{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5XK6IFV5CDOJSHCS5DRYA4U566","short_pith_number":"pith:5XK6IFV5","canonical_record":{"source":{"id":"1104.1412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T19:34:24Z","cross_cats_sorted":[],"title_canon_sha256":"1700dcb3a95d80a6474f9856e4f5ecfc43a7a37589142fba13e35439d53e0b3f","abstract_canon_sha256":"6aff7a249f045717246e478c914ed4295a3bd9f2ba18399dd30904191c27c077"},"schema_version":"1.0"},"canonical_sha256":"edd5e416bd10dc991c52e8e380729df7aaf7fbddbe7972ea785668f9811aca86","source":{"kind":"arxiv","id":"1104.1412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1412","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1412v1","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1412","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"5XK6IFV5CDOJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5XK6IFV5CDOJSHCS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5XK6IFV5","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5XK6IFV5CDOJSHCS5DRYA4U566","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T19:34:24Z","cross_cats_sorted":[],"title_canon_sha256":"1700dcb3a95d80a6474f9856e4f5ecfc43a7a37589142fba13e35439d53e0b3f","abstract_canon_sha256":"6aff7a249f045717246e478c914ed4295a3bd9f2ba18399dd30904191c27c077"},"schema_version":"1.0"},"canonical_sha256":"edd5e416bd10dc991c52e8e380729df7aaf7fbddbe7972ea785668f9811aca86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:52.302917Z","signature_b64":"Vg5IHznK4Cf6vE8bH+6d0Qzi/XxzKO0wCujJCN7/JWwwWS8dtFx4zswkXZ8KreDfvBLtOJZhn8FBKf2up1aZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edd5e416bd10dc991c52e8e380729df7aaf7fbddbe7972ea785668f9811aca86","last_reissued_at":"2026-05-18T04:24:52.302452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:52.302452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1412","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":"2026-05-18T04:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+1xBFrgxi6bfEurMk71Ag6QMF2G3jesVH3H3tuQHLtU1L56eAnLfWBz0mpPh/mxGIWuZ9N6NgX7kwJ1VBg1LBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:21:16.400333Z"},"content_sha256":"1c49416be87af4b8a84c90dea47cb7606656c2b0da7e0a227b00c5d4622b91b1","schema_version":"1.0","event_id":"sha256:1c49416be87af4b8a84c90dea47cb7606656c2b0da7e0a227b00c5d4622b91b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5XK6IFV5CDOJSHCS5DRYA4U566","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On completeness of integral manifolds of nullity distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Carlos Olmos, Francisco Vittone","submitted_at":"2011-04-07T19:34:24Z","abstract_excerpt":"We give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are complete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1412","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":"2026-05-18T04:24:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/lEX9c76bWf4f31pwMd9gCI3fxRNgdpCViKR0r9W2M0rpKxRrnMrHGg3K6vlcjz460+Wrxkzhj2yRz/VcW49DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:21:16.400678Z"},"content_sha256":"726ee1e2dcc9b0a156504854f43830e08210e378fa44ac2f27aafd4ceb2be3cd","schema_version":"1.0","event_id":"sha256:726ee1e2dcc9b0a156504854f43830e08210e378fa44ac2f27aafd4ceb2be3cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XK6IFV5CDOJSHCS5DRYA4U566/bundle.json","state_url":"https://pith.science/pith/5XK6IFV5CDOJSHCS5DRYA4U566/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XK6IFV5CDOJSHCS5DRYA4U566/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":"2026-06-03T05:21:16Z","links":{"resolver":"https://pith.science/pith/5XK6IFV5CDOJSHCS5DRYA4U566","bundle":"https://pith.science/pith/5XK6IFV5CDOJSHCS5DRYA4U566/bundle.json","state":"https://pith.science/pith/5XK6IFV5CDOJSHCS5DRYA4U566/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XK6IFV5CDOJSHCS5DRYA4U566/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5XK6IFV5CDOJSHCS5DRYA4U566","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":"6aff7a249f045717246e478c914ed4295a3bd9f2ba18399dd30904191c27c077","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T19:34:24Z","title_canon_sha256":"1700dcb3a95d80a6474f9856e4f5ecfc43a7a37589142fba13e35439d53e0b3f"},"schema_version":"1.0","source":{"id":"1104.1412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1412","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1412v1","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1412","created_at":"2026-05-18T04:24:52Z"},{"alias_kind":"pith_short_12","alias_value":"5XK6IFV5CDOJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"5XK6IFV5CDOJSHCS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"5XK6IFV5","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:726ee1e2dcc9b0a156504854f43830e08210e378fa44ac2f27aafd4ceb2be3cd","target":"graph","created_at":"2026-05-18T04:24:52Z","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 give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are complete.","authors_text":"Carlos Olmos, Francisco Vittone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T19:34:24Z","title":"On completeness of integral manifolds of nullity distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1412","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":"sha256:1c49416be87af4b8a84c90dea47cb7606656c2b0da7e0a227b00c5d4622b91b1","target":"record","created_at":"2026-05-18T04:24:52Z","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":"6aff7a249f045717246e478c914ed4295a3bd9f2ba18399dd30904191c27c077","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T19:34:24Z","title_canon_sha256":"1700dcb3a95d80a6474f9856e4f5ecfc43a7a37589142fba13e35439d53e0b3f"},"schema_version":"1.0","source":{"id":"1104.1412","kind":"arxiv","version":1}},"canonical_sha256":"edd5e416bd10dc991c52e8e380729df7aaf7fbddbe7972ea785668f9811aca86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edd5e416bd10dc991c52e8e380729df7aaf7fbddbe7972ea785668f9811aca86","first_computed_at":"2026-05-18T04:24:52.302452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:52.302452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vg5IHznK4Cf6vE8bH+6d0Qzi/XxzKO0wCujJCN7/JWwwWS8dtFx4zswkXZ8KreDfvBLtOJZhn8FBKf2up1aZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:52.302917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c49416be87af4b8a84c90dea47cb7606656c2b0da7e0a227b00c5d4622b91b1","sha256:726ee1e2dcc9b0a156504854f43830e08210e378fa44ac2f27aafd4ceb2be3cd"],"state_sha256":"b3a1a1d164cc26511e9fff0f7709470464c5528ef725bee26e897daa0949ee16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XfzLBPekEkCFYt/9tMHnAQFhJpVR8r7wwjm4GEGpSVWPDcO2aZtyy+ATHvPPOA0Ge6gCRkaze8Ej/CV9cGAWDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:21:16.402859Z","bundle_sha256":"c0e5d2c8b7198a6e84688142a9c291a1d790bff9b9e4e9fc1ca39aaf4e88f017"}}