{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TARYDFY2LGZT3SDINDEHEXWCXL","short_pith_number":"pith:TARYDFY2","schema_version":"1.0","canonical_sha256":"982381971a59b33dc86868c8725ec2bafb5ab923189979987730675217f33b83","source":{"kind":"arxiv","id":"1307.2069","version":5},"attestation_state":"computed","paper":{"title":"On the curvature of level sets of harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Stefan Steinerberger","submitted_at":"2013-07-08T12:48:23Z","abstract_excerpt":"If a real harmonic function inside the open unit disk $B(0,1) \\subset \\mathbb{R}^2$ has its level set $\\left\\{x: u(x) = u(0)\\right\\}$ diffeomorphic to an interval, then we prove the sharp bound $\\kappa \\leq 8$ on the curvature of the level set $\\left\\{x: u(x) = u(0)\\right\\}$ in the origin. The bound is sharp and we give the unique (up to symmetries) extremizer."},"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":"1307.2069","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-08T12:48:23Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5fa0415618c8598abe3202dfb9996329c3583541948056921c61a3eba897a4ae","abstract_canon_sha256":"b4225ce02babe34b5deb725d97aba73d32bd2355545393eb072b5b64e54d0948"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:37.392272Z","signature_b64":"S6vMgrliN8jSS+9Ky1/yhV9cQHU3B5gEbWoOJP9SY8s1W56D+pTsZk/u9cWo1K/aMEWnEnQOoFXU34zb5N7aDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"982381971a59b33dc86868c8725ec2bafb5ab923189979987730675217f33b83","last_reissued_at":"2026-05-18T02:48:37.391595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:37.391595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the curvature of level sets of harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Stefan Steinerberger","submitted_at":"2013-07-08T12:48:23Z","abstract_excerpt":"If a real harmonic function inside the open unit disk $B(0,1) \\subset \\mathbb{R}^2$ has its level set $\\left\\{x: u(x) = u(0)\\right\\}$ diffeomorphic to an interval, then we prove the sharp bound $\\kappa \\leq 8$ on the curvature of the level set $\\left\\{x: u(x) = u(0)\\right\\}$ in the origin. The bound is sharp and we give the unique (up to symmetries) extremizer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2069","kind":"arxiv","version":5},"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":"1307.2069","created_at":"2026-05-18T02:48:37.391692+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2069v5","created_at":"2026-05-18T02:48:37.391692+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2069","created_at":"2026-05-18T02:48:37.391692+00:00"},{"alias_kind":"pith_short_12","alias_value":"TARYDFY2LGZT","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"TARYDFY2LGZT3SDI","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"TARYDFY2","created_at":"2026-05-18T12:27:59.945178+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.01986","citing_title":"Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL","json":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL.json","graph_json":"https://pith.science/api/pith-number/TARYDFY2LGZT3SDINDEHEXWCXL/graph.json","events_json":"https://pith.science/api/pith-number/TARYDFY2LGZT3SDINDEHEXWCXL/events.json","paper":"https://pith.science/paper/TARYDFY2"},"agent_actions":{"view_html":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL","download_json":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL.json","view_paper":"https://pith.science/paper/TARYDFY2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2069&json=true","fetch_graph":"https://pith.science/api/pith-number/TARYDFY2LGZT3SDINDEHEXWCXL/graph.json","fetch_events":"https://pith.science/api/pith-number/TARYDFY2LGZT3SDINDEHEXWCXL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL/action/storage_attestation","attest_author":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL/action/author_attestation","sign_citation":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL/action/citation_signature","submit_replication":"https://pith.science/pith/TARYDFY2LGZT3SDINDEHEXWCXL/action/replication_record"}},"created_at":"2026-05-18T02:48:37.391692+00:00","updated_at":"2026-05-18T02:48:37.391692+00:00"}