{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WJCLYLQT7ONS6ZMY2RYI54WE2Y","short_pith_number":"pith:WJCLYLQT","canonical_record":{"source":{"id":"1512.08766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-29T19:51:33Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"75807c95bd9f5522bad0a0542e5de2b790050ee305473e113a983ff11c70f778","abstract_canon_sha256":"15de8d97cf3a31ab33a35085fe833f7ec45d3524cd23badb91d6494ce30df5d4"},"schema_version":"1.0"},"canonical_sha256":"b244bc2e13fb9b2f6598d4708ef2c4d61b59a1737a8d98b6fbd4cdcccf857414","source":{"kind":"arxiv","id":"1512.08766","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08766","created_at":"2026-05-18T00:53:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08766v2","created_at":"2026-05-18T00:53:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08766","created_at":"2026-05-18T00:53:08Z"},{"alias_kind":"pith_short_12","alias_value":"WJCLYLQT7ONS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJCLYLQT7ONS6ZMY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJCLYLQT","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WJCLYLQT7ONS6ZMY2RYI54WE2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-29T19:51:33Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"75807c95bd9f5522bad0a0542e5de2b790050ee305473e113a983ff11c70f778","abstract_canon_sha256":"15de8d97cf3a31ab33a35085fe833f7ec45d3524cd23badb91d6494ce30df5d4"},"schema_version":"1.0"},"canonical_sha256":"b244bc2e13fb9b2f6598d4708ef2c4d61b59a1737a8d98b6fbd4cdcccf857414","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:08.636263Z","signature_b64":"HZF46VCOy2N2UlBXIwvrWq+JdoN1989XjxXvbkNm9g0sH5D3d1nRuKjCxxig+rRc7c0MEy9DDhrnsvIJpeHyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b244bc2e13fb9b2f6598d4708ef2c4d61b59a1737a8d98b6fbd4cdcccf857414","last_reissued_at":"2026-05-18T00:53:08.635776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:08.635776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08766","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":"2026-05-18T00:53:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MNQKUiAu10cZXzE4oD8OFbunTRfF9z0NMJwD/GWsTIj+taBRWY4dtL2rk22QWTyVsHnySlzaeh87ENzYdFGbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:07:21.373364Z"},"content_sha256":"b04cd350d18cdcb541afc6a2d4e1e17671236d3adfc16c97ffbcede1d20d1384","schema_version":"1.0","event_id":"sha256:b04cd350d18cdcb541afc6a2d4e1e17671236d3adfc16c97ffbcede1d20d1384"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WJCLYLQT7ONS6ZMY2RYI54WE2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive semidefinite rank and nested spectrahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Elina Robeva, Kaie Kubjas, Richard Z. Robinson","submitted_at":"2015-12-29T19:51:33Z","abstract_excerpt":"The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture for the description of this boundary. Our proof techniques are geometric in nature and rely on nesting spectrahedra between polytopes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08766","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":"2026-05-18T00:53:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pVGHNn1NVDPoOGeqolPsedjW77V3hzvNaD2VndHU+uFTy+/DXG3PdaNyurIylAYBsVbDR0bTY0eAGiCIPlIYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:07:21.374082Z"},"content_sha256":"821f02ae9011d5414e569a1ef069a794e874150deedc0d8611df4047301ccad2","schema_version":"1.0","event_id":"sha256:821f02ae9011d5414e569a1ef069a794e874150deedc0d8611df4047301ccad2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y/bundle.json","state_url":"https://pith.science/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y/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":"2026-05-26T07:07:21Z","links":{"resolver":"https://pith.science/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y","bundle":"https://pith.science/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y/bundle.json","state":"https://pith.science/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJCLYLQT7ONS6ZMY2RYI54WE2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WJCLYLQT7ONS6ZMY2RYI54WE2Y","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":"15de8d97cf3a31ab33a35085fe833f7ec45d3524cd23badb91d6494ce30df5d4","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-29T19:51:33Z","title_canon_sha256":"75807c95bd9f5522bad0a0542e5de2b790050ee305473e113a983ff11c70f778"},"schema_version":"1.0","source":{"id":"1512.08766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08766","created_at":"2026-05-18T00:53:08Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08766v2","created_at":"2026-05-18T00:53:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08766","created_at":"2026-05-18T00:53:08Z"},{"alias_kind":"pith_short_12","alias_value":"WJCLYLQT7ONS","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJCLYLQT7ONS6ZMY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJCLYLQT","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:821f02ae9011d5414e569a1ef069a794e874150deedc0d8611df4047301ccad2","target":"graph","created_at":"2026-05-18T00:53:08Z","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":"The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture for the description of this boundary. Our proof techniques are geometric in nature and rely on nesting spectrahedra between polytopes.","authors_text":"Elina Robeva, Kaie Kubjas, Richard Z. Robinson","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-29T19:51:33Z","title":"Positive semidefinite rank and nested spectrahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08766","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:b04cd350d18cdcb541afc6a2d4e1e17671236d3adfc16c97ffbcede1d20d1384","target":"record","created_at":"2026-05-18T00:53:08Z","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":"15de8d97cf3a31ab33a35085fe833f7ec45d3524cd23badb91d6494ce30df5d4","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-29T19:51:33Z","title_canon_sha256":"75807c95bd9f5522bad0a0542e5de2b790050ee305473e113a983ff11c70f778"},"schema_version":"1.0","source":{"id":"1512.08766","kind":"arxiv","version":2}},"canonical_sha256":"b244bc2e13fb9b2f6598d4708ef2c4d61b59a1737a8d98b6fbd4cdcccf857414","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b244bc2e13fb9b2f6598d4708ef2c4d61b59a1737a8d98b6fbd4cdcccf857414","first_computed_at":"2026-05-18T00:53:08.635776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:08.635776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZF46VCOy2N2UlBXIwvrWq+JdoN1989XjxXvbkNm9g0sH5D3d1nRuKjCxxig+rRc7c0MEy9DDhrnsvIJpeHyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:08.636263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b04cd350d18cdcb541afc6a2d4e1e17671236d3adfc16c97ffbcede1d20d1384","sha256:821f02ae9011d5414e569a1ef069a794e874150deedc0d8611df4047301ccad2"],"state_sha256":"c8e15747b26d7f3d605a4b3efb51c9bdf257e7f58ee9d038091900639e52897d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1B+c6dP3xsl6ChQPi5PsO3TQr5wikmOdxP5Ko98gLU6yBMPv4OmoNuC20nvuQ5+XW8Et8yBPse2h6KS7ijKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:07:21.378047Z","bundle_sha256":"3400746534bb6f770cb812ba1398b52cc89d3c21a58259176e70f9c617f167fb"}}