{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BJJHY3PIJ7Q775V5AQ5BP3YRVE","short_pith_number":"pith:BJJHY3PI","schema_version":"1.0","canonical_sha256":"0a527c6de84fe1fff6bd043a17ef11a9243518ee806346e1b090ae78264cee71","source":{"kind":"arxiv","id":"1406.1306","version":1},"attestation_state":"computed","paper":{"title":"Heisenberg Hausdorff dimension of Besicovitch sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Laura Venieri","submitted_at":"2014-06-05T09:27:12Z","abstract_excerpt":"We consider (bounded) Besicovitch sets in the Heisenberg group and prove that $L^p$ estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension."},"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":"1406.1306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-06-05T09:27:12Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"52b6de01ad7ba67e21ab34ef74539eba27947ab7d4ec5d433a7e76efc4ae5f07","abstract_canon_sha256":"f2eb3161a806be2fc1f67168930c244ddbd6ba872927fb83a8f6ead31f77a212"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:00.396109Z","signature_b64":"DfsPl9CEQTVmjXilMDR+ve5e9pDIowMWiCLpfAHQNO0vEoirCfO1+cmaeVQ5eRS5ZYIm1i63ZOlQT9+l+oCKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a527c6de84fe1fff6bd043a17ef11a9243518ee806346e1b090ae78264cee71","last_reissued_at":"2026-05-18T00:49:00.395398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:00.395398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heisenberg Hausdorff dimension of Besicovitch sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Laura Venieri","submitted_at":"2014-06-05T09:27:12Z","abstract_excerpt":"We consider (bounded) Besicovitch sets in the Heisenberg group and prove that $L^p$ estimates for the Kakeya maximal function imply lower bounds for their Heisenberg Hausdorff dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1306","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":"1406.1306","created_at":"2026-05-18T00:49:00.395518+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.1306v1","created_at":"2026-05-18T00:49:00.395518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1306","created_at":"2026-05-18T00:49:00.395518+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJJHY3PIJ7Q7","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJJHY3PIJ7Q775V5","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJJHY3PI","created_at":"2026-05-18T12:28:22.404517+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/BJJHY3PIJ7Q775V5AQ5BP3YRVE","json":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE.json","graph_json":"https://pith.science/api/pith-number/BJJHY3PIJ7Q775V5AQ5BP3YRVE/graph.json","events_json":"https://pith.science/api/pith-number/BJJHY3PIJ7Q775V5AQ5BP3YRVE/events.json","paper":"https://pith.science/paper/BJJHY3PI"},"agent_actions":{"view_html":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE","download_json":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE.json","view_paper":"https://pith.science/paper/BJJHY3PI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.1306&json=true","fetch_graph":"https://pith.science/api/pith-number/BJJHY3PIJ7Q775V5AQ5BP3YRVE/graph.json","fetch_events":"https://pith.science/api/pith-number/BJJHY3PIJ7Q775V5AQ5BP3YRVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE/action/storage_attestation","attest_author":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE/action/author_attestation","sign_citation":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE/action/citation_signature","submit_replication":"https://pith.science/pith/BJJHY3PIJ7Q775V5AQ5BP3YRVE/action/replication_record"}},"created_at":"2026-05-18T00:49:00.395518+00:00","updated_at":"2026-05-18T00:49:00.395518+00:00"}