{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZKFB6I4UDK4ESDS7CXRBODA7W6","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":"88d768762c54b5a57c3cebda2314aeed5c076da0b86221093caa523122994a6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-01-19T20:14:16Z","title_canon_sha256":"83c3f27a5dc0f15e1e99ea5f054de17fa73d309da4005b75f599cc65f717fdb3"},"schema_version":"1.0","source":{"id":"1001.3398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3398","created_at":"2026-07-04T17:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3398v1","created_at":"2026-07-04T17:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3398","created_at":"2026-07-04T17:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZKFB6I4UDK4E","created_at":"2026-07-04T17:19:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZKFB6I4UDK4ESDS7","created_at":"2026-07-04T17:19:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZKFB6I4U","created_at":"2026-07-04T17:19:53Z"}],"graph_snapshots":[{"event_id":"sha256:648f2884625f22e75b68ff8bac60022fc298baa5657eb6b818a22e31b94c3c76","target":"graph","created_at":"2026-07-04T17:19:53Z","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/1001.3398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the geometry of warped foliations. After examining the Levi-Civita connection, we describe the formulae for sectional, Ricci and scalar curvatures. In the final part of this note, we present some examples.","authors_text":"Szymon M. Walczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-01-19T20:14:16Z","title":"On the geometry of warped foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3398","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:d0a33c336d45471c588db953a558ab56d1fa4053b868f893a23b54d0294f4b92","target":"record","created_at":"2026-07-04T17:19:53Z","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":"88d768762c54b5a57c3cebda2314aeed5c076da0b86221093caa523122994a6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-01-19T20:14:16Z","title_canon_sha256":"83c3f27a5dc0f15e1e99ea5f054de17fa73d309da4005b75f599cc65f717fdb3"},"schema_version":"1.0","source":{"id":"1001.3398","kind":"arxiv","version":1}},"canonical_sha256":"ca8a1f23941ab8490e5f15e2170c1fb7a79d69e4ea17250f9df0d7106a767425","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca8a1f23941ab8490e5f15e2170c1fb7a79d69e4ea17250f9df0d7106a767425","first_computed_at":"2026-07-04T17:19:53.903343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:19:53.903343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nyZo3YtGp9/ojlfhumgn/4YL7wViFkZ303mrFJcgJcAccAn9PuTtX/cpEm/S6Gie2Xm4t5Zp4emvjQ9BIjbHBg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:19:53.903754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0a33c336d45471c588db953a558ab56d1fa4053b868f893a23b54d0294f4b92","sha256:648f2884625f22e75b68ff8bac60022fc298baa5657eb6b818a22e31b94c3c76"],"state_sha256":"31d7ff65f1e86f3d9f48ed0242be865f9930c5dd524308f039a4583fe876c2dc"}