{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GGDEGMRTO2TRPCAX5JBQ6YEDOI","short_pith_number":"pith:GGDEGMRT","canonical_record":{"source":{"id":"1907.01931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-02T16:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"5f1c93304693c5ace6ab75ac54d94b61822362be91ba87d26672c0ce40af63d6","abstract_canon_sha256":"4dc09b86db59d73280a2aaaa2939e092f8ad73851253d54bbea19041595f52f5"},"schema_version":"1.0"},"canonical_sha256":"318643323376a7178817ea430f60837205cdd250b751840070259a1bc83e3b38","source":{"kind":"arxiv","id":"1907.01931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01931","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01931v1","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01931","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"GGDEGMRTO2TR","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GGDEGMRTO2TRPCAX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GGDEGMRT","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GGDEGMRTO2TRPCAX5JBQ6YEDOI","target":"record","payload":{"canonical_record":{"source":{"id":"1907.01931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-02T16:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"5f1c93304693c5ace6ab75ac54d94b61822362be91ba87d26672c0ce40af63d6","abstract_canon_sha256":"4dc09b86db59d73280a2aaaa2939e092f8ad73851253d54bbea19041595f52f5"},"schema_version":"1.0"},"canonical_sha256":"318643323376a7178817ea430f60837205cdd250b751840070259a1bc83e3b38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:34.477841Z","signature_b64":"4zGi28tGK/8xOoeotz5VqRSQSjZb+DCsJpKUJG/057eU5U1w62ipvHVHekFyA+wo6jhNDeKq7CPiCm8PVCuQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"318643323376a7178817ea430f60837205cdd250b751840070259a1bc83e3b38","last_reissued_at":"2026-05-17T23:41:34.477125Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:34.477125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.01931","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":"2026-05-17T23:41:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTk7RzXaZq+y1C/Czd/YWWN4TQzjaCC1xjD5updtoHALYCe31FqVJ7wM+0MEELd6gT/qRngNPiZi5VW30fplDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T13:40:23.471770Z"},"content_sha256":"b07d30620c6fbe965992c416773633be633158d5dca80b93cf0c1eeaa23784e5","schema_version":"1.0","event_id":"sha256:b07d30620c6fbe965992c416773633be633158d5dca80b93cf0c1eeaa23784e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GGDEGMRTO2TRPCAX5JBQ6YEDOI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Pseudo-Umbilical Spacelike Submanifolds in Indefinite Space Form Mn+p p (c)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Majid Ali Choudhary","submitted_at":"2019-07-02T16:52:38Z","abstract_excerpt":"In the present note, first we derive an intrinsic inequality for Pseudo-umbilical spacelike submanifold in an indefinite space form. We use this inequality to show that such submanifold is totally geodesic. In the rest part of this paper, using a result of Aiyama [1], we prove that Pseudo-umbilical spacelike subamnifold is totally umbilical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01931","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":"2026-05-17T23:41:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5Cp+DB9sINo7HLWfEmyGTpW+AntexeuOey9+bbkPzInMCuZzlhFREOPCfdISoOcvJaUTXP+BKQ5NTiUyaXfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T13:40:23.472110Z"},"content_sha256":"1b447348b2ce0ad707f485794941a6a3f238f2d290ec1c9fcb80aa81d2b71541","schema_version":"1.0","event_id":"sha256:1b447348b2ce0ad707f485794941a6a3f238f2d290ec1c9fcb80aa81d2b71541"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI/bundle.json","state_url":"https://pith.science/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI/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":"2026-06-28T13:40:23Z","links":{"resolver":"https://pith.science/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI","bundle":"https://pith.science/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI/bundle.json","state":"https://pith.science/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGDEGMRTO2TRPCAX5JBQ6YEDOI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GGDEGMRTO2TRPCAX5JBQ6YEDOI","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":"4dc09b86db59d73280a2aaaa2939e092f8ad73851253d54bbea19041595f52f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-02T16:52:38Z","title_canon_sha256":"5f1c93304693c5ace6ab75ac54d94b61822362be91ba87d26672c0ce40af63d6"},"schema_version":"1.0","source":{"id":"1907.01931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01931","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01931v1","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01931","created_at":"2026-05-17T23:41:34Z"},{"alias_kind":"pith_short_12","alias_value":"GGDEGMRTO2TR","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GGDEGMRTO2TRPCAX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GGDEGMRT","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:1b447348b2ce0ad707f485794941a6a3f238f2d290ec1c9fcb80aa81d2b71541","target":"graph","created_at":"2026-05-17T23:41:34Z","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 note, first we derive an intrinsic inequality for Pseudo-umbilical spacelike submanifold in an indefinite space form. We use this inequality to show that such submanifold is totally geodesic. In the rest part of this paper, using a result of Aiyama [1], we prove that Pseudo-umbilical spacelike subamnifold is totally umbilical.","authors_text":"Majid Ali Choudhary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-02T16:52:38Z","title":"On Pseudo-Umbilical Spacelike Submanifolds in Indefinite Space Form Mn+p p (c)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01931","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:b07d30620c6fbe965992c416773633be633158d5dca80b93cf0c1eeaa23784e5","target":"record","created_at":"2026-05-17T23:41:34Z","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":"4dc09b86db59d73280a2aaaa2939e092f8ad73851253d54bbea19041595f52f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-07-02T16:52:38Z","title_canon_sha256":"5f1c93304693c5ace6ab75ac54d94b61822362be91ba87d26672c0ce40af63d6"},"schema_version":"1.0","source":{"id":"1907.01931","kind":"arxiv","version":1}},"canonical_sha256":"318643323376a7178817ea430f60837205cdd250b751840070259a1bc83e3b38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"318643323376a7178817ea430f60837205cdd250b751840070259a1bc83e3b38","first_computed_at":"2026-05-17T23:41:34.477125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:34.477125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4zGi28tGK/8xOoeotz5VqRSQSjZb+DCsJpKUJG/057eU5U1w62ipvHVHekFyA+wo6jhNDeKq7CPiCm8PVCuQCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:34.477841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b07d30620c6fbe965992c416773633be633158d5dca80b93cf0c1eeaa23784e5","sha256:1b447348b2ce0ad707f485794941a6a3f238f2d290ec1c9fcb80aa81d2b71541"],"state_sha256":"1ad2e57fff507ca86dbdbb1076c4751b1f2ff977926016326c60e5e0c086b944"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHODxMMBZB6SmEDgALMuD7kQ/qlGNQzj7g3x/gq3WADNtCHekBS00ufDkb6h/yuDemLEDsciMqQQg9mLG+rWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T13:40:23.473957Z","bundle_sha256":"f5201396449aa1a16e5f85520fb10a5939cea627971d8dd6b3f5200a27b913a4"}}