{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PRLQ76P5UUGCIVZWNBXOPQKJD2","short_pith_number":"pith:PRLQ76P5","canonical_record":{"source":{"id":"1608.03252","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-10T18:38:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cc6d90b92c390100d79817b180467d83e172268f63864710b6aca8a1020bfc75","abstract_canon_sha256":"54f11e9ae09ba9fdf71d955383ecac4fadfaf14e24f48611f36b5bd64bf441d3"},"schema_version":"1.0"},"canonical_sha256":"7c570ff9fda50c245736686ee7c1491e8b19e41e002ebb7422c5bff2bd7cbb23","source":{"kind":"arxiv","id":"1608.03252","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03252","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03252v2","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03252","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"PRLQ76P5UUGC","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PRLQ76P5UUGCIVZW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PRLQ76P5","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PRLQ76P5UUGCIVZWNBXOPQKJD2","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03252","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-10T18:38:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cc6d90b92c390100d79817b180467d83e172268f63864710b6aca8a1020bfc75","abstract_canon_sha256":"54f11e9ae09ba9fdf71d955383ecac4fadfaf14e24f48611f36b5bd64bf441d3"},"schema_version":"1.0"},"canonical_sha256":"7c570ff9fda50c245736686ee7c1491e8b19e41e002ebb7422c5bff2bd7cbb23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:50.116533Z","signature_b64":"5nSFYYxGlb//IhNW3XNv8jE7AqDMSQXZXwgJNYffkyrXjMz9MvWM4ulg34kn7ytOZJGNgtSkm5V2T/UIWZRmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c570ff9fda50c245736686ee7c1491e8b19e41e002ebb7422c5bff2bd7cbb23","last_reissued_at":"2026-05-18T00:02:50.115902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:50.115902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03252","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//KM3zNG98oXu8SYH4641xl9wyf7G+q2btBCN4KkuTcO+bHxx2LuSY+W9BZuWPHK2G5kZk5PU9ppsFAXDkixAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T00:21:56.615687Z"},"content_sha256":"ea8ecfd3bd83045682abfb61b7f58a03a35e993fe91446ab9777ca2c720e3957","schema_version":"1.0","event_id":"sha256:ea8ecfd3bd83045682abfb61b7f58a03a35e993fe91446ab9777ca2c720e3957"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PRLQ76P5UUGCIVZWNBXOPQKJD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On special submanifolds of the Page space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Mustafa Kalafat, Ramazan Sari","submitted_at":"2016-08-10T18:38:31Z","abstract_excerpt":"In this paper, we study some classes of submanifolds of codimension one and two in the Page space. These submanifolds are totally geodesic. We also compute their curvature and show that some of them are constant curvature spaces. Finally we give information on how the Page space is related to some other metrics on the same underlying smooth manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03252","kind":"arxiv","version":2},"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":"2026-05-18T00:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RoJxF/UhCBEJosGUjco2kDrtZe93JudDTtUkaeYHJ1OM/k8Hn20O2cpaXBp3CSq1Dj0CbwBQ4HsTvk3AvroZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T00:21:56.616031Z"},"content_sha256":"a7db27f6231b64eeeba70e844f24a4856a986674e06111676fdae2fa512d9d4c","schema_version":"1.0","event_id":"sha256:a7db27f6231b64eeeba70e844f24a4856a986674e06111676fdae2fa512d9d4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2/bundle.json","state_url":"https://pith.science/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2/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":"2026-07-04T00:21:56Z","links":{"resolver":"https://pith.science/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2","bundle":"https://pith.science/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2/bundle.json","state":"https://pith.science/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PRLQ76P5UUGCIVZWNBXOPQKJD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PRLQ76P5UUGCIVZWNBXOPQKJD2","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":"54f11e9ae09ba9fdf71d955383ecac4fadfaf14e24f48611f36b5bd64bf441d3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-10T18:38:31Z","title_canon_sha256":"cc6d90b92c390100d79817b180467d83e172268f63864710b6aca8a1020bfc75"},"schema_version":"1.0","source":{"id":"1608.03252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03252","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03252v2","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03252","created_at":"2026-05-18T00:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"PRLQ76P5UUGC","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PRLQ76P5UUGCIVZW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PRLQ76P5","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:a7db27f6231b64eeeba70e844f24a4856a986674e06111676fdae2fa512d9d4c","target":"graph","created_at":"2026-05-18T00:02:50Z","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 this paper, we study some classes of submanifolds of codimension one and two in the Page space. These submanifolds are totally geodesic. We also compute their curvature and show that some of them are constant curvature spaces. Finally we give information on how the Page space is related to some other metrics on the same underlying smooth manifold.","authors_text":"Mustafa Kalafat, Ramazan Sari","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-10T18:38:31Z","title":"On special submanifolds of the Page space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03252","kind":"arxiv","version":2},"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:ea8ecfd3bd83045682abfb61b7f58a03a35e993fe91446ab9777ca2c720e3957","target":"record","created_at":"2026-05-18T00:02:50Z","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":"54f11e9ae09ba9fdf71d955383ecac4fadfaf14e24f48611f36b5bd64bf441d3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-10T18:38:31Z","title_canon_sha256":"cc6d90b92c390100d79817b180467d83e172268f63864710b6aca8a1020bfc75"},"schema_version":"1.0","source":{"id":"1608.03252","kind":"arxiv","version":2}},"canonical_sha256":"7c570ff9fda50c245736686ee7c1491e8b19e41e002ebb7422c5bff2bd7cbb23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c570ff9fda50c245736686ee7c1491e8b19e41e002ebb7422c5bff2bd7cbb23","first_computed_at":"2026-05-18T00:02:50.115902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:50.115902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5nSFYYxGlb//IhNW3XNv8jE7AqDMSQXZXwgJNYffkyrXjMz9MvWM4ulg34kn7ytOZJGNgtSkm5V2T/UIWZRmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:50.116533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea8ecfd3bd83045682abfb61b7f58a03a35e993fe91446ab9777ca2c720e3957","sha256:a7db27f6231b64eeeba70e844f24a4856a986674e06111676fdae2fa512d9d4c"],"state_sha256":"3477ea71882e9025f40c3be65e676b8ed407e08b60942448cf2df9cfd5fd7a0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6DCzttjhm7NxY59Wsdp7AbVAcbj/gasMhPGyxJZlGC87bKWyrM0JPrqWnGCu7Nl0fMpieSmscal//A9IT9MAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T00:21:56.618080Z","bundle_sha256":"3bd1bae844a43d485ce250070f1466a524d259a694e0a14ba140b1e5d101582a"}}