{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KWWMKQPTCCQDJWA6DEQKMXGIEE","short_pith_number":"pith:KWWMKQPT","canonical_record":{"source":{"id":"2401.03684","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-01-08T06:18:37Z","cross_cats_sorted":["math.CO","math.OC"],"title_canon_sha256":"c0e2fce24e9c5b66e5f9fc03f00b99aa0f648b280a833899f9fefa44e48b9509","abstract_canon_sha256":"bd5833cea0e2bfd314309e9fda54c75cd963fd8ffb2e0fc74b30835af774b7ca"},"schema_version":"1.0"},"canonical_sha256":"55acc541f310a034d81e1920a65cc821346fd357db1efc4789e0e3013fd3ffe5","source":{"kind":"arxiv","id":"2401.03684","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.03684","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"2401.03684v3","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.03684","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"KWWMKQPTCCQD","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"pith_short_16","alias_value":"KWWMKQPTCCQDJWA6","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"pith_short_8","alias_value":"KWWMKQPT","created_at":"2026-07-05T08:40:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KWWMKQPTCCQDJWA6DEQKMXGIEE","target":"record","payload":{"canonical_record":{"source":{"id":"2401.03684","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-01-08T06:18:37Z","cross_cats_sorted":["math.CO","math.OC"],"title_canon_sha256":"c0e2fce24e9c5b66e5f9fc03f00b99aa0f648b280a833899f9fefa44e48b9509","abstract_canon_sha256":"bd5833cea0e2bfd314309e9fda54c75cd963fd8ffb2e0fc74b30835af774b7ca"},"schema_version":"1.0"},"canonical_sha256":"55acc541f310a034d81e1920a65cc821346fd357db1efc4789e0e3013fd3ffe5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:40:12.126955Z","signature_b64":"TKbKQfP5wK64cMlWoeLR64yRYaCh5s32ulVFqss5bQKGvnn8RDNo6s8kTplzU0Ph91eTk3FW7n6QReAuw7/RDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55acc541f310a034d81e1920a65cc821346fd357db1efc4789e0e3013fd3ffe5","last_reissued_at":"2026-07-05T08:40:12.126452Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:40:12.126452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.03684","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":"2026-07-05T08:40:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghSvY+Meof8a128maX7+s+MB+v509Q4CZfK7einJj5F9iGqSCtKWBE2HdJD0unUOP2h/16K9IlR6+4FP1d+PCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:09:32.985054Z"},"content_sha256":"b89829246de170a8f83b5a4d67681fb242f41ee42a6eef50801f346eabc0d425","schema_version":"1.0","event_id":"sha256:b89829246de170a8f83b5a4d67681fb242f41ee42a6eef50801f346eabc0d425"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KWWMKQPTCCQDJWA6DEQKMXGIEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Two Lives of the Grassmannian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.OC"],"primary_cat":"math.AG","authors_text":"Bernd Sturmfels, Bernhard Reinke, Hannah Friedman, Karel Devriendt","submitted_at":"2024-01-08T06:18:37Z","abstract_excerpt":"The real Grassmannian is both a projective variety (via Pl\\\"ucker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develop the commutative algebra of the latter variety. We introduce the squared Grassmannian, and we study applications to determinantal point processes in statistics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03684","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/2401.03684/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":"2026-07-05T08:40:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64vk26AdbC5nwKq63dJ2SvIt5itwQU3EeftibuH+EWckNVWkeLB1SnOH/6xf9BNueIZJbHrNNQeWeO9D5azWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:09:32.985800Z"},"content_sha256":"70ddf04610e9e118f2d6d87b5c790ca92270e264f57e68d0157cf3976e7f68d5","schema_version":"1.0","event_id":"sha256:70ddf04610e9e118f2d6d87b5c790ca92270e264f57e68d0157cf3976e7f68d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE/bundle.json","state_url":"https://pith.science/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE/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":"2026-08-06T08:09:32Z","links":{"resolver":"https://pith.science/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE","bundle":"https://pith.science/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE/bundle.json","state":"https://pith.science/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWWMKQPTCCQDJWA6DEQKMXGIEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KWWMKQPTCCQDJWA6DEQKMXGIEE","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":"bd5833cea0e2bfd314309e9fda54c75cd963fd8ffb2e0fc74b30835af774b7ca","cross_cats_sorted":["math.CO","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-01-08T06:18:37Z","title_canon_sha256":"c0e2fce24e9c5b66e5f9fc03f00b99aa0f648b280a833899f9fefa44e48b9509"},"schema_version":"1.0","source":{"id":"2401.03684","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.03684","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"2401.03684v3","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.03684","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"KWWMKQPTCCQD","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"pith_short_16","alias_value":"KWWMKQPTCCQDJWA6","created_at":"2026-07-05T08:40:12Z"},{"alias_kind":"pith_short_8","alias_value":"KWWMKQPT","created_at":"2026-07-05T08:40:12Z"}],"graph_snapshots":[{"event_id":"sha256:70ddf04610e9e118f2d6d87b5c790ca92270e264f57e68d0157cf3976e7f68d5","target":"graph","created_at":"2026-07-05T08:40:12Z","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/2401.03684/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The real Grassmannian is both a projective variety (via Pl\\\"ucker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develop the commutative algebra of the latter variety. We introduce the squared Grassmannian, and we study applications to determinantal point processes in statistics.","authors_text":"Bernd Sturmfels, Bernhard Reinke, Hannah Friedman, Karel Devriendt","cross_cats":["math.CO","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-01-08T06:18:37Z","title":"The Two Lives of the Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03684","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:b89829246de170a8f83b5a4d67681fb242f41ee42a6eef50801f346eabc0d425","target":"record","created_at":"2026-07-05T08:40:12Z","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":"bd5833cea0e2bfd314309e9fda54c75cd963fd8ffb2e0fc74b30835af774b7ca","cross_cats_sorted":["math.CO","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-01-08T06:18:37Z","title_canon_sha256":"c0e2fce24e9c5b66e5f9fc03f00b99aa0f648b280a833899f9fefa44e48b9509"},"schema_version":"1.0","source":{"id":"2401.03684","kind":"arxiv","version":3}},"canonical_sha256":"55acc541f310a034d81e1920a65cc821346fd357db1efc4789e0e3013fd3ffe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55acc541f310a034d81e1920a65cc821346fd357db1efc4789e0e3013fd3ffe5","first_computed_at":"2026-07-05T08:40:12.126452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:40:12.126452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TKbKQfP5wK64cMlWoeLR64yRYaCh5s32ulVFqss5bQKGvnn8RDNo6s8kTplzU0Ph91eTk3FW7n6QReAuw7/RDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:40:12.126955Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.03684","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b89829246de170a8f83b5a4d67681fb242f41ee42a6eef50801f346eabc0d425","sha256:70ddf04610e9e118f2d6d87b5c790ca92270e264f57e68d0157cf3976e7f68d5"],"state_sha256":"f10b0a8cda618e9fb3da0b3e0a53fe4e55bda57bcea1c3eabd446d6d5d901909"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cppkjHRXiVo04HPEUdHbhha0KTYw3LYpfEhTAj5cns5j5zZFzlnykzXtJCqSF53azkGIRE7pHyxipgX/7hooCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T08:09:32.993203Z","bundle_sha256":"45ea3c8787b7eec6acb3e260be26f744a05a0497e6ae978448ed8e144d6ae17e"}}