{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LYXU7UB6AFLLVVIZYBCPN2GFDC","short_pith_number":"pith:LYXU7UB6","schema_version":"1.0","canonical_sha256":"5e2f4fd03e0156bad519c044f6e8c518a2db9403c3ec150da9c12fae091414c0","source":{"kind":"arxiv","id":"1510.01019","version":2},"attestation_state":"computed","paper":{"title":"On weak$^*$-convergence in the Hardy space $H^1$ over spaces of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Ha Duy Hung, Luong Dang Ky","submitted_at":"2015-10-05T02:54:10Z","abstract_excerpt":"Let $\\mathcal X$ be a complete space of homogeneous type. In this note, we prove that the weak$^*$-convergence is true in the Hardy space $H^1(\\mathcal X)$ of Coifman and Weiss."},"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":"1510.01019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-05T02:54:10Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"f957752354bbf067416259ea5e5b5ebb768e8f148d439b0b9f0f93f99bd6412f","abstract_canon_sha256":"be497939418657d9f81b5d6ec20ccbda02649311185d17ebd3634a33a7f724aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:59.944197Z","signature_b64":"MeU9d/dkcpU1rACYhSPTEq3UVCAyzD76H0BRzXJJHplZnUn4ihmbZuEHV6r/M108iLG3TmbVJKKdHqq0qJRmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e2f4fd03e0156bad519c044f6e8c518a2db9403c3ec150da9c12fae091414c0","last_reissued_at":"2026-05-18T01:26:59.943424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:59.943424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On weak$^*$-convergence in the Hardy space $H^1$ over spaces of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Ha Duy Hung, Luong Dang Ky","submitted_at":"2015-10-05T02:54:10Z","abstract_excerpt":"Let $\\mathcal X$ be a complete space of homogeneous type. In this note, we prove that the weak$^*$-convergence is true in the Hardy space $H^1(\\mathcal X)$ of Coifman and Weiss."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01019","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":"1510.01019","created_at":"2026-05-18T01:26:59.943558+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01019v2","created_at":"2026-05-18T01:26:59.943558+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01019","created_at":"2026-05-18T01:26:59.943558+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYXU7UB6AFLL","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYXU7UB6AFLLVVIZ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYXU7UB6","created_at":"2026-05-18T12:29:29.992203+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/LYXU7UB6AFLLVVIZYBCPN2GFDC","json":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC.json","graph_json":"https://pith.science/api/pith-number/LYXU7UB6AFLLVVIZYBCPN2GFDC/graph.json","events_json":"https://pith.science/api/pith-number/LYXU7UB6AFLLVVIZYBCPN2GFDC/events.json","paper":"https://pith.science/paper/LYXU7UB6"},"agent_actions":{"view_html":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC","download_json":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC.json","view_paper":"https://pith.science/paper/LYXU7UB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01019&json=true","fetch_graph":"https://pith.science/api/pith-number/LYXU7UB6AFLLVVIZYBCPN2GFDC/graph.json","fetch_events":"https://pith.science/api/pith-number/LYXU7UB6AFLLVVIZYBCPN2GFDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC/action/storage_attestation","attest_author":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC/action/author_attestation","sign_citation":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC/action/citation_signature","submit_replication":"https://pith.science/pith/LYXU7UB6AFLLVVIZYBCPN2GFDC/action/replication_record"}},"created_at":"2026-05-18T01:26:59.943558+00:00","updated_at":"2026-05-18T01:26:59.943558+00:00"}