{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TNNYSVPICFSXFNAS6NBYY5SFFC","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":"b3213075f1039f91c1733094450f685f44d85d8242cc1427037b3f81a6a67bc8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T04:07:19Z","title_canon_sha256":"889af8d45b5f5931925157b0ef38934b3bb6e744de70f5c3b46b6921ca6e6050"},"schema_version":"1.0","source":{"id":"2605.25408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25408","created_at":"2026-05-26T02:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25408v1","created_at":"2026-05-26T02:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25408","created_at":"2026-05-26T02:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"TNNYSVPICFSX","created_at":"2026-05-26T02:04:33Z"},{"alias_kind":"pith_short_16","alias_value":"TNNYSVPICFSXFNAS","created_at":"2026-05-26T02:04:33Z"},{"alias_kind":"pith_short_8","alias_value":"TNNYSVPI","created_at":"2026-05-26T02:04:33Z"}],"graph_snapshots":[{"event_id":"sha256:c3289c87e8c87c5b7574a1ff337fdf1442a7e0a3b035856b58d2eafe3f15cf7b","target":"graph","created_at":"2026-05-26T02:04:33Z","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/2605.25408/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study tautness properties of a Riemannian foliation by investigating a symmetric 2-tensor associated with the mean curvature of the foliation. As a consequence, we prove a tautness condition for Riemannian foliations on compact manifolds via the symmetric tautness tensor. Moreover, several applications of the aforementioned tensor are provided under various geometric conditions.","authors_text":"Jungwoo Moon","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T04:07:19Z","title":"Symmetric tautness tensor on Riemannian foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25408","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":"sha256:10a6a239a4021f1278a3132e6e84579ddaf70518ce4de7de0ee93d1c828bcded","target":"record","created_at":"2026-05-26T02:04:33Z","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":"b3213075f1039f91c1733094450f685f44d85d8242cc1427037b3f81a6a67bc8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T04:07:19Z","title_canon_sha256":"889af8d45b5f5931925157b0ef38934b3bb6e744de70f5c3b46b6921ca6e6050"},"schema_version":"1.0","source":{"id":"2605.25408","kind":"arxiv","version":1}},"canonical_sha256":"9b5b8955e8116572b412f3438c7645288b5caddeff01a3286f6c75af0234078f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b5b8955e8116572b412f3438c7645288b5caddeff01a3286f6c75af0234078f","first_computed_at":"2026-05-26T02:04:33.242688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:33.242688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BN6x57XEzEyQQJcSoU7Cpl3mX8zvlodm7qhss0PUoV5mbRa4W8DxHRKYISW10toznfAcoaILGsQCiBK6Jyk4AA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:33.243586Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10a6a239a4021f1278a3132e6e84579ddaf70518ce4de7de0ee93d1c828bcded","sha256:c3289c87e8c87c5b7574a1ff337fdf1442a7e0a3b035856b58d2eafe3f15cf7b"],"state_sha256":"d51cd628400933e2a2c8b970626249b83cbe432956e62f0a76efa7a38db1ad91"}