{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XP7UKXFWAYVBA252XPJSUHCN7Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"12590ae91709f91b5550b8d1710b023d926d45b6be69a803690d707227709eb5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-12T09:10:43Z","title_canon_sha256":"ef811cf917b904f2eaa5d9cb62089617155989485f70afb79ce0c8e8b935d09f"},"schema_version":"1.0","source":{"id":"1406.3158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3158","created_at":"2026-05-18T02:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3158v1","created_at":"2026-05-18T02:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3158","created_at":"2026-05-18T02:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"XP7UKXFWAYVB","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XP7UKXFWAYVBA252","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XP7UKXFW","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:16e306ebbeab59074aabe7bb1ed11b919833b5f596c70741373b6f7fd6601f2f","target":"graph","created_at":"2026-05-18T02:49:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove pointwise estimates to the modified Riesz potential. We show the boundedness of its Luxemburg norm. As an application we obtain Orlicz embedding results. We study the sharpness of the results.","authors_text":"Petteri Harjulehto, Ritva Hurri-Syrj\\\"anen","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-12T09:10:43Z","title":"Pointwise estimates to the modified Riesz potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3158","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f1dc5a9d122c71460ccb1bc9669bac873565ce9a864aa1fcf41f78a506ef3473","target":"record","created_at":"2026-05-18T02:49:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"12590ae91709f91b5550b8d1710b023d926d45b6be69a803690d707227709eb5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-12T09:10:43Z","title_canon_sha256":"ef811cf917b904f2eaa5d9cb62089617155989485f70afb79ce0c8e8b935d09f"},"schema_version":"1.0","source":{"id":"1406.3158","kind":"arxiv","version":1}},"canonical_sha256":"bbff455cb6062a106bbabbd32a1c4dfc379d17dff116482393bf57e6e43524d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbff455cb6062a106bbabbd32a1c4dfc379d17dff116482393bf57e6e43524d6","first_computed_at":"2026-05-18T02:49:52.891528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:52.891528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m+eMylmO1jA36onIboKXAsEsxqyIVV3S7G9WbxMX9UDXrU+POEq/5kFr6DwEmb9zc0cfZQfKYhfH56dG43nDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:52.892011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1dc5a9d122c71460ccb1bc9669bac873565ce9a864aa1fcf41f78a506ef3473","sha256:16e306ebbeab59074aabe7bb1ed11b919833b5f596c70741373b6f7fd6601f2f"],"state_sha256":"6c9ba2926a90c1c7e77d75f28b69fdd365502cdb91b85b24dcca0f9739ed62b9"}