{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M2EQOUYGR24YPSWSB7O5Q4YJHG","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e2b779b9ea4f0a9e4914c601df879383cf1e2c24845d59af851f059ac02eee21","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-15T11:01:45Z","title_canon_sha256":"62ef11c25f4da47a3be7f237de9a0cb9c3f18d257f68641c73a487d7a758a817"},"schema_version":"1.0","source":{"id":"2607.13701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13701","created_at":"2026-07-16T01:23:01Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13701v1","created_at":"2026-07-16T01:23:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13701","created_at":"2026-07-16T01:23:01Z"},{"alias_kind":"pith_short_12","alias_value":"M2EQOUYGR24Y","created_at":"2026-07-16T01:23:01Z"},{"alias_kind":"pith_short_16","alias_value":"M2EQOUYGR24YPSWS","created_at":"2026-07-16T01:23:01Z"},{"alias_kind":"pith_short_8","alias_value":"M2EQOUYG","created_at":"2026-07-16T01:23:01Z"}],"graph_snapshots":[{"event_id":"sha256:56c04c1f596e0cbc8491bda233273251f0ac6ba724823dd5a0767489aa4f8bf9","target":"graph","created_at":"2026-07-16T01:23:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.13701/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quadratic Sum-Of-Squares (QSOS) optimization problems appear in system identification and machine learning, but standard Schur-complement and second-order cone liftings enlarge conic dimensions and create computational bottlenecks for interior-point methods. This paper introduces a lifting-free regularization that preserves the original conic structure by adding a norm penalty to SOS variables, yielding closed-form primal updates and an unconstrained, concave dual with Lipschitz-continuous gradient. Accelerated first-order methods efficiently maximize this dual, and convergence analysis shows ","authors_text":"Gabriel F. Machado, Morgan Jones, Ross Drummond","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-15T11:01:45Z","title":"Lifting-Free Quadratic Sum-Of-Squares Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13701","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":"sha256:0a267b24a78d269c7a88621bd1e9c7713c31e15f8c98a2f941b3c902e3407a9e","target":"record","created_at":"2026-07-16T01:23:01Z","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":"e2b779b9ea4f0a9e4914c601df879383cf1e2c24845d59af851f059ac02eee21","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-15T11:01:45Z","title_canon_sha256":"62ef11c25f4da47a3be7f237de9a0cb9c3f18d257f68641c73a487d7a758a817"},"schema_version":"1.0","source":{"id":"2607.13701","kind":"arxiv","version":1}},"canonical_sha256":"66890753068eb987cad20fddd8730939be25d3192d58108e1d0f335be9f22e36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66890753068eb987cad20fddd8730939be25d3192d58108e1d0f335be9f22e36","first_computed_at":"2026-07-16T01:23:01.753135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:23:01.753135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XCKHpOYSBkmYQJzrDJyGFexudBFnVrvxdxcaAdjbZalmX8OpKhJZt7CPAQ3hDs0S7S5Gmquit4BmjDSsNl7lAA==","signature_status":"signed_v1","signed_at":"2026-07-16T01:23:01.753975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a267b24a78d269c7a88621bd1e9c7713c31e15f8c98a2f941b3c902e3407a9e","sha256:56c04c1f596e0cbc8491bda233273251f0ac6ba724823dd5a0767489aa4f8bf9","sha256:caf76e9ed315d75fc04072b91d74e1f172896d8b1475ebed87264c709ac1b8d6"],"state_sha256":"ab8d8144f0090d701192383ac1bc56d5f12c82045314348d8caa1fc41813c1c7"}