{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AXJP4G3LVXVHG4KUY32UKDC6D6","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":"e84d14edc0502400f0436d66e18858419748ed31c83466bad2854180915f203b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-27T07:29:30Z","title_canon_sha256":"80ec82f0ab75e310948869fcbc5c78f308af88aa29552275fcd69662cc52234a"},"schema_version":"1.0","source":{"id":"1204.6125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6125","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6125v1","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6125","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"AXJP4G3LVXVH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AXJP4G3LVXVHG4KU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AXJP4G3L","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:d54501eac1cf2c1bb9e056f8d9a5eab9d6f184331f2bb6cabcbe0c79354185d6","target":"graph","created_at":"2026-05-18T03:56:46Z","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"},"paper":{"abstract_excerpt":"In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if $M = N^{\\perp} \\times_f N^T$ is a warped CR-submanifold such that $N^{\\perp}$ is $\\phi$?-anti-invariant and NT is $\\phi$?-invariant, then M is a CR-product. We show that the second fundamental form of a contact CR warped product of a indefinite S space form satisfies a geometric inequality, $\\|h\\|^2 \\geq p{3\\|\\nabla lnf\\|^2 - \\triangle lnf + (c + 2)k + 1}$.","authors_text":"Khushwant Singh, S. S. Bhatia","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-27T07:29:30Z","title":"Warped product contact CR-submanifolds of globally framed f-manifolds with Lorentz metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6125","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":"sha256:059581d3b5f0f981495ace1005171a7fe93960b96371604cc3fdcd6ba6f0a564","target":"record","created_at":"2026-05-18T03:56:46Z","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":"e84d14edc0502400f0436d66e18858419748ed31c83466bad2854180915f203b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-27T07:29:30Z","title_canon_sha256":"80ec82f0ab75e310948869fcbc5c78f308af88aa29552275fcd69662cc52234a"},"schema_version":"1.0","source":{"id":"1204.6125","kind":"arxiv","version":1}},"canonical_sha256":"05d2fe1b6badea737154c6f5450c5e1fb86e9ce2470ed0f1bd1a7d5a11d467f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05d2fe1b6badea737154c6f5450c5e1fb86e9ce2470ed0f1bd1a7d5a11d467f8","first_computed_at":"2026-05-18T03:56:46.944913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:46.944913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nGrGpXFMAv+AKqgucE4br7X/OOCunlzPE2AQTUSKGvqLJOQ7JvOrLs6QlyRkWW+k9gNnwDUYS2J99/bwLZicBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:46.945446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:059581d3b5f0f981495ace1005171a7fe93960b96371604cc3fdcd6ba6f0a564","sha256:d54501eac1cf2c1bb9e056f8d9a5eab9d6f184331f2bb6cabcbe0c79354185d6"],"state_sha256":"b4d6e4129b0c94e7192a4808d6ecc3e966edbb7dcb5e1c03ce24eeb60ea72ed2"}