{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:M6AY7AMCE3VUA2LFA3HBACFJ55","short_pith_number":"pith:M6AY7AMC","canonical_record":{"source":{"id":"1908.04361","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-08-12T20:09:04Z","cross_cats_sorted":[],"title_canon_sha256":"2bb1d1100dc60fa08f5763fa6baa2f0ad5ee197bc7e9ff8bcb2e32b85f0d3716","abstract_canon_sha256":"b27601a75bd12b05b842c0c624d4bd88f2de9c3228d017518198851ff242c6c1"},"schema_version":"1.0"},"canonical_sha256":"67818f818226eb40696506ce1008a9ef434a76364db838b55e35b00869fe84b7","source":{"kind":"arxiv","id":"1908.04361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04361","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04361v1","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04361","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"M6AY7AMCE3VU","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"pith_short_16","alias_value":"M6AY7AMCE3VUA2LF","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"pith_short_8","alias_value":"M6AY7AMC","created_at":"2026-07-04T23:54:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:M6AY7AMCE3VUA2LFA3HBACFJ55","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04361","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-08-12T20:09:04Z","cross_cats_sorted":[],"title_canon_sha256":"2bb1d1100dc60fa08f5763fa6baa2f0ad5ee197bc7e9ff8bcb2e32b85f0d3716","abstract_canon_sha256":"b27601a75bd12b05b842c0c624d4bd88f2de9c3228d017518198851ff242c6c1"},"schema_version":"1.0"},"canonical_sha256":"67818f818226eb40696506ce1008a9ef434a76364db838b55e35b00869fe84b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:54:30.073438Z","signature_b64":"IJ35e02TSDcScV5BELxbPBexZ1OURjlyvr+t2Yqwzp/I9iKWEM0LK/kA0imj0Nq1QXzd8YaaH9HgOZ0/pq3eCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67818f818226eb40696506ce1008a9ef434a76364db838b55e35b00869fe84b7","last_reissued_at":"2026-07-04T23:54:30.072972Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:54:30.072972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04361","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":"2026-07-04T23:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKCdGMt4YxO+HoaecWs9JhdHjCCF1x/x1/0W0R5oRM477wpu1N/b7nBIzJgN455kn5T61WHeYWxV8EiS1zWJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:13:34.514457Z"},"content_sha256":"55a3960315a04bd20cb7093f5c79413efae0bd48ba9eb0054cf093a9021424dd","schema_version":"1.0","event_id":"sha256:55a3960315a04bd20cb7093f5c79413efae0bd48ba9eb0054cf093a9021424dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:M6AY7AMCE3VUA2LFA3HBACFJ55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic and exterior Dirichlet problems for the minimal surface equation in the Heisenberg group with a balanced metric","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Edson S. Figueiredo, Fidelis Bittencourt, Jaime Ripoll, Pedro Fusieger","submitted_at":"2019-08-12T20:09:04Z","abstract_excerpt":"It is proved that the Heisenberg group $\\operatorname*{Nil}\\nolimits_{3}$ with a balanced metric, the sum of the left and right invariant metrics, splits as a Riemannian product $\\mathbb{T\\times Z}$, where $\\mathbb{T}$ is a totally geodesic surface and $\\mathbb{Z}$ the center of $\\operatorname*{Nil}% \\nolimits_{3}.$ It is then proved the existence of complete properly embedded minimal surfaces in $\\operatorname*{Nil}\\nolimits_{3}$ by solving the asymptotic Dirichlet problem for the minimal surface equation on $\\mathbb{T}$. It is also proved the existence of complete properly embedded minimal s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04361","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04361/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:54:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wfzkDIIaGL5qFl+aaiNJ5vm5u3VpAQyqgvONjdVhVWBTNjXjMViwp36+6oBrnYFNoFb2tRpPVMDpxQ/LoiKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:13:34.514834Z"},"content_sha256":"ff74850962996e8419250f8cd5e0f284edc928f9fd21dbabcf080b89b0d14989","schema_version":"1.0","event_id":"sha256:ff74850962996e8419250f8cd5e0f284edc928f9fd21dbabcf080b89b0d14989"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6AY7AMCE3VUA2LFA3HBACFJ55/bundle.json","state_url":"https://pith.science/pith/M6AY7AMCE3VUA2LFA3HBACFJ55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6AY7AMCE3VUA2LFA3HBACFJ55/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":"2026-07-06T08:13:34Z","links":{"resolver":"https://pith.science/pith/M6AY7AMCE3VUA2LFA3HBACFJ55","bundle":"https://pith.science/pith/M6AY7AMCE3VUA2LFA3HBACFJ55/bundle.json","state":"https://pith.science/pith/M6AY7AMCE3VUA2LFA3HBACFJ55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6AY7AMCE3VUA2LFA3HBACFJ55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M6AY7AMCE3VUA2LFA3HBACFJ55","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":"b27601a75bd12b05b842c0c624d4bd88f2de9c3228d017518198851ff242c6c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-08-12T20:09:04Z","title_canon_sha256":"2bb1d1100dc60fa08f5763fa6baa2f0ad5ee197bc7e9ff8bcb2e32b85f0d3716"},"schema_version":"1.0","source":{"id":"1908.04361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04361","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04361v1","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04361","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"pith_short_12","alias_value":"M6AY7AMCE3VU","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"pith_short_16","alias_value":"M6AY7AMCE3VUA2LF","created_at":"2026-07-04T23:54:30Z"},{"alias_kind":"pith_short_8","alias_value":"M6AY7AMC","created_at":"2026-07-04T23:54:30Z"}],"graph_snapshots":[{"event_id":"sha256:ff74850962996e8419250f8cd5e0f284edc928f9fd21dbabcf080b89b0d14989","target":"graph","created_at":"2026-07-04T23:54:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is proved that the Heisenberg group $\\operatorname*{Nil}\\nolimits_{3}$ with a balanced metric, the sum of the left and right invariant metrics, splits as a Riemannian product $\\mathbb{T\\times Z}$, where $\\mathbb{T}$ is a totally geodesic surface and $\\mathbb{Z}$ the center of $\\operatorname*{Nil}% \\nolimits_{3}.$ It is then proved the existence of complete properly embedded minimal surfaces in $\\operatorname*{Nil}\\nolimits_{3}$ by solving the asymptotic Dirichlet problem for the minimal surface equation on $\\mathbb{T}$. It is also proved the existence of complete properly embedded minimal s","authors_text":"Edson S. Figueiredo, Fidelis Bittencourt, Jaime Ripoll, Pedro Fusieger","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-08-12T20:09:04Z","title":"Asymptotic and exterior Dirichlet problems for the minimal surface equation in the Heisenberg group with a balanced metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04361","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":"sha256:55a3960315a04bd20cb7093f5c79413efae0bd48ba9eb0054cf093a9021424dd","target":"record","created_at":"2026-07-04T23:54:30Z","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":"b27601a75bd12b05b842c0c624d4bd88f2de9c3228d017518198851ff242c6c1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-08-12T20:09:04Z","title_canon_sha256":"2bb1d1100dc60fa08f5763fa6baa2f0ad5ee197bc7e9ff8bcb2e32b85f0d3716"},"schema_version":"1.0","source":{"id":"1908.04361","kind":"arxiv","version":1}},"canonical_sha256":"67818f818226eb40696506ce1008a9ef434a76364db838b55e35b00869fe84b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67818f818226eb40696506ce1008a9ef434a76364db838b55e35b00869fe84b7","first_computed_at":"2026-07-04T23:54:30.072972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:54:30.072972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJ35e02TSDcScV5BELxbPBexZ1OURjlyvr+t2Yqwzp/I9iKWEM0LK/kA0imj0Nq1QXzd8YaaH9HgOZ0/pq3eCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:54:30.073438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55a3960315a04bd20cb7093f5c79413efae0bd48ba9eb0054cf093a9021424dd","sha256:ff74850962996e8419250f8cd5e0f284edc928f9fd21dbabcf080b89b0d14989"],"state_sha256":"c85731e6322a966c15afe9af9dbfbcad1bf30da975237dd641db05fc0b9504a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"My78uX28qQTwT6ZYIPDttLHej15p1T/DOpHg3SvKAC96fc6azN0PQ5w9qQMSOKtmGKnZ282C2PMBvf2JLaTFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T08:13:34.517417Z","bundle_sha256":"579570c45b233b21080bdc9e1b804b73d1ae266bddba3a46fa99fbd578053cae"}}