A variational-calculus conformance agent needs the exact Euler-Lagrange differen...
https://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/polynomial-euler-lagrange-variational-derivativeOverview
A variational-calculus conformance agent needs the exact Euler-Lagrange differentialpolynomial for a supplied finite polynomial Lagrangian,including boundary-term cancellation and coupledvariables. No physicscorrectness/modeling inference.
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detect
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2026-11-02 17:26:22
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Input Schema
{
"body": {
"artifact": {
"variational": {
"claim": [
[
{
"coefficient": "999",
"exponents": [
0,
0,
0,
0,
0,
0
]
}
]
],
"fields": 1,
"terms": [
{
"coefficient": 1,
"exponents": [
0,
0,
2,
0
]
},
{
"coefficient": -1,
"exponents": [
0,
2,
0,
0
]
}
]
}
}
},
"bodyType": "json",
"method": "POST",
"type": "http"
}
Output Schema
{
"example": {
"billable": true,
"findings": [
{
"confidence": 95,
"evidence": [
{
"page_indices": [],
"page_url": null,
"pattern": "polynomial-euler-lagrange-variational-derivative_scoped_evidence",
"type": "artifact"
}
],
"limits": [
"One independent formal timevariable,1–2anonymousfields,inputjets through secondorder,≤24integerterms,totaldegree≤8. Output exact signed decimalcoefficients andcanonical exponentvectors [t,q0,q0′,q0″,q0‴,q0⁗,q1,...].",
"Only formal variational derivative; does not solveEuler–Lagrange equations,chooseboundaryconditions,validatephysics,proveanextremum or predictsafety. No symbolicSDK finalanswerwrapper."
],
"module": "polynomial-euler-lagrange-variational-derivative",
"state": "observed",
"value": {
"claim_matches": false,
"equations": [
[
{
"coefficient": "-2",
"exponents": [
0,
0,
0,
1,
0,
0
]
},
{
"coefficient": "-2",
"exponents": [
0,
1,
0,
0,
0,
0
]
}
]
],
"fields": 1,
"output_jet_order": 4
},
"warnings": []
}
],
"known_count": 1,
"scope": {
"contact_values_returned": false,
"network": false,
"supplied_artifact_only": true
},
"warnings": []
},
"type": "json"
}