{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7JGWPFSUANJFQ6R23ZZSA5ZUJG","short_pith_number":"pith:7JGWPFSU","schema_version":"1.0","canonical_sha256":"fa4d6796540352587a3ade73207734499d381607e9745d1389e784bd5a0f8802","source":{"kind":"arxiv","id":"1403.5090","version":1},"attestation_state":"computed","paper":{"title":"On $3$-dimensional $\\left(\\varepsilon \\right)$-para Sasakian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Punam Gupta","submitted_at":"2014-03-20T10:35:29Z","abstract_excerpt":"The purpose of the present paper is to study the globally and locally $\\varphi $-${\\cal T}$-symmetric $\\left( \\varepsilon \\right) $-para Sasakian manifold in dimension $3$. The globally $\\varphi $-$ {\\cal T}$-symmetric $3$-dimensional $\\left( \\varepsilon \\right) $-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally $\\varphi $-${\\cal T}$ -symmetric is given. A $3$-dimensional $% \\left( \\varepsilon \\right) $ -para Sasakian manifold is locally $\\varphi $-$ {\\cal T}$-symmetric if and only"},"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":"1403.5090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-20T10:35:29Z","cross_cats_sorted":[],"title_canon_sha256":"3bdb69636e756ea22e459b12d99c8cd68d324ada5886895436e79e9de44958c4","abstract_canon_sha256":"07034497ce04661c4fea0dfcb9e1517a24ab3987ac494d6e398a03cbd0c6e639"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:58.233509Z","signature_b64":"+RH98LqJD5Iwnp7VyARiWmRGWoRFaXCBBVEm7HjZNEPb8c7/00I/5YRLh1xvclwdGvbfkaT6X0pV3JljrZ5+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa4d6796540352587a3ade73207734499d381607e9745d1389e784bd5a0f8802","last_reissued_at":"2026-05-18T02:55:58.233136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:58.233136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $3$-dimensional $\\left(\\varepsilon \\right)$-para Sasakian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Punam Gupta","submitted_at":"2014-03-20T10:35:29Z","abstract_excerpt":"The purpose of the present paper is to study the globally and locally $\\varphi $-${\\cal T}$-symmetric $\\left( \\varepsilon \\right) $-para Sasakian manifold in dimension $3$. The globally $\\varphi $-$ {\\cal T}$-symmetric $3$-dimensional $\\left( \\varepsilon \\right) $-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally $\\varphi $-${\\cal T}$ -symmetric is given. A $3$-dimensional $% \\left( \\varepsilon \\right) $ -para Sasakian manifold is locally $\\varphi $-$ {\\cal T}$-symmetric if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5090","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":""},"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":"1403.5090","created_at":"2026-05-18T02:55:58.233187+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5090v1","created_at":"2026-05-18T02:55:58.233187+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5090","created_at":"2026-05-18T02:55:58.233187+00:00"},{"alias_kind":"pith_short_12","alias_value":"7JGWPFSUANJF","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7JGWPFSUANJFQ6R2","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7JGWPFSU","created_at":"2026-05-18T12:28:19.803747+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/7JGWPFSUANJFQ6R23ZZSA5ZUJG","json":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG.json","graph_json":"https://pith.science/api/pith-number/7JGWPFSUANJFQ6R23ZZSA5ZUJG/graph.json","events_json":"https://pith.science/api/pith-number/7JGWPFSUANJFQ6R23ZZSA5ZUJG/events.json","paper":"https://pith.science/paper/7JGWPFSU"},"agent_actions":{"view_html":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG","download_json":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG.json","view_paper":"https://pith.science/paper/7JGWPFSU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5090&json=true","fetch_graph":"https://pith.science/api/pith-number/7JGWPFSUANJFQ6R23ZZSA5ZUJG/graph.json","fetch_events":"https://pith.science/api/pith-number/7JGWPFSUANJFQ6R23ZZSA5ZUJG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG/action/storage_attestation","attest_author":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG/action/author_attestation","sign_citation":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG/action/citation_signature","submit_replication":"https://pith.science/pith/7JGWPFSUANJFQ6R23ZZSA5ZUJG/action/replication_record"}},"created_at":"2026-05-18T02:55:58.233187+00:00","updated_at":"2026-05-18T02:55:58.233187+00:00"}