{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:6HJX3WZYSBBHXNHTOKIMT6C2EB","short_pith_number":"pith:6HJX3WZY","schema_version":"1.0","canonical_sha256":"f1d37ddb3890427bb4f37290c9f85a206a5356634fad7b827b6b12cdb922cd68","source":{"kind":"arxiv","id":"0901.2910","version":4},"attestation_state":"computed","paper":{"title":"Multi-parameter Carnot-Caratheodory balls and the theorem of Frobenius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.CA","authors_text":"Brian Street","submitted_at":"2009-01-19T18:19:25Z","abstract_excerpt":"We study multi-parameter Carnot-Caratheodory balls, generalizing results due to Nagel, Stein, and Wainger in the single parameter setting. The main technical result is seen as a uniform version of the theorem of Frobenius. In addition, we study maximal functions associated to certain multi-parameter families of Carnot-Caratheodory balls."},"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":"0901.2910","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-01-19T18:19:25Z","cross_cats_sorted":["math.DG","math.MG"],"title_canon_sha256":"0206f6fd33537e99a7cf06b00a829eca87c4f2b2360a4540c19d2fefc52b07b6","abstract_canon_sha256":"c16180b4ad9166132af67150663fbb56d0dd09f918c7e56e00bf692369f8d451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:41.590180Z","signature_b64":"PzYYZ7obtbvkZrU2pmHHgsi6vrg1N/x3lQzkFu3nKg3E58il3Tg6Y6Sm1Cv7GOZFIV+dkFSD1Hyd2KUXMdjdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d37ddb3890427bb4f37290c9f85a206a5356634fad7b827b6b12cdb922cd68","last_reissued_at":"2026-05-18T04:31:41.589624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:41.589624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-parameter Carnot-Caratheodory balls and the theorem of Frobenius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.CA","authors_text":"Brian Street","submitted_at":"2009-01-19T18:19:25Z","abstract_excerpt":"We study multi-parameter Carnot-Caratheodory balls, generalizing results due to Nagel, Stein, and Wainger in the single parameter setting. The main technical result is seen as a uniform version of the theorem of Frobenius. In addition, we study maximal functions associated to certain multi-parameter families of Carnot-Caratheodory balls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2910","kind":"arxiv","version":4},"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":"0901.2910","created_at":"2026-05-18T04:31:41.589721+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.2910v4","created_at":"2026-05-18T04:31:41.589721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.2910","created_at":"2026-05-18T04:31:41.589721+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HJX3WZYSBBH","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HJX3WZYSBBHXNHT","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HJX3WZY","created_at":"2026-05-18T12:25:58.837520+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/6HJX3WZYSBBHXNHTOKIMT6C2EB","json":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB.json","graph_json":"https://pith.science/api/pith-number/6HJX3WZYSBBHXNHTOKIMT6C2EB/graph.json","events_json":"https://pith.science/api/pith-number/6HJX3WZYSBBHXNHTOKIMT6C2EB/events.json","paper":"https://pith.science/paper/6HJX3WZY"},"agent_actions":{"view_html":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB","download_json":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB.json","view_paper":"https://pith.science/paper/6HJX3WZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.2910&json=true","fetch_graph":"https://pith.science/api/pith-number/6HJX3WZYSBBHXNHTOKIMT6C2EB/graph.json","fetch_events":"https://pith.science/api/pith-number/6HJX3WZYSBBHXNHTOKIMT6C2EB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB/action/storage_attestation","attest_author":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB/action/author_attestation","sign_citation":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB/action/citation_signature","submit_replication":"https://pith.science/pith/6HJX3WZYSBBHXNHTOKIMT6C2EB/action/replication_record"}},"created_at":"2026-05-18T04:31:41.589721+00:00","updated_at":"2026-05-18T04:31:41.589721+00:00"}