{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3GYKZETDWGKHAUM7VL3YQ2OSED","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":"3923e9d9541559e647b1caa3bff53ec5a1bc704cc7b9a87424f0b5ab23c75583","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-03T10:37:03Z","title_canon_sha256":"4050957bd542bc2da31c530838e25df6fd87c1b1372b1917fc2a03fd50ca3636"},"schema_version":"1.0","source":{"id":"1207.0630","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0630","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0630v3","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0630","created_at":"2026-05-18T01:15:07Z"},{"alias_kind":"pith_short_12","alias_value":"3GYKZETDWGKH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3GYKZETDWGKHAUM7","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3GYKZETD","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:117e00cdc999684516d3167d8e4b3d8c25f352dc0d1ee5b9e29d2e789aacc296","target":"graph","created_at":"2026-05-18T01:15:07Z","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 present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. The problem of approximate GCD is transfered to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the grad","authors_text":"Akira Terui","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-03T10:37:03Z","title":"GPGCD: An iterative method for calculating approximate GCD of univariate polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0630","kind":"arxiv","version":3},"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:fa470061fea8468a5310c1cb3ad8d47fe42da1221d7d34ebf3115fc5b21c9a06","target":"record","created_at":"2026-05-18T01:15:07Z","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":"3923e9d9541559e647b1caa3bff53ec5a1bc704cc7b9a87424f0b5ab23c75583","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-03T10:37:03Z","title_canon_sha256":"4050957bd542bc2da31c530838e25df6fd87c1b1372b1917fc2a03fd50ca3636"},"schema_version":"1.0","source":{"id":"1207.0630","kind":"arxiv","version":3}},"canonical_sha256":"d9b0ac9263b19470519faaf78869d220cfccc4e873b6c1eb1b5755cd5e818147","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9b0ac9263b19470519faaf78869d220cfccc4e873b6c1eb1b5755cd5e818147","first_computed_at":"2026-05-18T01:15:07.272524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:07.272524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qjWL/uakvUfz6veCWZ84kEXOz2TYbggNhOFiZ3dj8+r7TMc7W3uxBk8DMG7uWZR3T18LpDQDfSYxxUtNo3GVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:07.273168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0630","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa470061fea8468a5310c1cb3ad8d47fe42da1221d7d34ebf3115fc5b21c9a06","sha256:117e00cdc999684516d3167d8e4b3d8c25f352dc0d1ee5b9e29d2e789aacc296"],"state_sha256":"3c73e9eef403ca4fd297bb08f978de26930953c8b998d1f8555bc431306f85fc"}