{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LVW6MXSXTA7VE57QTZNKFHEPVB","short_pith_number":"pith:LVW6MXSX","canonical_record":{"source":{"id":"1907.05721","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-10T18:59:00Z","cross_cats_sorted":[],"title_canon_sha256":"8c32467f536452ac491cdb9f4247de2195b9d2512dd28b2075b92959e31d4a22","abstract_canon_sha256":"3e8cdfe993119d4e4d52f24469974888e9fd8623b95f5da5df7f7a2953e28117"},"schema_version":"1.0"},"canonical_sha256":"5d6de65e57983f5277f09e5aa29c8fa86ae727b6b8f7fcffacdfea849a445913","source":{"kind":"arxiv","id":"1907.05721","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05721","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05721v1","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05721","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"LVW6MXSXTA7V","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LVW6MXSXTA7VE57Q","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LVW6MXSX","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LVW6MXSXTA7VE57QTZNKFHEPVB","target":"record","payload":{"canonical_record":{"source":{"id":"1907.05721","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-10T18:59:00Z","cross_cats_sorted":[],"title_canon_sha256":"8c32467f536452ac491cdb9f4247de2195b9d2512dd28b2075b92959e31d4a22","abstract_canon_sha256":"3e8cdfe993119d4e4d52f24469974888e9fd8623b95f5da5df7f7a2953e28117"},"schema_version":"1.0"},"canonical_sha256":"5d6de65e57983f5277f09e5aa29c8fa86ae727b6b8f7fcffacdfea849a445913","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:44.650001Z","signature_b64":"mrios6yBPzYG0DtiFgtNyrERlaAAYX64v4JaauMBsZfbIYkfBGfCB0aB/vPrvFr7UNcixl0u5kCbUCukTLu1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d6de65e57983f5277f09e5aa29c8fa86ae727b6b8f7fcffacdfea849a445913","last_reissued_at":"2026-05-17T23:40:44.649344Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:44.649344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.05721","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ohag9EfORc7c1Xe4dIqNtCWxRK8TSaSBtEhEHP96J3lLRzXv9TUim6NXEaabLSIlrORAgLZzM5jKIhk3BJhlAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:20:14.421725Z"},"content_sha256":"eeb447bcab9a76419e663e82dc055eb0880a8a2c6d6e0810ca2f54d2ebef70b3","schema_version":"1.0","event_id":"sha256:eeb447bcab9a76419e663e82dc055eb0880a8a2c6d6e0810ca2f54d2ebef70b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LVW6MXSXTA7VE57QTZNKFHEPVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New classes of null hypersurfaces in indefinite Sasakian space-forms","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Samuel Ssekajja","submitted_at":"2019-07-10T18:59:00Z","abstract_excerpt":"We introduce two classes of null hypersurfaces of an indefinite Sasakian manifold, $(\\overline{M}, \\overline{\\phi},\\zeta, \\eta)$, tangent to the characteristic vector field $\\zeta$, called; {\\it contact screen conformal} and {\\it contact screen umbilic} null hypersurfaces. These hypersurfaces come in to fill the existing gap in screen conformal and screen totally umbilic null hypersurfaces. We prove that such hypersurfaces are contained in indefinite Sasakian space forms of constant $\\overline{\\phi}$-sectional curvature of $-3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05721","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPHlAOWhelFBl5d7PUFeMVAZNA+jTlb4yYvU/9v8OuIULAewqI5waMsOWi2I04Xq+FFqSZX70No2G9IYJ/X3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:20:14.422115Z"},"content_sha256":"bcdef8d70885832ad975bcd4cd0528ebb1260fde8ad1884cc953d58ffac777e0","schema_version":"1.0","event_id":"sha256:bcdef8d70885832ad975bcd4cd0528ebb1260fde8ad1884cc953d58ffac777e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVW6MXSXTA7VE57QTZNKFHEPVB/bundle.json","state_url":"https://pith.science/pith/LVW6MXSXTA7VE57QTZNKFHEPVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVW6MXSXTA7VE57QTZNKFHEPVB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T18:20:14Z","links":{"resolver":"https://pith.science/pith/LVW6MXSXTA7VE57QTZNKFHEPVB","bundle":"https://pith.science/pith/LVW6MXSXTA7VE57QTZNKFHEPVB/bundle.json","state":"https://pith.science/pith/LVW6MXSXTA7VE57QTZNKFHEPVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVW6MXSXTA7VE57QTZNKFHEPVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LVW6MXSXTA7VE57QTZNKFHEPVB","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":"3e8cdfe993119d4e4d52f24469974888e9fd8623b95f5da5df7f7a2953e28117","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-10T18:59:00Z","title_canon_sha256":"8c32467f536452ac491cdb9f4247de2195b9d2512dd28b2075b92959e31d4a22"},"schema_version":"1.0","source":{"id":"1907.05721","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05721","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05721v1","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05721","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"LVW6MXSXTA7V","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LVW6MXSXTA7VE57Q","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LVW6MXSX","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:bcdef8d70885832ad975bcd4cd0528ebb1260fde8ad1884cc953d58ffac777e0","target":"graph","created_at":"2026-05-17T23:40:44Z","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":"We introduce two classes of null hypersurfaces of an indefinite Sasakian manifold, $(\\overline{M}, \\overline{\\phi},\\zeta, \\eta)$, tangent to the characteristic vector field $\\zeta$, called; {\\it contact screen conformal} and {\\it contact screen umbilic} null hypersurfaces. These hypersurfaces come in to fill the existing gap in screen conformal and screen totally umbilic null hypersurfaces. We prove that such hypersurfaces are contained in indefinite Sasakian space forms of constant $\\overline{\\phi}$-sectional curvature of $-3$.","authors_text":"Samuel Ssekajja","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-10T18:59:00Z","title":"New classes of null hypersurfaces in indefinite Sasakian space-forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05721","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:eeb447bcab9a76419e663e82dc055eb0880a8a2c6d6e0810ca2f54d2ebef70b3","target":"record","created_at":"2026-05-17T23:40:44Z","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":"3e8cdfe993119d4e4d52f24469974888e9fd8623b95f5da5df7f7a2953e28117","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-10T18:59:00Z","title_canon_sha256":"8c32467f536452ac491cdb9f4247de2195b9d2512dd28b2075b92959e31d4a22"},"schema_version":"1.0","source":{"id":"1907.05721","kind":"arxiv","version":1}},"canonical_sha256":"5d6de65e57983f5277f09e5aa29c8fa86ae727b6b8f7fcffacdfea849a445913","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d6de65e57983f5277f09e5aa29c8fa86ae727b6b8f7fcffacdfea849a445913","first_computed_at":"2026-05-17T23:40:44.649344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:44.649344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mrios6yBPzYG0DtiFgtNyrERlaAAYX64v4JaauMBsZfbIYkfBGfCB0aB/vPrvFr7UNcixl0u5kCbUCukTLu1Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:44.650001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05721","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeb447bcab9a76419e663e82dc055eb0880a8a2c6d6e0810ca2f54d2ebef70b3","sha256:bcdef8d70885832ad975bcd4cd0528ebb1260fde8ad1884cc953d58ffac777e0"],"state_sha256":"42fc2b45537cdb8becf87e10523e7e20b917256c515fa99fe413f6518815b5c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxzAxYjUZZeFD8JnK9k2J1dDuVq6DfedAyZ8zb2ePeg5C37BSVrEc1Y3bpAdJoSCjPpbk980yjyQeom1Oy84Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:20:14.425376Z","bundle_sha256":"f1b516ba01718389b80e11d3bf6eb47d0a35936f907e9423ee83fdb995666255"}}