{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:TM2QHSQVONZUCOX4B3LMCS2LLA","short_pith_number":"pith:TM2QHSQV","canonical_record":{"source":{"id":"0908.0364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-08-03T23:06:39Z","cross_cats_sorted":[],"title_canon_sha256":"0d96b1392fc917e3590e02e804af77806895638ebcdae884b6393edcfacedbc3","abstract_canon_sha256":"5699bf92477d9c33aad891cadb0c8472acda4936902cf8f9aff0b5b8523de76a"},"schema_version":"1.0"},"canonical_sha256":"9b3503ca157373413afc0ed6c14b4b582967346a2e365cd9270d6b30148e57a1","source":{"kind":"arxiv","id":"0908.0364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0364","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0364v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0364","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"TM2QHSQVONZU","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TM2QHSQVONZUCOX4","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TM2QHSQV","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:TM2QHSQVONZUCOX4B3LMCS2LLA","target":"record","payload":{"canonical_record":{"source":{"id":"0908.0364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-08-03T23:06:39Z","cross_cats_sorted":[],"title_canon_sha256":"0d96b1392fc917e3590e02e804af77806895638ebcdae884b6393edcfacedbc3","abstract_canon_sha256":"5699bf92477d9c33aad891cadb0c8472acda4936902cf8f9aff0b5b8523de76a"},"schema_version":"1.0"},"canonical_sha256":"9b3503ca157373413afc0ed6c14b4b582967346a2e365cd9270d6b30148e57a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:37.952541Z","signature_b64":"7SevMc7T7NkhmEirsL1LFXw1rC/FnKdQqkTQb+8Bas1K82yPWGevxDuYkgNYxsfN3cmKi9ElhvWopXvvDhCjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3503ca157373413afc0ed6c14b4b582967346a2e365cd9270d6b30148e57a1","last_reissued_at":"2026-05-18T04:25:37.952085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:37.952085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.0364","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mu6PSdmksroB4bzRQz30dqQ8clWGJ00ErmCCSLZorvBZVwwJ0E8GmPa/hfzfRdqtBhazr1Vx4UxJsQ3KnrjCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:46:02.784059Z"},"content_sha256":"729ca1cd633d9e4ddaeb86e0d5be53553d4636df79b7274fec083ddf20996f05","schema_version":"1.0","event_id":"sha256:729ca1cd633d9e4ddaeb86e0d5be53553d4636df79b7274fec083ddf20996f05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:TM2QHSQVONZUCOX4B3LMCS2LLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Matrix Inequality and Semidefinite Representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiawang Nie","submitted_at":"2009-08-03T23:06:39Z","abstract_excerpt":"Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper studies sufficient conditions guaranteeing semidefinite representability of S. We prove that S is semidefinite representable in the following cases: (i) the domain is the whole space and the matrix polynomial is matrix sos-concave; (ii) the domain is compact convex and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0364","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YP5HRq6K5ZZ1pZ03aKbkpfuJ+p+GKoOGcNnOXsG0zKNOz69OgH5ggnLjgwtIIcEJ/0O1m9C8I7OR5uXu0F0DDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:46:02.784427Z"},"content_sha256":"9639690a44904ad8af3a3eea2ad3417f347562fb2b4546375e66f45f4e764a13","schema_version":"1.0","event_id":"sha256:9639690a44904ad8af3a3eea2ad3417f347562fb2b4546375e66f45f4e764a13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TM2QHSQVONZUCOX4B3LMCS2LLA/bundle.json","state_url":"https://pith.science/pith/TM2QHSQVONZUCOX4B3LMCS2LLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TM2QHSQVONZUCOX4B3LMCS2LLA/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":"2026-06-01T16:46:02Z","links":{"resolver":"https://pith.science/pith/TM2QHSQVONZUCOX4B3LMCS2LLA","bundle":"https://pith.science/pith/TM2QHSQVONZUCOX4B3LMCS2LLA/bundle.json","state":"https://pith.science/pith/TM2QHSQVONZUCOX4B3LMCS2LLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TM2QHSQVONZUCOX4B3LMCS2LLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TM2QHSQVONZUCOX4B3LMCS2LLA","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":"5699bf92477d9c33aad891cadb0c8472acda4936902cf8f9aff0b5b8523de76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-08-03T23:06:39Z","title_canon_sha256":"0d96b1392fc917e3590e02e804af77806895638ebcdae884b6393edcfacedbc3"},"schema_version":"1.0","source":{"id":"0908.0364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0364","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0364v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0364","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"TM2QHSQVONZU","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TM2QHSQVONZUCOX4","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TM2QHSQV","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:9639690a44904ad8af3a3eea2ad3417f347562fb2b4546375e66f45f4e764a13","target":"graph","created_at":"2026-05-18T04:25:37Z","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":"Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper studies sufficient conditions guaranteeing semidefinite representability of S. We prove that S is semidefinite representable in the following cases: (i) the domain is the whole space and the matrix polynomial is matrix sos-concave; (ii) the domain is compact convex and th","authors_text":"Jiawang Nie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-08-03T23:06:39Z","title":"Polynomial Matrix Inequality and Semidefinite Representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0364","kind":"arxiv","version":2},"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":"sha256:729ca1cd633d9e4ddaeb86e0d5be53553d4636df79b7274fec083ddf20996f05","target":"record","created_at":"2026-05-18T04:25:37Z","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":"5699bf92477d9c33aad891cadb0c8472acda4936902cf8f9aff0b5b8523de76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-08-03T23:06:39Z","title_canon_sha256":"0d96b1392fc917e3590e02e804af77806895638ebcdae884b6393edcfacedbc3"},"schema_version":"1.0","source":{"id":"0908.0364","kind":"arxiv","version":2}},"canonical_sha256":"9b3503ca157373413afc0ed6c14b4b582967346a2e365cd9270d6b30148e57a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b3503ca157373413afc0ed6c14b4b582967346a2e365cd9270d6b30148e57a1","first_computed_at":"2026-05-18T04:25:37.952085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:37.952085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SevMc7T7NkhmEirsL1LFXw1rC/FnKdQqkTQb+8Bas1K82yPWGevxDuYkgNYxsfN3cmKi9ElhvWopXvvDhCjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:37.952541Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.0364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:729ca1cd633d9e4ddaeb86e0d5be53553d4636df79b7274fec083ddf20996f05","sha256:9639690a44904ad8af3a3eea2ad3417f347562fb2b4546375e66f45f4e764a13"],"state_sha256":"7f41e3cdb6655fa6295662dd4ca96fd8b4acd36a2e2bfc14c92da0855964251c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWRrySES9uDo6bt8w7nRcGycNh+H/SDiXCqeajPJoM0BtqUErrCdA8wEUqfXGbdrwOQheaOc0jrkOcitTgwuCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:46:02.786414Z","bundle_sha256":"8236bbaf3ec7030fcf54d4b7c0b010baed4d9776169ee3d5a4bf4c09adb5f7a0"}}