{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:35REBZ5QTXZKSENQHE7MQ6TQN6","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":"81864e168f5e31ac313c148d4836859873b09c5bd4d7a7e2ac0a40799f4b7590","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-26T13:35:00Z","title_canon_sha256":"4afc67669897fdc266d94b963908271d8d1663e96e5bd91d72486da806cc4538"},"schema_version":"1.0","source":{"id":"1211.5947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5947","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5947v1","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5947","created_at":"2026-05-18T03:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"35REBZ5QTXZK","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"35REBZ5QTXZKSENQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"35REBZ5Q","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:e36c9e2e95fb2983ddd7d6c86a85421defe812c48bca296d63a1e92836452a09","target":"graph","created_at":"2026-05-18T03:39:53Z","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":"The interpolation property of Ces{\\`a}ro sequence and function spaces is investigated. It is shown that $Ces_p(I)$ is an interpolation space between $Ces_{p_0}(I)$ and $Ces_{p_1}(I)$ for $1 < p_0 < p_1 \\leq \\infty$ and $1/p = (1 - \\theta)/p_0 + \\theta /p_1$ with $0 < \\theta < 1$, where $I = [0, \\infty)$ or $[0, 1]$. The same result is true for Ces{\\`a}ro sequence spaces. On the other hand, $Ces_p[0, 1]$ is not an interpolation space between $Ces_1[0, 1]$ and $Ces_{\\infty}[0, 1]$.","authors_text":"Lech Maligranda, Sergey V. Astashkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-26T13:35:00Z","title":"Interpolation of Ces{\\`a}ro sequence and function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5947","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:f86a0c53361fd87a71e75ed1a68251750b29af84355d83b244797fcf669f523a","target":"record","created_at":"2026-05-18T03:39:53Z","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":"81864e168f5e31ac313c148d4836859873b09c5bd4d7a7e2ac0a40799f4b7590","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-26T13:35:00Z","title_canon_sha256":"4afc67669897fdc266d94b963908271d8d1663e96e5bd91d72486da806cc4538"},"schema_version":"1.0","source":{"id":"1211.5947","kind":"arxiv","version":1}},"canonical_sha256":"df6240e7b09df2a911b0393ec87a706f813831b638af4d1047570a09187a5ce7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df6240e7b09df2a911b0393ec87a706f813831b638af4d1047570a09187a5ce7","first_computed_at":"2026-05-18T03:39:53.744193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:53.744193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"syF5kU9DPVHBE/OJryfhJJ/HJRDcxFUiUviTYSCT+q7cUdVwesr9CZksKcnVfVXvs8jUbHtXF8m0eU7zl+QfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:53.744777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f86a0c53361fd87a71e75ed1a68251750b29af84355d83b244797fcf669f523a","sha256:e36c9e2e95fb2983ddd7d6c86a85421defe812c48bca296d63a1e92836452a09"],"state_sha256":"f7659170e47e8525e1077820e92cee765efc346bf689f8b557f52c00e25fee8e"}