{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AJOJEBC3W3HE4TZEZOYYITJ7VZ","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":"8b65c20144327a4406dce680660934e2f432c27995bf0e5d0c410a8306557612","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-03-14T16:40:31Z","title_canon_sha256":"0860f0618f5e953ca0798a34910ae9537fe8136d3ab55a0c65a84080cb5153aa"},"schema_version":"1.0","source":{"id":"2503.11574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.11574","created_at":"2026-07-05T10:31:35Z"},{"alias_kind":"arxiv_version","alias_value":"2503.11574v1","created_at":"2026-07-05T10:31:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.11574","created_at":"2026-07-05T10:31:35Z"},{"alias_kind":"pith_short_12","alias_value":"AJOJEBC3W3HE","created_at":"2026-07-05T10:31:35Z"},{"alias_kind":"pith_short_16","alias_value":"AJOJEBC3W3HE4TZE","created_at":"2026-07-05T10:31:35Z"},{"alias_kind":"pith_short_8","alias_value":"AJOJEBC3","created_at":"2026-07-05T10:31:35Z"}],"graph_snapshots":[{"event_id":"sha256:2e15e5c3b2872e48cc5cf5675caa7e8afaf460d42c3845a28a2dd8c712d471d6","target":"graph","created_at":"2026-07-05T10:31:35Z","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/2503.11574/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study curved Kakeya sets associated with phase functions satisfying Bourgain's condition. In particular, we show that the analysis of curved Kakeya sets arising from translation-invariant phase functions under Bourgain's condition, as well as Nikodym sets on manifolds with constant sectional curvature, can be reduced to the study of standard Kakeya sets in Euclidean space. Combined with the recent breakthrough of Wang and Zahl, our work establishes the Nikodym conjecture for three-dimensional manifolds with constant sectional curvature.\n  Moreover, we consider $(d,k)$-Nikodym","authors_text":"Chuanwei Gao, Diankun Liu, Yakun Xi","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-03-14T16:40:31Z","title":"Curved Kakeya sets and Nikodym problems on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.11574","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":"sha256:4f5137cafae64eb477acebaea15b5396b4e523b6b7e9544106439bf55dcf1744","target":"record","created_at":"2026-07-05T10:31:35Z","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":"8b65c20144327a4406dce680660934e2f432c27995bf0e5d0c410a8306557612","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-03-14T16:40:31Z","title_canon_sha256":"0860f0618f5e953ca0798a34910ae9537fe8136d3ab55a0c65a84080cb5153aa"},"schema_version":"1.0","source":{"id":"2503.11574","kind":"arxiv","version":1}},"canonical_sha256":"025c92045bb6ce4e4f24cbb1844d3fae59b822f63b711c2cd636f68916945265","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"025c92045bb6ce4e4f24cbb1844d3fae59b822f63b711c2cd636f68916945265","first_computed_at":"2026-07-05T10:31:35.005127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:35.005127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQI2jtL6YTNX1Q3dXhfHalRfso6863S1y4b6RPsnuexh2A6T9wN2pdwXIpi+mivE5urZn35Wy9SVK9gxClHtCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:35.005732Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.11574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f5137cafae64eb477acebaea15b5396b4e523b6b7e9544106439bf55dcf1744","sha256:2e15e5c3b2872e48cc5cf5675caa7e8afaf460d42c3845a28a2dd8c712d471d6"],"state_sha256":"7a765baeb068dbd52d22605066d321cff969c7523b172f6cfddb00e5b8a8ccd4"}