{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5K5XZKBFIXJAW7P5C3LIRAGS7R","short_pith_number":"pith:5K5XZKBF","schema_version":"1.0","canonical_sha256":"eabb7ca82545d20b7dfd16d68880d2fc46673ea27083d1a68477be401ca473fb","source":{"kind":"arxiv","id":"1802.10339","version":1},"attestation_state":"computed","paper":{"title":"On Exact Polya and Putinar's Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Mohab Safey El Din, Victor Magron","submitted_at":"2018-02-28T10:17:04Z","abstract_excerpt":"We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers.\n  We start by providing a hybrid numeric-symbolic algorithm computing exact rational SOS decompositions for polynomials lying in the interior of the SOS cone. It computes an approximate SOS decomposition for a perturbation of the input polynomial with an arbitrary-precision SDP solver. An exact SOS decomposition is obtained thanks to the perturbation terms. We prove that bit complexity estimates on output "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.10339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-28T10:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"f623d0f6365cb89e12800ee6398a023d779193e9cd325604f36ea925fed799f9","abstract_canon_sha256":"6deb1d1fd6010751887ba7dcb707014ebb9ded52e348bec1fcdec7a8f43bac25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:17.442768Z","signature_b64":"GGZNamuvcq0TCj+4zDgZeLIEiv19kRNUXh4QsuU8WQD+nMLg39f2a6SGEH55Yv2hQNGTlexKzhKxnIbelocTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eabb7ca82545d20b7dfd16d68880d2fc46673ea27083d1a68477be401ca473fb","last_reissued_at":"2026-05-18T00:22:17.442151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:17.442151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Exact Polya and Putinar's Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Mohab Safey El Din, Victor Magron","submitted_at":"2018-02-28T10:17:04Z","abstract_excerpt":"We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers.\n  We start by providing a hybrid numeric-symbolic algorithm computing exact rational SOS decompositions for polynomials lying in the interior of the SOS cone. It computes an approximate SOS decomposition for a perturbation of the input polynomial with an arbitrary-precision SDP solver. An exact SOS decomposition is obtained thanks to the perturbation terms. We prove that bit complexity estimates on output "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10339","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.10339","created_at":"2026-05-18T00:22:17.442249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.10339v1","created_at":"2026-05-18T00:22:17.442249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10339","created_at":"2026-05-18T00:22:17.442249+00:00"},{"alias_kind":"pith_short_12","alias_value":"5K5XZKBFIXJA","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5K5XZKBFIXJAW7P5","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5K5XZKBF","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R","json":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R.json","graph_json":"https://pith.science/api/pith-number/5K5XZKBFIXJAW7P5C3LIRAGS7R/graph.json","events_json":"https://pith.science/api/pith-number/5K5XZKBFIXJAW7P5C3LIRAGS7R/events.json","paper":"https://pith.science/paper/5K5XZKBF"},"agent_actions":{"view_html":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R","download_json":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R.json","view_paper":"https://pith.science/paper/5K5XZKBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.10339&json=true","fetch_graph":"https://pith.science/api/pith-number/5K5XZKBFIXJAW7P5C3LIRAGS7R/graph.json","fetch_events":"https://pith.science/api/pith-number/5K5XZKBFIXJAW7P5C3LIRAGS7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R/action/storage_attestation","attest_author":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R/action/author_attestation","sign_citation":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R/action/citation_signature","submit_replication":"https://pith.science/pith/5K5XZKBFIXJAW7P5C3LIRAGS7R/action/replication_record"}},"created_at":"2026-05-18T00:22:17.442249+00:00","updated_at":"2026-05-18T00:22:17.442249+00:00"}