A p-adic algebra conformance agent needs the exact valuation multiset of all roo...
https://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/padic-newton-polygon-root-valuationsOverview
A p-adic algebra conformance agent needs the exact valuation multiset of all roots over an algebraicclosure ofQ_p for a complete supplied polynomial. No coefficientfactorization,realroots or one fieldroot lift.
Protocol
x402 (POST)
Price
$0.0030
Payment Asset
USD Coin
Payment Network
eip155:8453
Category
uncategorized
Provider
detect
Source
bazaar
Indexed
2026-11-02 17:26:22
Health
Status
unknown
Latency (p50)
—
Uptime (30d)
—
Reliability Score
—
Last Checked
Never
Last Healthy
Never
Consecutive Failures
0
x402 Payment Validation
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Asset Verified
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Facilitator
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Input Schema
{
"body": {
"artifact": {
"newton": {
"claim": {
"degree": 2,
"nonzero_root_valuations": [
{
"denominator": 1,
"multiplicity": 1,
"numerator": 0
},
{
"denominator": 1,
"multiplicity": 1,
"numerator": 3
}
],
"polygon_vertices": [
{
"degree": 0,
"valuation": 3
},
{
"degree": 1,
"valuation": 0
},
{
"degree": 2,
"valuation": 0
}
],
"zero_roots": 1
},
"coefficients": [
8,
-9,
1
],
"prime": 2
}
}
},
"bodyType": "json",
"method": "POST",
"type": "http"
}
Output Schema
{
"example": {
"billable": true,
"findings": [
{
"confidence": 95,
"evidence": [
{
"page_indices": [],
"page_url": null,
"pattern": "padic-newton-polygon-root-valuations_scoped_evidence",
"type": "artifact"
}
],
"limits": [
"Integerpolynomialdegree0–16,coefficientsabs≤10^9,nonzeroleadingcoefficient,prime2–101. Zero coefficients omitted fromfinitehull;firstnonzero degree iszero-rootmultiplicity. Rootvaluations reducedrationalnumbers sortedascending.",
"Doesnot factorpolynomial,returnactualroots,assertrootsinQ_p,findHensellifts orreal/complexroots. Multiplicities overalgebraicclosure only;no inferredeconomic/physicaltruth."
],
"module": "padic-newton-polygon-root-valuations",
"state": "observed",
"value": {
"claim_matches": false,
"degree": 2,
"nonzero_root_valuations": [
{
"denominator": 1,
"multiplicity": 1,
"numerator": 0
},
{
"denominator": 1,
"multiplicity": 1,
"numerator": 3
}
],
"polygon_vertices": [
{
"degree": 0,
"valuation": 3
},
{
"degree": 1,
"valuation": 0
},
{
"degree": 2,
"valuation": 0
}
],
"zero_roots": 0
},
"warnings": []
}
],
"known_count": 1,
"scope": {
"contact_values_returned": false,
"network": false,
"supplied_artifact_only": true
},
"warnings": []
},
"type": "json"
}