CVP reproduce

mechanical.statics.planar_equilibrium

Independent re-run pack: fixed input vectors, O3 expected values, oracle version, commands, and the last result summary. This is how a reader moves from “CalculatorX says it passed” to “I can reproduce why it passed.”

Reproduce JSON CVP Manifest O3 table Generator REST checker Calculator

Identity

Calculation version, protocol version, and evidence revision are distinct.

Calculation version: 1.0.0
CVP protocol: 1.0.0-proposed · proposed
Evidence revision: 2026-09-27.o2-o3.v2
Oracle: O3 · mpmath 1.4.1 · 80 dps
Generator: planar-equilibrium-mpmath-o3 · seed 20260927.planar-equilibrium-o3
Table SHA-256: fb7e0e5f7f76ee45392fe5d8b91cc0a1c14619556632445838de938dfa268f45

Numerical claim

O3 PASS is a tabulated-vector claim, not a whole-domain proof.

O2: planar ΣF/ΣM vs a separate-module identity (≤2 ULP). Not beam deflection, not distributed load, and not 3-D. ≤2 ULP vs O3 applies only to the published tabulated planar-equilibrium vectors. Not beam deflection.

Last O3 run 8 / 8
Max error observed 0 ULP
Threshold ≤ 2 ULP

Commands

Regenerate the table from the public generator. Independent REST check needs only this page's reproduce.json plus stdlib Python — no repo clone and no mpmath. The CVP runner remains a maintainer command.

Regenerate O3 table: python3 generate-planar-equilibrium-o3.py after downloading the public generator next to the table
Repo maintainer path: python3 scripts/lib/cvp/oracles/generate-planar-equilibrium-o3.py
Independent REST check: Compare POST /api/v1/calc/planar-equilibrium against /developers/cvp/reproduce/planar-equilibrium-o3-tables.json after downloading check-math-o3-rest.py next to planar-equilibrium-o3-tables.json (or pass --reproduce reproduce.json)
Re-run CVP: npm run cvp:run -- --capability mechanical.statics.planar_equilibrium
REST check: POST https://www.calculatorx.com/api/v1/calc/planar-equilibrium with a tabulated input from the table below

Re-running the generator without changing seed or inputs should reproduce table SHA-256 fb7e0e5f7f76ee45392fe5d8b91cc0a1c14619556632445838de938dfa268f45. Compare each expected_f64 to the production result within the declared ULP threshold.

Tabulated vectors

Every O3 vector used for the ≤2 ULP claim. Expected values come from the published mpmath table, not from the implementation under test.

ID	Kind	Inputs	Expected (f64)	Actual	Status
`o3-345`	resultant	`{"mode":"resultant","forces":"3,0; 0,4"}`	{"oracle_layer":"analytic","resultant_n":5,"sum_fx":3,"sum_fy":4,"sum_m":0}	{"mode":"resultant","model":"planar_equilibrium","sum_fx":3,"sum_fy":4,"sum_m":0,"resultant_n":5,"angle_deg":53.13010235415598,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":false,"unknowns":[],"solver":"math.vector add + cross"}	PASS
`o3-moment`	moment	`{"mode":"resultant","forces":"0,-10,2,0"}`	{"oracle_layer":"analytic","resultant_n":10,"sum_fx":0,"sum_fy":-10,"sum_m":-20}	{"mode":"resultant","model":"planar_equilibrium","sum_fx":0,"sum_fy":-10,"sum_m":-20,"resultant_n":10,"angle_deg":-90,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":false,"unknowns":[],"solver":"math.vector add + cross"}	PASS
`o3-bracket`	equilibrium3	`{"mode":"equilibrium","forces":"0,-100,2,0; 0,0,0,0,fx+fy","moments":"0,m"}`	{"oracle_layer":"analytic","resultant_n":100,"sum_fx":0,"sum_fy":-100,"sum_m":-200}	{"mode":"equilibrium","model":"planar_equilibrium","sum_fx":0,"sum_fy":-100,"sum_m":-200,"resultant_n":100,"angle_deg":-90,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":true,"unknowns":[{"id":"F2.fx","value":0},{"id":"F2.fy","value":100},{"id":"M1","value":200}],"solver":"math.linear_algebra solve order 3"}	PASS
`o3-two`	equilibrium2	`{"mode":"equilibrium","forces":"0,-10; 0,0,fx+fy"}`	{"oracle_layer":"analytic","resultant_n":10,"sum_fx":0,"sum_fy":-10,"sum_m":0}	{"mode":"equilibrium","model":"planar_equilibrium","sum_fx":0,"sum_fy":-10,"sum_m":0,"resultant_n":10,"angle_deg":-90,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":true,"unknowns":[{"id":"F2.fx","value":0},{"id":"F2.fy","value":10}],"solver":"math.linear_algebra solve order 2"}	PASS
`o3-awkward`	awkward	`{"mode":"resultant","forces":"1.37,-2.5,0.83,0.2"}`	{"oracle_layer":"analytic","resultant_n":2.85077182531,"sum_fx":1.37,"sum_fy":-2.5,"sum_m":-2.349}	{"mode":"resultant","model":"planar_equilibrium","sum_fx":1.37,"sum_fy":-2.5,"sum_m":-2.349,"resultant_n":2.85077182531,"angle_deg":-61.27725871500539,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":false,"unknowns":[],"solver":"math.vector add + cross"}	PASS
`o3-alias`	alias	`{"mode":"resultant","F":"5,0; -3,4"}`	{"oracle_layer":"analytic","resultant_n":4.472135955,"sum_fx":2,"sum_fy":4,"sum_m":0}	{"mode":"resultant","model":"planar_equilibrium","sum_fx":2,"sum_fy":4,"sum_m":0,"resultant_n":4.472135955,"angle_deg":63.43494882292201,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":false,"unknowns":[],"solver":"math.vector add + cross"}	PASS
`o3-moments-only`	moments	`{"mode":"resultant","moments":"12; -4"}`	{"oracle_layer":"analytic","resultant_n":0,"sum_fx":0,"sum_fy":0,"sum_m":8}	{"mode":"resultant","model":"planar_equilibrium","sum_fx":0,"sum_fy":0,"sum_m":8,"resultant_n":0,"angle_deg":null,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":false,"unknowns":[],"solver":"math.vector add + cross"}	PASS
`o3-cancel`	cancel	`{"mode":"resultant","forces":"2,3; -2,-3"}`	{"oracle_layer":"analytic","resultant_n":0,"sum_fx":0,"sum_fy":0,"sum_m":0}	{"mode":"resultant","model":"planar_equilibrium","sum_fx":0,"sum_fy":0,"sum_m":0,"resultant_n":0,"angle_deg":null,"convention":"CCW positive; M = x Fy − y Fx about the origin","balanced":true,"unknowns":[],"solver":"math.vector add + cross"}	PASS