{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:73KUANXGTDW6KPRGFSG2R523FF","short_pith_number":"pith:73KUANXG","schema_version":"1.0","canonical_sha256":"fed54036e698ede53e262c8da8f75b295e54c4063be1c176d7fab47860dafbe2","source":{"kind":"arxiv","id":"1409.3811","version":2},"attestation_state":"computed","paper":{"title":"Solyanik estimates and local H\\\"older continuity of halo functions of geometric maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein","submitted_at":"2014-09-12T18:20:59Z","abstract_excerpt":"Let $\\mathcal{B}$ be a homothecy invariant basis consisting of convex sets in $\\mathbb{R}^n$, and define the associated geometric maximal operator $M_{\\mathcal{B}}$ by $$ M_{\\mathcal{B}} f(x) :=\\sup_{x \\in R \\in \\mathcal{B}}\\frac{1}{|R|}\\int_R |f| $$ and the halo function $\\phi_{\\mathcal{B}}(\\alpha)$ on $(1,\\infty)$ by $$\\phi_{\\mathcal B}(\\alpha) :=\\sup_{E \\subset \\mathbb{R}^n :\\, 0 < |E| < \\infty}\\frac{1}{|E|}|\\{x\\in \\mathbb{R}^n : M_{\\mathcal{B}} \\chi_E (x) >1/\\alpha\\}|. $$ It is shown that if $\\phi_{\\mathcal{B}}(\\alpha)$ satisfies the Solyanik estimate $\\phi_{\\mathcal B}(\\alpha) - 1 \\leq C "},"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":"1409.3811","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-12T18:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"539626f07d9713541d8371a07dbb62b0a948ddbb0c98b06e17710159d15cd7eb","abstract_canon_sha256":"635f13a218e186e0bc11f577871e84533847c042a5ddc8de89b60c0d71fc24d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:35.522444Z","signature_b64":"+VILnwhwcQlZU7tLq5NkCEOrnmc4rEnVZa02XMvmE+KNpKCYg+/nW/xlLes51k8GJy/YSKoZDFImo+/qlTs+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fed54036e698ede53e262c8da8f75b295e54c4063be1c176d7fab47860dafbe2","last_reissued_at":"2026-05-18T01:34:35.521789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:35.521789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solyanik estimates and local H\\\"older continuity of halo functions of geometric maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein","submitted_at":"2014-09-12T18:20:59Z","abstract_excerpt":"Let $\\mathcal{B}$ be a homothecy invariant basis consisting of convex sets in $\\mathbb{R}^n$, and define the associated geometric maximal operator $M_{\\mathcal{B}}$ by $$ M_{\\mathcal{B}} f(x) :=\\sup_{x \\in R \\in \\mathcal{B}}\\frac{1}{|R|}\\int_R |f| $$ and the halo function $\\phi_{\\mathcal{B}}(\\alpha)$ on $(1,\\infty)$ by $$\\phi_{\\mathcal B}(\\alpha) :=\\sup_{E \\subset \\mathbb{R}^n :\\, 0 < |E| < \\infty}\\frac{1}{|E|}|\\{x\\in \\mathbb{R}^n : M_{\\mathcal{B}} \\chi_E (x) >1/\\alpha\\}|. $$ It is shown that if $\\phi_{\\mathcal{B}}(\\alpha)$ satisfies the Solyanik estimate $\\phi_{\\mathcal B}(\\alpha) - 1 \\leq C "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3811","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":"1409.3811","created_at":"2026-05-18T01:34:35.521916+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3811v2","created_at":"2026-05-18T01:34:35.521916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3811","created_at":"2026-05-18T01:34:35.521916+00:00"},{"alias_kind":"pith_short_12","alias_value":"73KUANXGTDW6","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"73KUANXGTDW6KPRG","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"73KUANXG","created_at":"2026-05-18T12:28:16.859392+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/73KUANXGTDW6KPRGFSG2R523FF","json":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF.json","graph_json":"https://pith.science/api/pith-number/73KUANXGTDW6KPRGFSG2R523FF/graph.json","events_json":"https://pith.science/api/pith-number/73KUANXGTDW6KPRGFSG2R523FF/events.json","paper":"https://pith.science/paper/73KUANXG"},"agent_actions":{"view_html":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF","download_json":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF.json","view_paper":"https://pith.science/paper/73KUANXG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3811&json=true","fetch_graph":"https://pith.science/api/pith-number/73KUANXGTDW6KPRGFSG2R523FF/graph.json","fetch_events":"https://pith.science/api/pith-number/73KUANXGTDW6KPRGFSG2R523FF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF/action/storage_attestation","attest_author":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF/action/author_attestation","sign_citation":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF/action/citation_signature","submit_replication":"https://pith.science/pith/73KUANXGTDW6KPRGFSG2R523FF/action/replication_record"}},"created_at":"2026-05-18T01:34:35.521916+00:00","updated_at":"2026-05-18T01:34:35.521916+00:00"}