{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RYZ4HVV3CFKTF65WZ3NAUZJXZ2","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":"df6b2fdf3f819564b2e329990056cfc464d7ed07ecaf14005a0017fa41ce8190","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-14T07:34:28Z","title_canon_sha256":"4adf4f44bf913a5eb7267e917259c482009382814dfe98f57e921b07e9743497"},"schema_version":"1.0","source":{"id":"2505.09204","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.09204","created_at":"2026-05-20T14:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"2505.09204v2","created_at":"2026-05-20T14:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.09204","created_at":"2026-05-20T14:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"RYZ4HVV3CFKT","created_at":"2026-05-20T14:03:19Z"},{"alias_kind":"pith_short_16","alias_value":"RYZ4HVV3CFKTF65W","created_at":"2026-05-20T14:03:19Z"},{"alias_kind":"pith_short_8","alias_value":"RYZ4HVV3","created_at":"2026-05-20T14:03:19Z"}],"graph_snapshots":[{"event_id":"sha256:bdf5c0ecd2665e8831613e8bb93a8f6ebc147b4260ecb18a0b07fe26c7322006","target":"graph","created_at":"2026-05-20T14:03:19Z","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/2505.09204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Segre determinant is a polynomial which encodes the condition for points to lie on a bilinear hypersurface in the product of projective spaces. We study Segre determinants and compute them in various coordinate systems. We show that the Segre determinant represents the Chow-Lam form of a generic torus orbit in the Grassmannian. These Chow-Lam forms were introduced as a generalization of Chow forms for projective varieties, and enjoy many similar properties. We also present applications to algebraic vision and to Chow quotients of Grassmannians.","authors_text":"Elizabeth Pratt","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-14T07:34:28Z","title":"The Segre Determinant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09204","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":"sha256:089c288d632c5fc8a88664c364de537abed625fc9846a9d680d7c2f22d32fc74","target":"record","created_at":"2026-05-20T14:03:19Z","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":"df6b2fdf3f819564b2e329990056cfc464d7ed07ecaf14005a0017fa41ce8190","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-14T07:34:28Z","title_canon_sha256":"4adf4f44bf913a5eb7267e917259c482009382814dfe98f57e921b07e9743497"},"schema_version":"1.0","source":{"id":"2505.09204","kind":"arxiv","version":2}},"canonical_sha256":"8e33c3d6bb115532fbb6ceda0a6537ce85fb93a55f375a6a7180d1eb5a6ffe57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e33c3d6bb115532fbb6ceda0a6537ce85fb93a55f375a6a7180d1eb5a6ffe57","first_computed_at":"2026-05-20T14:03:19.028949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:19.028949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O7GS0TNDEmgPrzEME2SZVVwqi1vg9o4huyZ9u41SJVQPn5FOcruklT39lgpNW5Pr/t2I9JK+ezs5UvN66Om5Bw==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:19.029418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.09204","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:089c288d632c5fc8a88664c364de537abed625fc9846a9d680d7c2f22d32fc74","sha256:bdf5c0ecd2665e8831613e8bb93a8f6ebc147b4260ecb18a0b07fe26c7322006"],"state_sha256":"1ed9226b489fb45a128c41f2511adac8c4f43989e3b44acdc104b98393abb635"}