinate O2 / Evidence published cases
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Euclidean plane
Not 3-D / spherical

Example

One numerical check. The calculator page holds worked steps and FAQ.

distance (0,0)(3,4) → 5

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes. 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.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Verified scope: all published modes
Assurance: Core
Declared partition coverage: PASS · 8/8 declared partitions (distance, midpoint, slope, line, point-line, intersect, angle, invalid-domain)
Calculation version: 1.8.0
Verification: 21/21 calculation tests · 8/8 legacy golden · 3/3 legacy boundary · 10/10 legacy property
Production surface contract: 6/6
Versions: Calculation 1.8.0 · CVP protocol 1.0.0-proposed · Evidence 2026-10-29.math-uuce-fields-v1
Verification revision: 2026-10-29.math-uuce-fields-v1 · 3/3 property · digest 93ec4c6ee843
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
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.
CVP suite: 309/309 golden · 4/4 CVP boundary · 12/12 invalid · 3/3 property · 12/12 metamorphic · 4/4 cross-interface · 2/2 cross-calculator · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.8.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.8.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

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/coordinate-geometry' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"mode":"distance","x1":0,"y1":0,"x2":3,"y2":4},"calculation_version":"1.8.0"}'

{
  "inputs": {
    "mode": "distance",
    "x1": 0,
    "y1": 0,
    "x2": 3,
    "y2": 4
  },
  "calculation_version": "1.8.0"
}

POST /api/v1/calc/coordinate-geometry. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: coordinate-geometry
Engine: coordinate-geometry
REST: POST /api/v1/calc/coordinate-geometry
MCP: execute_calculation with capability_id: "math.geometry.coordinate"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.8.0)
Versioned output schema: Immutable pin (1.8.0)

Operations

Declared calculation modes for this capability.

angle

References

Human-readable sources plus CVP reference evidence classes.

Sources

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

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.geometry.coordinate"},"_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.geometry.coordinate","inputs":{"mode":"distance","x1":0,"y1":0,"x2":3,"y2":4},"calculation_version":"1.8.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.8.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.