{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QAR7GJ6MNPGECAYMLG2YHAJXDL","short_pith_number":"pith:QAR7GJ6M","canonical_record":{"source":{"id":"1309.7415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-28T03:10:38Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"8484b831bd3d4c8b27e067934a94d5a0e84d018b18ef9dba4c163a83090073ca","abstract_canon_sha256":"2115b8b81c9b4ab0b559d8fc8158de6b759203a4fed4741779f81109bd2c715e"},"schema_version":"1.0"},"canonical_sha256":"8023f327cc6bcc41030c59b58381371ae8f4252dc83d1ecc951e7a20d1705042","source":{"kind":"arxiv","id":"1309.7415","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7415","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7415v1","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7415","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"QAR7GJ6MNPGE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QAR7GJ6MNPGECAYM","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QAR7GJ6M","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QAR7GJ6MNPGECAYMLG2YHAJXDL","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-28T03:10:38Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"8484b831bd3d4c8b27e067934a94d5a0e84d018b18ef9dba4c163a83090073ca","abstract_canon_sha256":"2115b8b81c9b4ab0b559d8fc8158de6b759203a4fed4741779f81109bd2c715e"},"schema_version":"1.0"},"canonical_sha256":"8023f327cc6bcc41030c59b58381371ae8f4252dc83d1ecc951e7a20d1705042","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:58.771380Z","signature_b64":"+HofRXhggB2992Y0Du9VpFepel60j30YihSuf7pi+CZgTllyEyOR4lyo8piCg6PmT4XQY8E32T9Hdi9+ViUoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8023f327cc6bcc41030c59b58381371ae8f4252dc83d1ecc951e7a20d1705042","last_reissued_at":"2026-05-18T03:11:58.770545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:58.770545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7415","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eUrseXK7C2WjKGlvA3dLe5r+VSiA41GbkoaE0pYCiZv306pyxXkGCxIFouOcR0EKS1kUUsNp+0JaI/U4b9lODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:14:56.663999Z"},"content_sha256":"81c4040c3c146013d5ea01170e5723cb08c6c36a29c636fac3a1de0a2a951ab7","schema_version":"1.0","event_id":"sha256:81c4040c3c146013d5ea01170e5723cb08c6c36a29c636fac3a1de0a2a951ab7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QAR7GJ6MNPGECAYMLG2YHAJXDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertices of Spectrahedra arising from the Elliptope, the Theta Body, and Their Relatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.OC","authors_text":"Levent Tun\\c{c}el, Marcel K. de Carli Silva","submitted_at":"2013-09-28T03:10:38Z","abstract_excerpt":"Utilizing dual descriptions of the normal cone of convex optimization problems in conic form, we characterize the vertices of semidefinite representations arising from Lov\\'asz theta body, generalizations of the elliptope, and related convex sets. Our results generalize vertex characterizations due to Laurent and Poljak from the 1990's. Our approach also leads us to nice characterizations of strict complementarity and to connections with some of the related literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7415","kind":"arxiv","version":1},"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":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqCJOTjVSVnQLLLuLdI0FKqr75+dknakChM7JTAGQK21qqzq0sSa44eudVZbgEtho7j/N4Jl4xXNkn59H39EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:14:56.664358Z"},"content_sha256":"2dbb070e25e996ff6e4d4c572b978bae764973befa5a8ec07870516239373b25","schema_version":"1.0","event_id":"sha256:2dbb070e25e996ff6e4d4c572b978bae764973befa5a8ec07870516239373b25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL/bundle.json","state_url":"https://pith.science/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL/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":"2026-06-23T14:14:56Z","links":{"resolver":"https://pith.science/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL","bundle":"https://pith.science/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL/bundle.json","state":"https://pith.science/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QAR7GJ6MNPGECAYMLG2YHAJXDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QAR7GJ6MNPGECAYMLG2YHAJXDL","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":"2115b8b81c9b4ab0b559d8fc8158de6b759203a4fed4741779f81109bd2c715e","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-28T03:10:38Z","title_canon_sha256":"8484b831bd3d4c8b27e067934a94d5a0e84d018b18ef9dba4c163a83090073ca"},"schema_version":"1.0","source":{"id":"1309.7415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7415","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7415v1","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7415","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"QAR7GJ6MNPGE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QAR7GJ6MNPGECAYM","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QAR7GJ6M","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:2dbb070e25e996ff6e4d4c572b978bae764973befa5a8ec07870516239373b25","target":"graph","created_at":"2026-05-18T03:11:58Z","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":"Utilizing dual descriptions of the normal cone of convex optimization problems in conic form, we characterize the vertices of semidefinite representations arising from Lov\\'asz theta body, generalizations of the elliptope, and related convex sets. Our results generalize vertex characterizations due to Laurent and Poljak from the 1990's. Our approach also leads us to nice characterizations of strict complementarity and to connections with some of the related literature.","authors_text":"Levent Tun\\c{c}el, Marcel K. de Carli Silva","cross_cats":["math.CO","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-28T03:10:38Z","title":"Vertices of Spectrahedra arising from the Elliptope, the Theta Body, and Their Relatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7415","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":"sha256:81c4040c3c146013d5ea01170e5723cb08c6c36a29c636fac3a1de0a2a951ab7","target":"record","created_at":"2026-05-18T03:11:58Z","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":"2115b8b81c9b4ab0b559d8fc8158de6b759203a4fed4741779f81109bd2c715e","cross_cats_sorted":["math.CO","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-28T03:10:38Z","title_canon_sha256":"8484b831bd3d4c8b27e067934a94d5a0e84d018b18ef9dba4c163a83090073ca"},"schema_version":"1.0","source":{"id":"1309.7415","kind":"arxiv","version":1}},"canonical_sha256":"8023f327cc6bcc41030c59b58381371ae8f4252dc83d1ecc951e7a20d1705042","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8023f327cc6bcc41030c59b58381371ae8f4252dc83d1ecc951e7a20d1705042","first_computed_at":"2026-05-18T03:11:58.770545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:58.770545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+HofRXhggB2992Y0Du9VpFepel60j30YihSuf7pi+CZgTllyEyOR4lyo8piCg6PmT4XQY8E32T9Hdi9+ViUoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:58.771380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81c4040c3c146013d5ea01170e5723cb08c6c36a29c636fac3a1de0a2a951ab7","sha256:2dbb070e25e996ff6e4d4c572b978bae764973befa5a8ec07870516239373b25"],"state_sha256":"38b511c81398769bdddf570c03b41b08443471b0cc43ead1df969f084a99116a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOmhuwU9N/7L2jGeYLoJ7YUoP3iJPmSaBEg6QoGz9dCbkys2J/gPEw3wpnT0hh3jGjxpFzG0/kVweBDrIBFMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:14:56.666337Z","bundle_sha256":"6f5814d5ef3715ea1e389c59a07ef37c8183d3dd75c53fb8a78c7f758b9d716c"}}