{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:XVXSLRSI7CQMREQ5CC7WIBEIUZ","short_pith_number":"pith:XVXSLRSI","canonical_record":{"source":{"id":"2411.15479","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-23T07:23:17Z","cross_cats_sorted":[],"title_canon_sha256":"00448d1426e11b6a70cb1a54d839effa0bb4f206160fdf1a4d0ec4edf03c553d","abstract_canon_sha256":"5b68080f4004401cb084eeace62eb7c4fd0ef69af85ac10aea7307dfa01b8df2"},"schema_version":"1.0"},"canonical_sha256":"bd6f25c648f8a0c8921d10bf640488a664138af130c44853545c0b27cc124579","source":{"kind":"arxiv","id":"2411.15479","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15479","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15479v3","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15479","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"XVXSLRSI7CQM","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"pith_short_16","alias_value":"XVXSLRSI7CQMREQ5","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"pith_short_8","alias_value":"XVXSLRSI","created_at":"2026-07-05T11:16:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:XVXSLRSI7CQMREQ5CC7WIBEIUZ","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15479","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-23T07:23:17Z","cross_cats_sorted":[],"title_canon_sha256":"00448d1426e11b6a70cb1a54d839effa0bb4f206160fdf1a4d0ec4edf03c553d","abstract_canon_sha256":"5b68080f4004401cb084eeace62eb7c4fd0ef69af85ac10aea7307dfa01b8df2"},"schema_version":"1.0"},"canonical_sha256":"bd6f25c648f8a0c8921d10bf640488a664138af130c44853545c0b27cc124579","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:30.705887Z","signature_b64":"oU6hYzYmXY+CzBAFHBc8e0WmFMCMJaU/hIG9pwITxQOEsEZ4mpUMpOd1XI4EXzcLNNO+sBlwu6stEK2A/1l8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd6f25c648f8a0c8921d10bf640488a664138af130c44853545c0b27cc124579","last_reissued_at":"2026-07-05T11:16:30.705327Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:30.705327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15479","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KH451R/DMiy0Y1LZcIgp3ZaPElvHCdBUARU6DskuHA+XVHNbgjzM/GIypXy2z54BK5zcspwDQKsKC1d+2OimDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:21:51.906667Z"},"content_sha256":"e9ca2cf398eab925365c7c43124a30462cfb5289609889a9fafef469887f4a39","schema_version":"1.0","event_id":"sha256:e9ca2cf398eab925365c7c43124a30462cfb5289609889a9fafef469887f4a39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:XVXSLRSI7CQMREQ5CC7WIBEIUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Polynomial Matrix Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Feng Guo, Jared Miller, Jie Wang","submitted_at":"2024-11-23T07:23:17Z","abstract_excerpt":"A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of polynomial matrix inequalities. This work explores the use of sparsity methods in reducing the complexity of sum-of-squares based methods in verifying polynomial matrix inequalities or solving polynomial matrix optimization. In the unconstrained setting, Newton polytopes can be employed to sparsify the monomial basis, resulting in smaller semidefinite programs. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15479","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15479/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9VjxrFfmANvI5a8yWuITZz9UWqLxlI78+B3wB6FlmRDy/5gJ6yL/xpl3B0fOerqTUAkudZtAIPv0sAxkn8NyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:21:51.908034Z"},"content_sha256":"834f914be436fb62d2bd9908cd1f84105c806868471661efdc2daa9f98c4402c","schema_version":"1.0","event_id":"sha256:834f914be436fb62d2bd9908cd1f84105c806868471661efdc2daa9f98c4402c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ/bundle.json","state_url":"https://pith.science/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T05:21:51Z","links":{"resolver":"https://pith.science/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ","bundle":"https://pith.science/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ/bundle.json","state":"https://pith.science/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVXSLRSI7CQMREQ5CC7WIBEIUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XVXSLRSI7CQMREQ5CC7WIBEIUZ","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":"5b68080f4004401cb084eeace62eb7c4fd0ef69af85ac10aea7307dfa01b8df2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-23T07:23:17Z","title_canon_sha256":"00448d1426e11b6a70cb1a54d839effa0bb4f206160fdf1a4d0ec4edf03c553d"},"schema_version":"1.0","source":{"id":"2411.15479","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15479","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15479v3","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15479","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"XVXSLRSI7CQM","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"pith_short_16","alias_value":"XVXSLRSI7CQMREQ5","created_at":"2026-07-05T11:16:30Z"},{"alias_kind":"pith_short_8","alias_value":"XVXSLRSI","created_at":"2026-07-05T11:16:30Z"}],"graph_snapshots":[{"event_id":"sha256:834f914be436fb62d2bd9908cd1f84105c806868471661efdc2daa9f98c4402c","target":"graph","created_at":"2026-07-05T11:16:30Z","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/2411.15479/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of polynomial matrix inequalities. This work explores the use of sparsity methods in reducing the complexity of sum-of-squares based methods in verifying polynomial matrix inequalities or solving polynomial matrix optimization. In the unconstrained setting, Newton polytopes can be employed to sparsify the monomial basis, resulting in smaller semidefinite programs. I","authors_text":"Feng Guo, Jared Miller, Jie Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-23T07:23:17Z","title":"Sparse Polynomial Matrix Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15479","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:e9ca2cf398eab925365c7c43124a30462cfb5289609889a9fafef469887f4a39","target":"record","created_at":"2026-07-05T11:16:30Z","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":"5b68080f4004401cb084eeace62eb7c4fd0ef69af85ac10aea7307dfa01b8df2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-23T07:23:17Z","title_canon_sha256":"00448d1426e11b6a70cb1a54d839effa0bb4f206160fdf1a4d0ec4edf03c553d"},"schema_version":"1.0","source":{"id":"2411.15479","kind":"arxiv","version":3}},"canonical_sha256":"bd6f25c648f8a0c8921d10bf640488a664138af130c44853545c0b27cc124579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd6f25c648f8a0c8921d10bf640488a664138af130c44853545c0b27cc124579","first_computed_at":"2026-07-05T11:16:30.705327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:30.705327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oU6hYzYmXY+CzBAFHBc8e0WmFMCMJaU/hIG9pwITxQOEsEZ4mpUMpOd1XI4EXzcLNNO+sBlwu6stEK2A/1l8BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:30.705887Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15479","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9ca2cf398eab925365c7c43124a30462cfb5289609889a9fafef469887f4a39","sha256:834f914be436fb62d2bd9908cd1f84105c806868471661efdc2daa9f98c4402c"],"state_sha256":"1a72449236a2e312787506b8c9b2d444ca9f3b406339fb8fac1b685523d7c924"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MnLiwaqRXKc3U3LjUtg1IJejbxpIX0cUOvrjZYGD7sCZ1VeRKPLrcoYJKS48Vttb118s6bvpSGdUb9KYWnVuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:21:51.914392Z","bundle_sha256":"3ef9f1ffeb39e9cbfc58d9e46073507f7056fa3bbabc76ba6ce16715d24324f6"}}