{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:F7VSKFQDWQTWTU5DALZPCTQXUP","short_pith_number":"pith:F7VSKFQD","schema_version":"1.0","canonical_sha256":"2feb251603b42769d3a302f2f14e17a3d454a0ab5a8d10a41dfb7c959c2ef8ae","source":{"kind":"arxiv","id":"1112.3849","version":2},"attestation_state":"computed","paper":{"title":"Capacities associated with Calder\\'on-Zygmund kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joan Mateu, Laura Prat, Vasilis Chousionis, Xavier Tolsa","submitted_at":"2011-12-16T15:26:11Z","abstract_excerpt":"Analytic capacity is associated with the Cauchy kernel $1/z$ and the $L^\\infty$-norm. For $n\\in\\mathbb{N}$, one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$, $1\\le i\\le 2$, $x=(x_1,x_2)\\in\\mathbb{R}^2$. The main result of this paper states that the capacities associated with the vectorial kernel $(K_1, K_2)$ are comparable to analytic capacity."},"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":"1112.3849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-12-16T15:26:11Z","cross_cats_sorted":[],"title_canon_sha256":"3201ee015d19358b84fadf147c02d77ebf49c4ca00f0a6c5037ab8d7e1ac2851","abstract_canon_sha256":"81b98a2cde09ae02116fbe514b413a5872da7dc23b4d8e9abc2334a8589e8e66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:21.509071Z","signature_b64":"IH+soqYc3l3KGRT+H/7cKJk0TAGEci7iAFxXd/i81KlyzU0EeoShWW3cROjTkBdgyC3v6rGR4AtfmvnOtzhiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2feb251603b42769d3a302f2f14e17a3d454a0ab5a8d10a41dfb7c959c2ef8ae","last_reissued_at":"2026-05-18T01:02:21.508460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:21.508460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Capacities associated with Calder\\'on-Zygmund kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Joan Mateu, Laura Prat, Vasilis Chousionis, Xavier Tolsa","submitted_at":"2011-12-16T15:26:11Z","abstract_excerpt":"Analytic capacity is associated with the Cauchy kernel $1/z$ and the $L^\\infty$-norm. For $n\\in\\mathbb{N}$, one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$, $1\\le i\\le 2$, $x=(x_1,x_2)\\in\\mathbb{R}^2$. The main result of this paper states that the capacities associated with the vectorial kernel $(K_1, K_2)$ are comparable to analytic capacity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3849","kind":"arxiv","version":2},"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":"1112.3849","created_at":"2026-05-18T01:02:21.508549+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3849v2","created_at":"2026-05-18T01:02:21.508549+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3849","created_at":"2026-05-18T01:02:21.508549+00:00"},{"alias_kind":"pith_short_12","alias_value":"F7VSKFQDWQTW","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"F7VSKFQDWQTWTU5D","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"F7VSKFQD","created_at":"2026-05-18T12:26:28.662955+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/F7VSKFQDWQTWTU5DALZPCTQXUP","json":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP.json","graph_json":"https://pith.science/api/pith-number/F7VSKFQDWQTWTU5DALZPCTQXUP/graph.json","events_json":"https://pith.science/api/pith-number/F7VSKFQDWQTWTU5DALZPCTQXUP/events.json","paper":"https://pith.science/paper/F7VSKFQD"},"agent_actions":{"view_html":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP","download_json":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP.json","view_paper":"https://pith.science/paper/F7VSKFQD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3849&json=true","fetch_graph":"https://pith.science/api/pith-number/F7VSKFQDWQTWTU5DALZPCTQXUP/graph.json","fetch_events":"https://pith.science/api/pith-number/F7VSKFQDWQTWTU5DALZPCTQXUP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP/action/storage_attestation","attest_author":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP/action/author_attestation","sign_citation":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP/action/citation_signature","submit_replication":"https://pith.science/pith/F7VSKFQDWQTWTU5DALZPCTQXUP/action/replication_record"}},"created_at":"2026-05-18T01:02:21.508549+00:00","updated_at":"2026-05-18T01:02:21.508549+00:00"}