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This was originally shown by Koskela, Nandi, and Nicolau with John domains in place of chord-arc domains when $n=2$, $s=1$, and $\\Omega$ is a simply connected planar domain.\n  Domains satisfying the conclusion of this result support $(p,\\beta)$-Hardy inequalities for $\\beta<p-n+t"},"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":"1807.04534","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-12T10:53:48Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"f5c4619b7e9d63578625d08c55c6f4e815523e5bddbeaa93d3f990d078067b58","abstract_canon_sha256":"1fa376e48dfbd701934cd8e6b9320057bff16762efc1eb1a0f788706416fbd28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:42.404531Z","signature_b64":"CBZyi3h0JZ5QbwIIa8OPTqOklFRZ0ZeAuvxH8B/rbwZwZYOiNLz20wRHECZIu0FrR+WQp4XlXi1z7rHh/iEUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee4c7f24226ea768f4b0fe91926499b23ed8e58250ef0aa73adb59c9acd0f1da","last_reissued_at":"2026-05-17T23:53:42.404106Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:42.404106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Accessible parts of the boundary for domains with lower content regular complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.MG","authors_text":"Jonas Azzam","submitted_at":"2018-07-12T10:53:48Z","abstract_excerpt":"We show that if $0<t<s\\leq n-1$, $\\Omega\\subseteq \\mathbb{R}^{n}$ with lower $s$-content regular complement, and $z\\in \\Omega$, there is a chord-arc domain $\\Omega_{z}\\subseteq \\Omega $ with center $z$ so that $\\mathscr{H}^{t}_{\\infty}(\\partial\\Omega_{z}\\cap \\partial\\Omega)\\gtrsim_{t} \\textrm{dist}(z,\\Omega^{c})^{t}$. This was originally shown by Koskela, Nandi, and Nicolau with John domains in place of chord-arc domains when $n=2$, $s=1$, and $\\Omega$ is a simply connected planar domain.\n  Domains satisfying the conclusion of this result support $(p,\\beta)$-Hardy inequalities for $\\beta<p-n+t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04534","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":"1807.04534","created_at":"2026-05-17T23:53:42.404165+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.04534v2","created_at":"2026-05-17T23:53:42.404165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04534","created_at":"2026-05-17T23:53:42.404165+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZGH6JBCN2TW","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZGH6JBCN2TWR5FQ","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZGH6JBC","created_at":"2026-05-18T12:32:08.215937+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/5ZGH6JBCN2TWR5FQ72IZEZEZWI","json":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI.json","graph_json":"https://pith.science/api/pith-number/5ZGH6JBCN2TWR5FQ72IZEZEZWI/graph.json","events_json":"https://pith.science/api/pith-number/5ZGH6JBCN2TWR5FQ72IZEZEZWI/events.json","paper":"https://pith.science/paper/5ZGH6JBC"},"agent_actions":{"view_html":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI","download_json":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI.json","view_paper":"https://pith.science/paper/5ZGH6JBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.04534&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZGH6JBCN2TWR5FQ72IZEZEZWI/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZGH6JBCN2TWR5FQ72IZEZEZWI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI/action/storage_attestation","attest_author":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI/action/author_attestation","sign_citation":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI/action/citation_signature","submit_replication":"https://pith.science/pith/5ZGH6JBCN2TWR5FQ72IZEZEZWI/action/replication_record"}},"created_at":"2026-05-17T23:53:42.404165+00:00","updated_at":"2026-05-17T23:53:42.404165+00:00"}