{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5K5XZKBFIXJAW7P5C3LIRAGS7R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6deb1d1fd6010751887ba7dcb707014ebb9ded52e348bec1fcdec7a8f43bac25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-28T10:17:04Z","title_canon_sha256":"f623d0f6365cb89e12800ee6398a023d779193e9cd325604f36ea925fed799f9"},"schema_version":"1.0","source":{"id":"1802.10339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10339","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10339v1","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10339","created_at":"2026-05-18T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"5K5XZKBFIXJA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5K5XZKBFIXJAW7P5","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5K5XZKBF","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:57178b31a705211c3daec1008fc1eb4dac6e8e0f7ab1e1d9cd35be50649b7247","target":"graph","created_at":"2026-05-18T00:22:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Mohab Safey El Din, Victor Magron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-28T10:17:04Z","title":"On Exact Polya and Putinar's Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10339","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:704511c03477d7045332865514ca7d929fc748ab7d9a55b9167fbd4ccddf6aef","target":"record","created_at":"2026-05-18T00:22:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6deb1d1fd6010751887ba7dcb707014ebb9ded52e348bec1fcdec7a8f43bac25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-28T10:17:04Z","title_canon_sha256":"f623d0f6365cb89e12800ee6398a023d779193e9cd325604f36ea925fed799f9"},"schema_version":"1.0","source":{"id":"1802.10339","kind":"arxiv","version":1}},"canonical_sha256":"eabb7ca82545d20b7dfd16d68880d2fc46673ea27083d1a68477be401ca473fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eabb7ca82545d20b7dfd16d68880d2fc46673ea27083d1a68477be401ca473fb","first_computed_at":"2026-05-18T00:22:17.442151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:17.442151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GGZNamuvcq0TCj+4zDgZeLIEiv19kRNUXh4QsuU8WQD+nMLg39f2a6SGEH55Yv2hQNGTlexKzhKxnIbelocTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:17.442768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.10339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:704511c03477d7045332865514ca7d929fc748ab7d9a55b9167fbd4ccddf6aef","sha256:57178b31a705211c3daec1008fc1eb4dac6e8e0f7ab1e1d9cd35be50649b7247"],"state_sha256":"b8d5452cd09f6f84461c329c9339e4cb8e1a156589179c053399867e591fad85"}