{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UXGSKHZYG36QAH4DTWKTHUIBJZ","short_pith_number":"pith:UXGSKHZY","canonical_record":{"source":{"id":"1504.04659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T23:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"6b1ecfa5756a7dba9932f6f920a03459d9fe7428a86e5504f0632ef63970ae8a","abstract_canon_sha256":"9df21005eee7824af76d888741117b976b2a76a90c35360d6d7578d741ee2023"},"schema_version":"1.0"},"canonical_sha256":"a5cd251f3836fd001f839d9533d1014e55149d575191d7534f95feb09b6bd4f4","source":{"kind":"arxiv","id":"1504.04659","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04659","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04659v2","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04659","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"UXGSKHZYG36Q","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UXGSKHZYG36QAH4D","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UXGSKHZY","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UXGSKHZYG36QAH4DTWKTHUIBJZ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T23:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"6b1ecfa5756a7dba9932f6f920a03459d9fe7428a86e5504f0632ef63970ae8a","abstract_canon_sha256":"9df21005eee7824af76d888741117b976b2a76a90c35360d6d7578d741ee2023"},"schema_version":"1.0"},"canonical_sha256":"a5cd251f3836fd001f839d9533d1014e55149d575191d7534f95feb09b6bd4f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:02.146502Z","signature_b64":"n7EwF1zWHNe9M6BN5IxwNKKYudN7yysuN2+8SYZTvzMxGsyydEo7wryv03QBRsW7u6TeYk2pVeNjtquwFhwcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5cd251f3836fd001f839d9533d1014e55149d575191d7534f95feb09b6bd4f4","last_reissued_at":"2026-05-18T00:23:02.145910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:02.145910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04659","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":"2026-05-18T00:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K6dWKAE9MXwl7QRDjHKVLTJsFgoVPxhuyv7kMElfh3pDpJHEvb51TwsWVySD6M0agz/GcpN/K5s9O1V1E+wIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T11:00:03.915583Z"},"content_sha256":"bcded65448fcbb93c2f6db63ca45f8dcbfbb338925243de90a221445fca13b12","schema_version":"1.0","event_id":"sha256:bcded65448fcbb93c2f6db63ca45f8dcbfbb338925243de90a221445fca13b12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UXGSKHZYG36QAH4DTWKTHUIBJZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A fundamental differential system of 3-dimensional Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rui Albuquerque","submitted_at":"2015-04-17T23:42:05Z","abstract_excerpt":"We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to a remarkable Weingarten type equation for surfaces on hyperbolic 3-space. An independent proof for low dimensions of the structural equations gives new insight on the intrinsic exterior differential system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04659","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":"2026-05-18T00:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXj06B+yVP2kyDXcq88NHaGXN+eKcRJZBLH3hJiN8L9Nz40CjCkm+ld59t+n0eEwrXbH7DlC6QFeKOBtWSN6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T11:00:03.915952Z"},"content_sha256":"dab32b8d1d5d23fd33ec57e4fa8a3c5c2512faf97a52eef6c353f31d4a6e8676","schema_version":"1.0","event_id":"sha256:dab32b8d1d5d23fd33ec57e4fa8a3c5c2512faf97a52eef6c353f31d4a6e8676"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ/bundle.json","state_url":"https://pith.science/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ/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":"2026-07-04T11:00:03Z","links":{"resolver":"https://pith.science/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ","bundle":"https://pith.science/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ/bundle.json","state":"https://pith.science/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXGSKHZYG36QAH4DTWKTHUIBJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UXGSKHZYG36QAH4DTWKTHUIBJZ","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":"9df21005eee7824af76d888741117b976b2a76a90c35360d6d7578d741ee2023","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T23:42:05Z","title_canon_sha256":"6b1ecfa5756a7dba9932f6f920a03459d9fe7428a86e5504f0632ef63970ae8a"},"schema_version":"1.0","source":{"id":"1504.04659","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04659","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04659v2","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04659","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"UXGSKHZYG36Q","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UXGSKHZYG36QAH4D","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UXGSKHZY","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:dab32b8d1d5d23fd33ec57e4fa8a3c5c2512faf97a52eef6c353f31d4a6e8676","target":"graph","created_at":"2026-05-18T00:23:02Z","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 briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to a remarkable Weingarten type equation for surfaces on hyperbolic 3-space. An independent proof for low dimensions of the structural equations gives new insight on the intrinsic exterior differential system.","authors_text":"Rui Albuquerque","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T23:42:05Z","title":"A fundamental differential system of 3-dimensional Riemannian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04659","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:bcded65448fcbb93c2f6db63ca45f8dcbfbb338925243de90a221445fca13b12","target":"record","created_at":"2026-05-18T00:23:02Z","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":"9df21005eee7824af76d888741117b976b2a76a90c35360d6d7578d741ee2023","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T23:42:05Z","title_canon_sha256":"6b1ecfa5756a7dba9932f6f920a03459d9fe7428a86e5504f0632ef63970ae8a"},"schema_version":"1.0","source":{"id":"1504.04659","kind":"arxiv","version":2}},"canonical_sha256":"a5cd251f3836fd001f839d9533d1014e55149d575191d7534f95feb09b6bd4f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5cd251f3836fd001f839d9533d1014e55149d575191d7534f95feb09b6bd4f4","first_computed_at":"2026-05-18T00:23:02.145910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:02.145910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n7EwF1zWHNe9M6BN5IxwNKKYudN7yysuN2+8SYZTvzMxGsyydEo7wryv03QBRsW7u6TeYk2pVeNjtquwFhwcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:02.146502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04659","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcded65448fcbb93c2f6db63ca45f8dcbfbb338925243de90a221445fca13b12","sha256:dab32b8d1d5d23fd33ec57e4fa8a3c5c2512faf97a52eef6c353f31d4a6e8676"],"state_sha256":"1d82a6c67d42aa8deb36e8bf666dadee262b86cd626adf61a5e352ea8629eee7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LG/4i+Bo2fn0dhW85xQsZLtJVYCU+DLSUuHzGuwdo0b8Y+2LlNEZW8U6wBHxFmrFZ0Wy9maoKIM5yCoxO7DfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T11:00:03.917914Z","bundle_sha256":"eb4076e407014a858ef36195208075cbd0f2a43d2cd74aeb8b77de308a6d8110"}}