{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:XAHMFUIQY45WYX56ZSXPDO5KD3","short_pith_number":"pith:XAHMFUIQ","schema_version":"1.0","canonical_sha256":"b80ec2d110c73b6c5fbeccaef1bbaa1ec019ddf77e7dbfe6c6564dcb76ebe233","source":{"kind":"arxiv","id":"0912.5111","version":3},"attestation_state":"computed","paper":{"title":"Buffon's needle landing near Besicovitch irregular self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Matt Bond","submitted_at":"2009-12-27T22:17:44Z","abstract_excerpt":"In this paper we get an estimate of Favard length of an arbitrary neighbourhood of an arbitrary self-similar Cantor set. Consider $L$ closed disjoint discs of radius $1/L$ inside the unit disc. By using linear maps of smaller disc onto the unit disc we can generate a self-similar Cantor set $G$. Then $\\G=\\bigcap_n\\G_n$. One may then ask the rate at which the Favard length - the average over all directions of the length of the orthogonal projection onto a line in that direction - of these sets $\\G_n$ decays to zero as a function of $n$. The quantitative results for the Favard length problem wer"},"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":"0912.5111","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-12-27T22:17:44Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"881903ed5fb8826bdc82050848303f77ee700e1af692853d16341caf28b1db08","abstract_canon_sha256":"b3c63a985f5792f5e23a9494ad649bee86d003792de1236cd90e518cc8e088a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:00.050825Z","signature_b64":"Qu41qkrNVRTlUqDV81CA0cnvJ3ngy+3LkZPchUEME8PxVrsSDMZ+F7C3L3Vyj8FwH4M+1b2KkB0wj7mIyxj4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80ec2d110c73b6c5fbeccaef1bbaa1ec019ddf77e7dbfe6c6564dcb76ebe233","last_reissued_at":"2026-05-18T04:32:00.050267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:00.050267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Buffon's needle landing near Besicovitch irregular self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Matt Bond","submitted_at":"2009-12-27T22:17:44Z","abstract_excerpt":"In this paper we get an estimate of Favard length of an arbitrary neighbourhood of an arbitrary self-similar Cantor set. Consider $L$ closed disjoint discs of radius $1/L$ inside the unit disc. By using linear maps of smaller disc onto the unit disc we can generate a self-similar Cantor set $G$. Then $\\G=\\bigcap_n\\G_n$. One may then ask the rate at which the Favard length - the average over all directions of the length of the orthogonal projection onto a line in that direction - of these sets $\\G_n$ decays to zero as a function of $n$. The quantitative results for the Favard length problem wer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5111","kind":"arxiv","version":3},"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":"0912.5111","created_at":"2026-05-18T04:32:00.050359+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.5111v3","created_at":"2026-05-18T04:32:00.050359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.5111","created_at":"2026-05-18T04:32:00.050359+00:00"},{"alias_kind":"pith_short_12","alias_value":"XAHMFUIQY45W","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"XAHMFUIQY45WYX56","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"XAHMFUIQ","created_at":"2026-05-18T12:26:02.257875+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/XAHMFUIQY45WYX56ZSXPDO5KD3","json":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3.json","graph_json":"https://pith.science/api/pith-number/XAHMFUIQY45WYX56ZSXPDO5KD3/graph.json","events_json":"https://pith.science/api/pith-number/XAHMFUIQY45WYX56ZSXPDO5KD3/events.json","paper":"https://pith.science/paper/XAHMFUIQ"},"agent_actions":{"view_html":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3","download_json":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3.json","view_paper":"https://pith.science/paper/XAHMFUIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.5111&json=true","fetch_graph":"https://pith.science/api/pith-number/XAHMFUIQY45WYX56ZSXPDO5KD3/graph.json","fetch_events":"https://pith.science/api/pith-number/XAHMFUIQY45WYX56ZSXPDO5KD3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3/action/storage_attestation","attest_author":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3/action/author_attestation","sign_citation":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3/action/citation_signature","submit_replication":"https://pith.science/pith/XAHMFUIQY45WYX56ZSXPDO5KD3/action/replication_record"}},"created_at":"2026-05-18T04:32:00.050359+00:00","updated_at":"2026-05-18T04:32:00.050359+00:00"}