{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:54DWQQFYR4Y24CCJKPJ7CW5T3I","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":"8ede1fe37693c9b7bf3bbc00387232ed67e35ea14167206b960a32703eeec2d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-17T20:07:29Z","title_canon_sha256":"58af25c9950458bfabf624a54e645ace7eb37ea6a4c66517a376c8b55a3fc053"},"schema_version":"1.0","source":{"id":"1304.4951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4951","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4951v2","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4951","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"54DWQQFYR4Y2","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"54DWQQFYR4Y24CCJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"54DWQQFY","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c20b8298d73896e7da965ea4204860eea9102aa8e6ce8d19a12b6857447fec21","target":"graph","created_at":"2026-05-18T02:17:52Z","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":"Denote by $[0,\\omega_1)$ the set of countable ordinals, equipped with the order topology, let $L_0$ be the disjoint union of the compact ordinal intervals $[0,\\alpha]$ for $\\alpha$ countable, and consider the Banach spaces $C_0[0,\\omega_1)$ and $C_0(L_0)$ consisting of all scalar-valued, continuous functions which are defined on the locally compact Hausdorff spaces $[0,\\omega_1)$ and $L_0$, respectively, and which vanish eventually. Our main result states that a bounded operator $T$ between any pair of these two Banach spaces fixes a copy of $C_0(L_0)$ if and only if the identity operator on $","authors_text":"Niels Jakob Laustsen, Tomasz Kania","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-17T20:07:29Z","title":"Operators on two Banach spaces of continuous functions on locally compact spaces of ordinals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4951","kind":"arxiv","version":2},"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":"sha256:0a399c0652af9dd35af58ee8d6bf15297f8159cefa5a5d7b946f19d6f3c516e2","target":"record","created_at":"2026-05-18T02:17:52Z","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":"8ede1fe37693c9b7bf3bbc00387232ed67e35ea14167206b960a32703eeec2d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-17T20:07:29Z","title_canon_sha256":"58af25c9950458bfabf624a54e645ace7eb37ea6a4c66517a376c8b55a3fc053"},"schema_version":"1.0","source":{"id":"1304.4951","kind":"arxiv","version":2}},"canonical_sha256":"ef076840b88f31ae084953d3f15bb3da17c68f3784797763c672fcbf42bbed8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef076840b88f31ae084953d3f15bb3da17c68f3784797763c672fcbf42bbed8a","first_computed_at":"2026-05-18T02:17:52.423824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:52.423824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BchLTHHOuVd4q/0G/RyfZjqDeZ7YfkBQ65wZD9/M04WN58EHCeRdD039N27fRHU4tmyw5TuLiLWnpmQfTTllAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:52.424533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a399c0652af9dd35af58ee8d6bf15297f8159cefa5a5d7b946f19d6f3c516e2","sha256:c20b8298d73896e7da965ea4204860eea9102aa8e6ce8d19a12b6857447fec21"],"state_sha256":"a057ac7c6b984bd1a69e65ec19d8f5a4d4b415439c885ad0ad6b48d051e07415"}