{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:256BMV6YKFYO3277OIXWM2RDR3","short_pith_number":"pith:256BMV6Y","canonical_record":{"source":{"id":"1804.01796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-05T12:02:53Z","cross_cats_sorted":["cs.SC","math.AG"],"title_canon_sha256":"b6bab2dffc5ffbd3194f34e1fc9c6f4d1d7c79f71ec0d8f736775cd59974a591","abstract_canon_sha256":"6b055c8a637b910f1c5f93833ed6cb4176b52cc255d329916f8bed7628880550"},"schema_version":"1.0"},"canonical_sha256":"d77c1657d85170edebff722f666a238ec16d98e54b3d4e211906f29af3af1dfa","source":{"kind":"arxiv","id":"1804.01796","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01796","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01796v2","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01796","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"pith_short_12","alias_value":"256BMV6YKFYO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"256BMV6YKFYO3277","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"256BMV6Y","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:256BMV6YKFYO3277OIXWM2RDR3","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-05T12:02:53Z","cross_cats_sorted":["cs.SC","math.AG"],"title_canon_sha256":"b6bab2dffc5ffbd3194f34e1fc9c6f4d1d7c79f71ec0d8f736775cd59974a591","abstract_canon_sha256":"6b055c8a637b910f1c5f93833ed6cb4176b52cc255d329916f8bed7628880550"},"schema_version":"1.0"},"canonical_sha256":"d77c1657d85170edebff722f666a238ec16d98e54b3d4e211906f29af3af1dfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:53.498662Z","signature_b64":"hokdM5NkaKbe8Fpk4c2o4LrDwjyVFyA9eFELNPBCaNruTRI6Jw/RwyQKqQBySi4r3fUjOKFZPFlOFxN3HE19Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d77c1657d85170edebff722f666a238ec16d98e54b3d4e211906f29af3af1dfa","last_reissued_at":"2026-05-17T23:56:53.498015Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:53.498015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01796","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":"2026-05-17T23:56:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpaxCEY230LGnipbCNbF1q5HH6uAy2mlRevfVSpTMA6TKE6PodqhHuwQQSRVkeMD6anX/aDelZpDQ7+u6LLsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:44:10.081987Z"},"content_sha256":"3c7e63cd7ce3286aaed5783217926a71fc6ee9ecb7033b0901a4797b65d8f14a","schema_version":"1.0","event_id":"sha256:3c7e63cd7ce3286aaed5783217926a71fc6ee9ecb7033b0901a4797b65d8f14a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:256BMV6YKFYO3277OIXWM2RDR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of SDP-Exactness in Quadratic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.AG"],"primary_cat":"math.OC","authors_text":"Bernd Sturmfels, Corey Harris, Diego Cifuentes","submitted_at":"2018-04-05T12:02:53Z","abstract_excerpt":"Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance problem, this is a bundle of spectrahedral shadows surrounding the given variety. We characterize the algebraic boundary of this region and we derive a formula for its degree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01796","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":"2026-05-17T23:56:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bppg2z9Zvih4LFwdZsV7/k9/70p/04GOKuipJ7vEc/uQ7f2qtThk7V2ybUAm5aauYnb4FmkGecFH3/2BPxMiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:44:10.082335Z"},"content_sha256":"0e159636323ffbf9ed981b1e0822d881d20c1c9cad62956864627fc3be328e33","schema_version":"1.0","event_id":"sha256:0e159636323ffbf9ed981b1e0822d881d20c1c9cad62956864627fc3be328e33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/256BMV6YKFYO3277OIXWM2RDR3/bundle.json","state_url":"https://pith.science/pith/256BMV6YKFYO3277OIXWM2RDR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/256BMV6YKFYO3277OIXWM2RDR3/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":"2026-06-25T11:44:10Z","links":{"resolver":"https://pith.science/pith/256BMV6YKFYO3277OIXWM2RDR3","bundle":"https://pith.science/pith/256BMV6YKFYO3277OIXWM2RDR3/bundle.json","state":"https://pith.science/pith/256BMV6YKFYO3277OIXWM2RDR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/256BMV6YKFYO3277OIXWM2RDR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:256BMV6YKFYO3277OIXWM2RDR3","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":"6b055c8a637b910f1c5f93833ed6cb4176b52cc255d329916f8bed7628880550","cross_cats_sorted":["cs.SC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-05T12:02:53Z","title_canon_sha256":"b6bab2dffc5ffbd3194f34e1fc9c6f4d1d7c79f71ec0d8f736775cd59974a591"},"schema_version":"1.0","source":{"id":"1804.01796","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01796","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01796v2","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01796","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"pith_short_12","alias_value":"256BMV6YKFYO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"256BMV6YKFYO3277","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"256BMV6Y","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:0e159636323ffbf9ed981b1e0822d881d20c1c9cad62956864627fc3be328e33","target":"graph","created_at":"2026-05-17T23:56:53Z","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 the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance problem, this is a bundle of spectrahedral shadows surrounding the given variety. We characterize the algebraic boundary of this region and we derive a formula for its degree.","authors_text":"Bernd Sturmfels, Corey Harris, Diego Cifuentes","cross_cats":["cs.SC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-05T12:02:53Z","title":"The Geometry of SDP-Exactness in Quadratic Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01796","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":"sha256:3c7e63cd7ce3286aaed5783217926a71fc6ee9ecb7033b0901a4797b65d8f14a","target":"record","created_at":"2026-05-17T23:56:53Z","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":"6b055c8a637b910f1c5f93833ed6cb4176b52cc255d329916f8bed7628880550","cross_cats_sorted":["cs.SC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-05T12:02:53Z","title_canon_sha256":"b6bab2dffc5ffbd3194f34e1fc9c6f4d1d7c79f71ec0d8f736775cd59974a591"},"schema_version":"1.0","source":{"id":"1804.01796","kind":"arxiv","version":2}},"canonical_sha256":"d77c1657d85170edebff722f666a238ec16d98e54b3d4e211906f29af3af1dfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d77c1657d85170edebff722f666a238ec16d98e54b3d4e211906f29af3af1dfa","first_computed_at":"2026-05-17T23:56:53.498015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:53.498015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hokdM5NkaKbe8Fpk4c2o4LrDwjyVFyA9eFELNPBCaNruTRI6Jw/RwyQKqQBySi4r3fUjOKFZPFlOFxN3HE19Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:53.498662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01796","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c7e63cd7ce3286aaed5783217926a71fc6ee9ecb7033b0901a4797b65d8f14a","sha256:0e159636323ffbf9ed981b1e0822d881d20c1c9cad62956864627fc3be328e33"],"state_sha256":"e7ba6244b306b70957bab3b8064ff46fba612d84415f327a3cc6338c72ff2674"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGf5P8Z/coFVpapRkMrhMX0i4oRBi0Ma8qWte7/qc8L5+KkAkRofnmT0199Vmn+bCaLcGk+1WBlvmy2EHAkVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:44:10.084280Z","bundle_sha256":"ed885ab4727f5c5383a7e30b239ac03852e1f9f2cffce64da2bd4cac52111c86"}}