{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:P44CALC2UFNNPRF3FAALRIXNIA","short_pith_number":"pith:P44CALC2","schema_version":"1.0","canonical_sha256":"7f38202c5aa15ad7c4bb2800b8a2ed403f4a21e1be9163ed63909ab78b7d0d9a","source":{"kind":"arxiv","id":"1110.5483","version":1},"attestation_state":"computed","paper":{"title":"The Area Formula for Lipschitz Mappings of Carnot--Carath\\'{e}odory Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Maria Karmanova","submitted_at":"2011-10-25T12:39:56Z","abstract_excerpt":"We prove the sub-Riemannian analog of the area formula for Lipschitz (in sub-Riemannian sense) mappings of equiregular Carnot--Carath\\'{e}odory spaces."},"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":"1110.5483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-10-25T12:39:56Z","cross_cats_sorted":[],"title_canon_sha256":"949f580e4e906186de63cd62850ed2e5fef6b9a9f69a1356d9887005ac781be0","abstract_canon_sha256":"4fc8fa25db1c9c4c100c27e4b97f2dda7fbf88d897b0b7aea210b58ba0f3d6fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:22.817788Z","signature_b64":"PyHfJF3srQsQT2LboNRdYIYhmW+buYkCXnIC281mFB4VSnAe3q7rxQtrt6+2rCMlxID5ADJ0He8AXdg5c5kmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f38202c5aa15ad7c4bb2800b8a2ed403f4a21e1be9163ed63909ab78b7d0d9a","last_reissued_at":"2026-05-18T04:10:22.817393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:22.817393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Area Formula for Lipschitz Mappings of Carnot--Carath\\'{e}odory Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Maria Karmanova","submitted_at":"2011-10-25T12:39:56Z","abstract_excerpt":"We prove the sub-Riemannian analog of the area formula for Lipschitz (in sub-Riemannian sense) mappings of equiregular Carnot--Carath\\'{e}odory spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5483","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":"1110.5483","created_at":"2026-05-18T04:10:22.817454+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.5483v1","created_at":"2026-05-18T04:10:22.817454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5483","created_at":"2026-05-18T04:10:22.817454+00:00"},{"alias_kind":"pith_short_12","alias_value":"P44CALC2UFNN","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"P44CALC2UFNNPRF3","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"P44CALC2","created_at":"2026-05-18T12:26:39.201973+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/P44CALC2UFNNPRF3FAALRIXNIA","json":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA.json","graph_json":"https://pith.science/api/pith-number/P44CALC2UFNNPRF3FAALRIXNIA/graph.json","events_json":"https://pith.science/api/pith-number/P44CALC2UFNNPRF3FAALRIXNIA/events.json","paper":"https://pith.science/paper/P44CALC2"},"agent_actions":{"view_html":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA","download_json":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA.json","view_paper":"https://pith.science/paper/P44CALC2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.5483&json=true","fetch_graph":"https://pith.science/api/pith-number/P44CALC2UFNNPRF3FAALRIXNIA/graph.json","fetch_events":"https://pith.science/api/pith-number/P44CALC2UFNNPRF3FAALRIXNIA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA/action/storage_attestation","attest_author":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA/action/author_attestation","sign_citation":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA/action/citation_signature","submit_replication":"https://pith.science/pith/P44CALC2UFNNPRF3FAALRIXNIA/action/replication_record"}},"created_at":"2026-05-18T04:10:22.817454+00:00","updated_at":"2026-05-18T04:10:22.817454+00:00"}