{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DIFJYEB77KFWT6D4QITER3V3SY","short_pith_number":"pith:DIFJYEB7","schema_version":"1.0","canonical_sha256":"1a0a9c103ffa8b69f87c822648eebb963b044cc827aab7112ec15f45076d629d","source":{"kind":"arxiv","id":"2605.20000","version":1},"attestation_state":"computed","paper":{"title":"Newman--Penrose formalism in $3$-dimensional trans-Sasakian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marie-Am\\'elie Lawn, Mukut Mani Tripathi, Prachi","submitted_at":"2026-05-19T15:33:48Z","abstract_excerpt":"We study $3$-dimensional trans-Sasakian manifolds using the Newman--Penrose formalism. In this framework, the geometry of the structure vector field is encoded by scalar spin coefficients: acceleration, shear, expansion, and twist. A central observation is that, in dimension $3$, the trans-Sasakian condition is equivalent to the characteristic vector field defining a shear-free geodesic congruence, or equivalently a conformal foliation by geodesics. Thus, the Newman--Penrose equations provide a direct scalar formulation of the conformal foliations studied by Baird and Wood in the theory of har"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.20000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-19T15:33:48Z","cross_cats_sorted":[],"title_canon_sha256":"90de25d6e9af0e5838dcc10073757edd22cdc8adaa058c15c7f134061c6154bd","abstract_canon_sha256":"539cbbbf8e473170b052689ff468dd3507fce49d1f3d9c0adf946a01f571468f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:05:58.575778Z","signature_b64":"bYd8+Qf3qsIDyoIWQBQ5oe9A94Dn8J4srBuWEePQZcEQ0b3iiXG7ARdge+IR/tocBLd+0Tmbf871nkiQVXq5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a0a9c103ffa8b69f87c822648eebb963b044cc827aab7112ec15f45076d629d","last_reissued_at":"2026-05-20T02:05:58.575302Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:05:58.575302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Newman--Penrose formalism in $3$-dimensional trans-Sasakian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marie-Am\\'elie Lawn, Mukut Mani Tripathi, Prachi","submitted_at":"2026-05-19T15:33:48Z","abstract_excerpt":"We study $3$-dimensional trans-Sasakian manifolds using the Newman--Penrose formalism. In this framework, the geometry of the structure vector field is encoded by scalar spin coefficients: acceleration, shear, expansion, and twist. A central observation is that, in dimension $3$, the trans-Sasakian condition is equivalent to the characteristic vector field defining a shear-free geodesic congruence, or equivalently a conformal foliation by geodesics. Thus, the Newman--Penrose equations provide a direct scalar formulation of the conformal foliations studied by Baird and Wood in the theory of har"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20000","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20000/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.20000","created_at":"2026-05-20T02:05:58.575372+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20000v1","created_at":"2026-05-20T02:05:58.575372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20000","created_at":"2026-05-20T02:05:58.575372+00:00"},{"alias_kind":"pith_short_12","alias_value":"DIFJYEB77KFW","created_at":"2026-05-20T02:05:58.575372+00:00"},{"alias_kind":"pith_short_16","alias_value":"DIFJYEB77KFWT6D4","created_at":"2026-05-20T02:05:58.575372+00:00"},{"alias_kind":"pith_short_8","alias_value":"DIFJYEB7","created_at":"2026-05-20T02:05:58.575372+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY","json":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY.json","graph_json":"https://pith.science/api/pith-number/DIFJYEB77KFWT6D4QITER3V3SY/graph.json","events_json":"https://pith.science/api/pith-number/DIFJYEB77KFWT6D4QITER3V3SY/events.json","paper":"https://pith.science/paper/DIFJYEB7"},"agent_actions":{"view_html":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY","download_json":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY.json","view_paper":"https://pith.science/paper/DIFJYEB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20000&json=true","fetch_graph":"https://pith.science/api/pith-number/DIFJYEB77KFWT6D4QITER3V3SY/graph.json","fetch_events":"https://pith.science/api/pith-number/DIFJYEB77KFWT6D4QITER3V3SY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY/action/storage_attestation","attest_author":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY/action/author_attestation","sign_citation":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY/action/citation_signature","submit_replication":"https://pith.science/pith/DIFJYEB77KFWT6D4QITER3V3SY/action/replication_record"}},"created_at":"2026-05-20T02:05:58.575372+00:00","updated_at":"2026-05-20T02:05:58.575372+00:00"}