{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IM2467QGLYKCYW4YNQID7VTWWP","short_pith_number":"pith:IM2467QG","schema_version":"1.0","canonical_sha256":"4335cf7e065e142c5b986c103fd676b3d34da7d9dc2a3c8dca4ad4b592fe21f5","source":{"kind":"arxiv","id":"1303.0020","version":3},"attestation_state":"computed","paper":{"title":"A weak*-topological dichotomy with applications in operator theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Piotr Koszmider, Tomasz Kania","submitted_at":"2013-02-28T21:26:05Z","abstract_excerpt":"Denote by $[0,\\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on $[0,\\omega_1)$ and vanish eventually. We show that a weakly$^*$ compact subset of the dual space of $C_0[0,\\omega_1)$ is either uniformly Eberlein compact, or it contains a homeomorphic copy of the ordinal interval $[0,\\omega_1]$.\n  Using this result, we deduce that a Banach space which is a quotient of $C_0[0,\\omega_1)$ can either be embedded in a Hilbert-ge"},"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":"1303.0020","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-28T21:26:05Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"96e3bc49712b005eb4ce7187f75b372e3cfcc50db4b2750b5620d69e4b220d0d","abstract_canon_sha256":"b1fe47d07da27cb37ecec3f2ebc82de35e798d2072e26b6f64f0937b712407ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:43.328386Z","signature_b64":"idb2fIfsErpHWmIJsP4M5NLsMMijh18zdjrQhrbpPpkKVcfEV0onHVM+zQbXE8FrZQBVrVXPFqzmyZdu2mbaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4335cf7e065e142c5b986c103fd676b3d34da7d9dc2a3c8dca4ad4b592fe21f5","last_reissued_at":"2026-05-18T02:17:43.327830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:43.327830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weak*-topological dichotomy with applications in operator theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Piotr Koszmider, Tomasz Kania","submitted_at":"2013-02-28T21:26:05Z","abstract_excerpt":"Denote by $[0,\\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on $[0,\\omega_1)$ and vanish eventually. We show that a weakly$^*$ compact subset of the dual space of $C_0[0,\\omega_1)$ is either uniformly Eberlein compact, or it contains a homeomorphic copy of the ordinal interval $[0,\\omega_1]$.\n  Using this result, we deduce that a Banach space which is a quotient of $C_0[0,\\omega_1)$ can either be embedded in a Hilbert-ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0020","kind":"arxiv","version":3},"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":"1303.0020","created_at":"2026-05-18T02:17:43.327921+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.0020v3","created_at":"2026-05-18T02:17:43.327921+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0020","created_at":"2026-05-18T02:17:43.327921+00:00"},{"alias_kind":"pith_short_12","alias_value":"IM2467QGLYKC","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IM2467QGLYKCYW4Y","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IM2467QG","created_at":"2026-05-18T12:27:46.883200+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/IM2467QGLYKCYW4YNQID7VTWWP","json":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP.json","graph_json":"https://pith.science/api/pith-number/IM2467QGLYKCYW4YNQID7VTWWP/graph.json","events_json":"https://pith.science/api/pith-number/IM2467QGLYKCYW4YNQID7VTWWP/events.json","paper":"https://pith.science/paper/IM2467QG"},"agent_actions":{"view_html":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP","download_json":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP.json","view_paper":"https://pith.science/paper/IM2467QG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.0020&json=true","fetch_graph":"https://pith.science/api/pith-number/IM2467QGLYKCYW4YNQID7VTWWP/graph.json","fetch_events":"https://pith.science/api/pith-number/IM2467QGLYKCYW4YNQID7VTWWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP/action/storage_attestation","attest_author":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP/action/author_attestation","sign_citation":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP/action/citation_signature","submit_replication":"https://pith.science/pith/IM2467QGLYKCYW4YNQID7VTWWP/action/replication_record"}},"created_at":"2026-05-18T02:17:43.327921+00:00","updated_at":"2026-05-18T02:17:43.327921+00:00"}