{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:T6ZVNNL6ZA5TC24QDST7QUEWF3","short_pith_number":"pith:T6ZVNNL6","schema_version":"1.0","canonical_sha256":"9fb356b57ec83b316b901ca7f850962ecbe39fe72157ee09835de0654c002810","source":{"kind":"arxiv","id":"1511.07240","version":2},"attestation_state":"computed","paper":{"title":"Quasicircles of dimension 1+k^2 do not exist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Oleg Ivrii","submitted_at":"2015-11-23T14:36:11Z","abstract_excerpt":"A well-known theorem of S. Smirnov states that the Hausdorff dimension of a $k$-quasicircle is at most $1+k^2$. Here, we show that the precise upper bound $D(k) = 1+\\Sigma^2 k^2 + \\mathcal O(k^{8/3-\\varepsilon})$ where $\\Sigma^2$ is the maximal asymptotic variance of the Beurling transform, taken over the unit ball of $L^\\infty$. The quantity $\\Sigma^2$ was introduced in a joint work with K. Astala, A. Per\\\"al\\\"a and I. Prause where it was proved that $0.879 < \\Sigma^2 \\le 1$, while recently, H. Hedenmalm discovered that surprisingly $\\Sigma^2 <1$. We deduce the asymptotic expansion of $D(k)$ "},"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":"1511.07240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-23T14:36:11Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b1353324322dbe89ade2459b48bf2ac11f9e5440426a5a2023661a1ce311185d","abstract_canon_sha256":"e589d12a1a9757ed1f151fa1dea0a8cebdd99e104e2127b202c1f9ec95f06a7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:04.974358Z","signature_b64":"LIT17NBQfmSfqsft0BOu5FhQeL1qypMhmGDkhJW7b1yeQw6zzNkFhBQC8qtU/FmSgdJjezk3oBZOu6QlHslkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fb356b57ec83b316b901ca7f850962ecbe39fe72157ee09835de0654c002810","last_reissued_at":"2026-05-18T01:17:04.973635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:04.973635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasicircles of dimension 1+k^2 do not exist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Oleg Ivrii","submitted_at":"2015-11-23T14:36:11Z","abstract_excerpt":"A well-known theorem of S. Smirnov states that the Hausdorff dimension of a $k$-quasicircle is at most $1+k^2$. Here, we show that the precise upper bound $D(k) = 1+\\Sigma^2 k^2 + \\mathcal O(k^{8/3-\\varepsilon})$ where $\\Sigma^2$ is the maximal asymptotic variance of the Beurling transform, taken over the unit ball of $L^\\infty$. The quantity $\\Sigma^2$ was introduced in a joint work with K. Astala, A. Per\\\"al\\\"a and I. Prause where it was proved that $0.879 < \\Sigma^2 \\le 1$, while recently, H. Hedenmalm discovered that surprisingly $\\Sigma^2 <1$. We deduce the asymptotic expansion of $D(k)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07240","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":"1511.07240","created_at":"2026-05-18T01:17:04.973762+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.07240v2","created_at":"2026-05-18T01:17:04.973762+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07240","created_at":"2026-05-18T01:17:04.973762+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6ZVNNL6ZA5T","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6ZVNNL6ZA5TC24Q","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6ZVNNL6","created_at":"2026-05-18T12:29:42.218222+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/T6ZVNNL6ZA5TC24QDST7QUEWF3","json":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3.json","graph_json":"https://pith.science/api/pith-number/T6ZVNNL6ZA5TC24QDST7QUEWF3/graph.json","events_json":"https://pith.science/api/pith-number/T6ZVNNL6ZA5TC24QDST7QUEWF3/events.json","paper":"https://pith.science/paper/T6ZVNNL6"},"agent_actions":{"view_html":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3","download_json":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3.json","view_paper":"https://pith.science/paper/T6ZVNNL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.07240&json=true","fetch_graph":"https://pith.science/api/pith-number/T6ZVNNL6ZA5TC24QDST7QUEWF3/graph.json","fetch_events":"https://pith.science/api/pith-number/T6ZVNNL6ZA5TC24QDST7QUEWF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3/action/storage_attestation","attest_author":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3/action/author_attestation","sign_citation":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3/action/citation_signature","submit_replication":"https://pith.science/pith/T6ZVNNL6ZA5TC24QDST7QUEWF3/action/replication_record"}},"created_at":"2026-05-18T01:17:04.973762+00:00","updated_at":"2026-05-18T01:17:04.973762+00:00"}