{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5NOZ6EUK6TVIMS7GDMVPNS44VA","short_pith_number":"pith:5NOZ6EUK","canonical_record":{"source":{"id":"1003.0281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-01T08:57:26Z","cross_cats_sorted":[],"title_canon_sha256":"80530c6d8139f492ac2b8cf2a82ee47d66b047bd0c8e6f91824565360e818412","abstract_canon_sha256":"0ccca3791f143fdb5a7cfebccd55a81c3cd546497e0cd83ec34f009910a1b708"},"schema_version":"1.0"},"canonical_sha256":"eb5d9f128af4ea864be61b2af6cb9ca838f50840ca2c64126bfd3cfa5f2fe57c","source":{"kind":"arxiv","id":"1003.0281","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0281","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0281v2","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0281","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"5NOZ6EUK6TVI","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5NOZ6EUK6TVIMS7G","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5NOZ6EUK","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5NOZ6EUK6TVIMS7GDMVPNS44VA","target":"record","payload":{"canonical_record":{"source":{"id":"1003.0281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-01T08:57:26Z","cross_cats_sorted":[],"title_canon_sha256":"80530c6d8139f492ac2b8cf2a82ee47d66b047bd0c8e6f91824565360e818412","abstract_canon_sha256":"0ccca3791f143fdb5a7cfebccd55a81c3cd546497e0cd83ec34f009910a1b708"},"schema_version":"1.0"},"canonical_sha256":"eb5d9f128af4ea864be61b2af6cb9ca838f50840ca2c64126bfd3cfa5f2fe57c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:10.680332Z","signature_b64":"rhIc7eviwQRmJbuRnrBomZJGk165x6LPo4MLHlL34MXNC18XX8ut7aK0WyOkWamHBr9egbidtQTtEMbbhNtpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb5d9f128af4ea864be61b2af6cb9ca838f50840ca2c64126bfd3cfa5f2fe57c","last_reissued_at":"2026-05-18T04:10:10.679621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:10.679621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.0281","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":"2026-05-18T04:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uu0Nvg8zEekC2JtmPRkrpZ2PysUF06TFBnee/q2Q+HOWZpPVFe+1bsw6Cn4Vb8S2wL5wo3iFP+vaCBa6DMMSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:37:06.814467Z"},"content_sha256":"f00afdcf71ecf11bf57fb5bf0763c20a27a5062278f4da21db41118824851194","schema_version":"1.0","event_id":"sha256:f00afdcf71ecf11bf57fb5bf0763c20a27a5062278f4da21db41118824851194"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5NOZ6EUK6TVIMS7GDMVPNS44VA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Characteristic Foliations of Metric Contact Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Amine Hadjar, Gianluca Bande","submitted_at":"2010-03-01T08:57:26Z","abstract_excerpt":"A contact pair on a manifold always admits an associated metric for which the two characteristic contact foliations are orthogonal. We show that all these metrics have the same volume element. We also prove that the leaves of the characteristic foliations are minimal with respect to these metrics. We give an example where these leaves are not totally geodesic submanifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0281","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":"2026-05-18T04:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Mx+d8VgACB4Vv8RF8XTVHpJcmoLgUuSfHrWRlK62O36ILDMvoMhLhKj10ofdmRfNG4EOZHtjoYoTr1jdumhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:37:06.815115Z"},"content_sha256":"1f4a5a347edba6cf40b8fd25762edd02d188e90f0cbe038d572d7faa97cdb9f7","schema_version":"1.0","event_id":"sha256:1f4a5a347edba6cf40b8fd25762edd02d188e90f0cbe038d572d7faa97cdb9f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA/bundle.json","state_url":"https://pith.science/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA/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":"2026-05-30T22:37:06Z","links":{"resolver":"https://pith.science/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA","bundle":"https://pith.science/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA/bundle.json","state":"https://pith.science/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NOZ6EUK6TVIMS7GDMVPNS44VA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5NOZ6EUK6TVIMS7GDMVPNS44VA","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":"0ccca3791f143fdb5a7cfebccd55a81c3cd546497e0cd83ec34f009910a1b708","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-01T08:57:26Z","title_canon_sha256":"80530c6d8139f492ac2b8cf2a82ee47d66b047bd0c8e6f91824565360e818412"},"schema_version":"1.0","source":{"id":"1003.0281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0281","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0281v2","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0281","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"5NOZ6EUK6TVI","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5NOZ6EUK6TVIMS7G","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5NOZ6EUK","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:1f4a5a347edba6cf40b8fd25762edd02d188e90f0cbe038d572d7faa97cdb9f7","target":"graph","created_at":"2026-05-18T04:10:10Z","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":"A contact pair on a manifold always admits an associated metric for which the two characteristic contact foliations are orthogonal. We show that all these metrics have the same volume element. We also prove that the leaves of the characteristic foliations are minimal with respect to these metrics. We give an example where these leaves are not totally geodesic submanifolds.","authors_text":"Amine Hadjar, Gianluca Bande","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-01T08:57:26Z","title":"On the Characteristic Foliations of Metric Contact Pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0281","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:f00afdcf71ecf11bf57fb5bf0763c20a27a5062278f4da21db41118824851194","target":"record","created_at":"2026-05-18T04:10:10Z","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":"0ccca3791f143fdb5a7cfebccd55a81c3cd546497e0cd83ec34f009910a1b708","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-01T08:57:26Z","title_canon_sha256":"80530c6d8139f492ac2b8cf2a82ee47d66b047bd0c8e6f91824565360e818412"},"schema_version":"1.0","source":{"id":"1003.0281","kind":"arxiv","version":2}},"canonical_sha256":"eb5d9f128af4ea864be61b2af6cb9ca838f50840ca2c64126bfd3cfa5f2fe57c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb5d9f128af4ea864be61b2af6cb9ca838f50840ca2c64126bfd3cfa5f2fe57c","first_computed_at":"2026-05-18T04:10:10.679621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:10.679621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rhIc7eviwQRmJbuRnrBomZJGk165x6LPo4MLHlL34MXNC18XX8ut7aK0WyOkWamHBr9egbidtQTtEMbbhNtpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:10.680332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f00afdcf71ecf11bf57fb5bf0763c20a27a5062278f4da21db41118824851194","sha256:1f4a5a347edba6cf40b8fd25762edd02d188e90f0cbe038d572d7faa97cdb9f7"],"state_sha256":"55aac871a511a1159ed4a0da3b9fa8d605d54a6ce5f671035a47df29b8353615"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MURBPgXyIKen2qcCjkG3k0TkveskV+jQp/yz5WcCNSJBVPlsDoE0KXtfAT7Ynv6R/jO+FFZqFpwri8gi98SrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:37:06.817943Z","bundle_sha256":"30d66a5c10c5788ea90039e1f3568636d892d423babc2bcf3a6d9f0f36d9b4d7"}}