{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:TYXPGNIFMMV5652F3KENPSHYGM","short_pith_number":"pith:TYXPGNIF","schema_version":"1.0","canonical_sha256":"9e2ef33505632bdf7745da88d7c8f83336eadf7654ea5f3e087ed110ad1a98eb","source":{"kind":"arxiv","id":"1011.0633","version":1},"attestation_state":"computed","paper":{"title":"Existence of isoperimetric regions in contact sub-Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Manuel Ritor\\'e, Matteo Galli","submitted_at":"2010-11-02T14:51:42Z","abstract_excerpt":"We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Riemannian metric is compact."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.0633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-02T14:51:42Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"e1e271f0f1deb11d018200b71382e25895c11d0c0d7e08c54d0af2e7064fd31b","abstract_canon_sha256":"a1f67e7d0e8212816256b2820212058718b3279583c21d0af38b52532ec72fd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:59.554791Z","signature_b64":"evB6QE4T/4EKd1tzKXEKN3u5PixnCnimNBw7XORMS/qfNb2mzXhyTm/IrgY2SiE6DvkY7gUlm954o1qO8cW9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e2ef33505632bdf7745da88d7c8f83336eadf7654ea5f3e087ed110ad1a98eb","last_reissued_at":"2026-05-18T02:43:59.554308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:59.554308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of isoperimetric regions in contact sub-Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Manuel Ritor\\'e, Matteo Galli","submitted_at":"2010-11-02T14:51:42Z","abstract_excerpt":"We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Riemannian metric is compact."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0633","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.0633","created_at":"2026-05-18T02:43:59.554405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.0633v1","created_at":"2026-05-18T02:43:59.554405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0633","created_at":"2026-05-18T02:43:59.554405+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYXPGNIFMMV5","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYXPGNIFMMV5652F","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYXPGNIF","created_at":"2026-05-18T12:26:15.391820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM","json":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM.json","graph_json":"https://pith.science/api/pith-number/TYXPGNIFMMV5652F3KENPSHYGM/graph.json","events_json":"https://pith.science/api/pith-number/TYXPGNIFMMV5652F3KENPSHYGM/events.json","paper":"https://pith.science/paper/TYXPGNIF"},"agent_actions":{"view_html":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM","download_json":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM.json","view_paper":"https://pith.science/paper/TYXPGNIF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.0633&json=true","fetch_graph":"https://pith.science/api/pith-number/TYXPGNIFMMV5652F3KENPSHYGM/graph.json","fetch_events":"https://pith.science/api/pith-number/TYXPGNIFMMV5652F3KENPSHYGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM/action/storage_attestation","attest_author":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM/action/author_attestation","sign_citation":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM/action/citation_signature","submit_replication":"https://pith.science/pith/TYXPGNIFMMV5652F3KENPSHYGM/action/replication_record"}},"created_at":"2026-05-18T02:43:59.554405+00:00","updated_at":"2026-05-18T02:43:59.554405+00:00"}