Prüft die behauptete kanonisch reduzierte positive binäre quadratische Form und ...

{ "body": { "artifact": { "claimed_reduced": [ 2, 1, 3 ], "claimed_transform": [ [ 1, -1 ], [ -1, 2 ] ], "claims": { "coefficient_count": 3, "primitive": true, "reduction_boundary": false }, "coefficients": [ 13, 17, 6 ] } }, "bodyType": "json", "method": "POST", "type": "http" }

{ "example": { "billable": true, "findings": [ { "confidence": 100, "evidence": [], "limits": [ "Charlton Primes of the form x²+ny² §5.1 Definition5.4/Theorem5.5: every positive-definite integral binary form has a unique properlySL2(Z)-equivalent reduced form with |b|<=a<=c, and b>=0 on either boundary. Own exact Gauss integer shear/exchange reduction: center b in(-a,a], exchange a/c and negate b until reduced; exact discriminant invariant checked.", "Caller unimodular transformation is a witness: determinant MUST equal+1 and exact substitution in the original form MUST give the computed canonical reduced triple. Any valid proper witness accepted, not only the producer path. Determinant−1 is improper even if length/discriminant agree. Own BigInt substitution and determinant, no lattice/form SDK or numerical reduction.", "Closed integer coefficients(a,b,c), each absolute<=2^32−1, a>0 and b²−4ac<0. Primitive and nonprimitive forms supported. At most4096reduction iterations, otherwise whole unknown. Not indefinite reduction, class-group composition/enumeration, cryptographic hardness, lattice-length heuristic, real geometry or runtime compatibility.", "Claims compare exact discrete integers; fractional coefficients in input outside profile=>unknown, fractional reduced/witness claims=>observed mismatch. Positive/negative middle coefficients in interior reduced forms can be different proper classes despite equal determinant; boundary tie conventions fixed by source.", "Only coefficient count and booleans output. No original/reduced coefficients, discriminant, transformation entries, caller claims or exception text returned, including legal phone-shaped coefficients. No identity/security/financial/legal judgement." ], "module": "gauss-proper-binary-quadratic-form-reduction", "state": "not_observed", "value": { "claim_mismatches": 0, "claims_match": true, "coefficient_count": 3, "primitive": true, "proper_witness_matches": true, "reduced_claim_matches": true, "reduction_boundary": false }, "warnings": [] } ], "known_count": 1, "scope": { "contact_values_returned": false, "network": false, "supplied_artifact_only": true }, "warnings": [] }, "type": "json" }