{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JUC4QVUNOLVHR4UX7DRJAWU7LB","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":"dbafeb643961f9359fb151e4e87be505c4b68b6161b9d9934a8ef7c69324a6cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-19T18:37:57Z","title_canon_sha256":"ebf3c82172f85343bc30a504c7f3f7f589811d451fba8ef303888a73d4ec8bd3"},"schema_version":"1.0","source":{"id":"2412.15161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15161","created_at":"2026-07-05T09:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15161v1","created_at":"2026-07-05T09:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15161","created_at":"2026-07-05T09:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"JUC4QVUNOLVH","created_at":"2026-07-05T09:51:58Z"},{"alias_kind":"pith_short_16","alias_value":"JUC4QVUNOLVHR4UX","created_at":"2026-07-05T09:51:58Z"},{"alias_kind":"pith_short_8","alias_value":"JUC4QVUN","created_at":"2026-07-05T09:51:58Z"}],"graph_snapshots":[{"event_id":"sha256:fa4eb2f5b1edfa0ce496b3804553b23174ab729af638316066a364a5342c913a","target":"graph","created_at":"2026-07-05T09:51:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.15161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of Cosines and geodesic triangle inequalities.","authors_text":"Tin-Yau Tam, Xiang Xiang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-19T18:37:57Z","title":"Geometric Properties and Distance Inequalities on Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15161","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:a7320602d3e475cf0b0552f46513cc15129acdf4d8c8bd7eb9156c949bcf90ea","target":"record","created_at":"2026-07-05T09:51:58Z","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":"dbafeb643961f9359fb151e4e87be505c4b68b6161b9d9934a8ef7c69324a6cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-19T18:37:57Z","title_canon_sha256":"ebf3c82172f85343bc30a504c7f3f7f589811d451fba8ef303888a73d4ec8bd3"},"schema_version":"1.0","source":{"id":"2412.15161","kind":"arxiv","version":1}},"canonical_sha256":"4d05c8568d72ea78f297f8e2905a9f585dee612e9b7d76faf979d7564c6e30bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d05c8568d72ea78f297f8e2905a9f585dee612e9b7d76faf979d7564c6e30bb","first_computed_at":"2026-07-05T09:51:58.740799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:51:58.740799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kKVskAN1qXOFOYWjtJSchpUKCKpaP97meO4QPTuasLCtCPa9MaHJqU1gUlHQcQLbEe4O8sL3uy0U1fjuQBA5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:51:58.741235Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.15161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7320602d3e475cf0b0552f46513cc15129acdf4d8c8bd7eb9156c949bcf90ea","sha256:fa4eb2f5b1edfa0ce496b3804553b23174ab729af638316066a364a5342c913a"],"state_sha256":"031930a7c02a872ae190a6564d0c52e33ad4b31254ce78cd5159750221237f93"}