{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SCOQ6AJEVNRRO2CPJISPNCACR5","short_pith_number":"pith:SCOQ6AJE","schema_version":"1.0","canonical_sha256":"909d0f0124ab6317684f4a24f688028f71dc76dd96d3ef32e087a1957bd1ffd8","source":{"kind":"arxiv","id":"1212.0346","version":1},"attestation_state":"computed","paper":{"title":"A short proof of some recent results related to Ces{\\`a}ro function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lech Maligranda, Sergey V. Astashkin","submitted_at":"2012-12-03T10:38:24Z","abstract_excerpt":"We give a short proof of the recent results that, for every $1\\leq p< \\infty,$ the Ces{\\`a}ro function space $Ces_p(I)$ is not a dual space, has the weak Banach-Saks property and does not have the Radon-Nikodym property."},"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":"1212.0346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-03T10:38:24Z","cross_cats_sorted":[],"title_canon_sha256":"6ab6323e859a42525fc310d49afc4d01ede2a4ecfc23c91cdbf5338f86c33dc8","abstract_canon_sha256":"92706c824c0fbd857a0bbd735d7f612c9079d01f49d96e08aaca9c3ad6c15979"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:17.794549Z","signature_b64":"4L+G/s9V1VVzQRwvLEMPMoP8QTqJbFQAtD7ANET8Qwm7UJk/ClLeNZbmA1D3ArGwhfMBCKwmgi1YYa06z8lpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"909d0f0124ab6317684f4a24f688028f71dc76dd96d3ef32e087a1957bd1ffd8","last_reissued_at":"2026-05-18T03:39:17.793813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:17.793813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short proof of some recent results related to Ces{\\`a}ro function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lech Maligranda, Sergey V. Astashkin","submitted_at":"2012-12-03T10:38:24Z","abstract_excerpt":"We give a short proof of the recent results that, for every $1\\leq p< \\infty,$ the Ces{\\`a}ro function space $Ces_p(I)$ is not a dual space, has the weak Banach-Saks property and does not have the Radon-Nikodym property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0346","kind":"arxiv","version":1},"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":"1212.0346","created_at":"2026-05-18T03:39:17.793910+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0346v1","created_at":"2026-05-18T03:39:17.793910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0346","created_at":"2026-05-18T03:39:17.793910+00:00"},{"alias_kind":"pith_short_12","alias_value":"SCOQ6AJEVNRR","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"SCOQ6AJEVNRRO2CP","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"SCOQ6AJE","created_at":"2026-05-18T12:27:20.899486+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/SCOQ6AJEVNRRO2CPJISPNCACR5","json":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5.json","graph_json":"https://pith.science/api/pith-number/SCOQ6AJEVNRRO2CPJISPNCACR5/graph.json","events_json":"https://pith.science/api/pith-number/SCOQ6AJEVNRRO2CPJISPNCACR5/events.json","paper":"https://pith.science/paper/SCOQ6AJE"},"agent_actions":{"view_html":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5","download_json":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5.json","view_paper":"https://pith.science/paper/SCOQ6AJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0346&json=true","fetch_graph":"https://pith.science/api/pith-number/SCOQ6AJEVNRRO2CPJISPNCACR5/graph.json","fetch_events":"https://pith.science/api/pith-number/SCOQ6AJEVNRRO2CPJISPNCACR5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5/action/storage_attestation","attest_author":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5/action/author_attestation","sign_citation":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5/action/citation_signature","submit_replication":"https://pith.science/pith/SCOQ6AJEVNRRO2CPJISPNCACR5/action/replication_record"}},"created_at":"2026-05-18T03:39:17.793910+00:00","updated_at":"2026-05-18T03:39:17.793910+00:00"}