{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZDB5M6KFSJFHHSX2UCFOF4GCCC","short_pith_number":"pith:ZDB5M6KF","schema_version":"1.0","canonical_sha256":"c8c3d67945924a73cafaa08ae2f0c2108284e4183689b3c9f5aceb6b61a9aaf4","source":{"kind":"arxiv","id":"1605.01969","version":1},"attestation_state":"computed","paper":{"title":"Szlenk and $w^*$-dentability indices of $C(K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ryan M Causey","submitted_at":"2016-05-06T15:21:39Z","abstract_excerpt":"Given any compact, Hausdorff space $K$ and $1<p<\\infty$, we compute the Szlenk and $w^*$-dentability indices of the spaces $C(K)$ and $L_p(C(K))$. We show that if $K$ is compact, Hausdorff, scattered, $CB(K)$ is the Cantor-Bendixson index of $K$, and $\\xi$ is the minimum ordinal such that $CB(K)\\leqslant \\omega^\\xi$, then $Sz(C(K))=\\omega^\\xi$ and $Dz(C(K))=Sz(L_p(C(K)))= \\omega^{1+\\xi}.$"},"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":"1605.01969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-06T15:21:39Z","cross_cats_sorted":[],"title_canon_sha256":"f26a560cea59879acd72700c3296ec5b83905d65297d841a7776baa126884281","abstract_canon_sha256":"f888c4ceebf68811e540fe8b18c67f5374e1791248ac8a9cbeadc4afe374eab9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:30.789160Z","signature_b64":"5OAocdKC/271JHcJYqFUOSoz2VtpkVyprvranEDvvX720vLAwUSvr/L+qkS4PwRyxqVKndDCop6ZKRR9ByJ9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8c3d67945924a73cafaa08ae2f0c2108284e4183689b3c9f5aceb6b61a9aaf4","last_reissued_at":"2026-05-18T01:15:30.788456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:30.788456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Szlenk and $w^*$-dentability indices of $C(K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ryan M Causey","submitted_at":"2016-05-06T15:21:39Z","abstract_excerpt":"Given any compact, Hausdorff space $K$ and $1<p<\\infty$, we compute the Szlenk and $w^*$-dentability indices of the spaces $C(K)$ and $L_p(C(K))$. We show that if $K$ is compact, Hausdorff, scattered, $CB(K)$ is the Cantor-Bendixson index of $K$, and $\\xi$ is the minimum ordinal such that $CB(K)\\leqslant \\omega^\\xi$, then $Sz(C(K))=\\omega^\\xi$ and $Dz(C(K))=Sz(L_p(C(K)))= \\omega^{1+\\xi}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01969","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":"1605.01969","created_at":"2026-05-18T01:15:30.788574+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.01969v1","created_at":"2026-05-18T01:15:30.788574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01969","created_at":"2026-05-18T01:15:30.788574+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDB5M6KFSJFH","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDB5M6KFSJFHHSX2","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDB5M6KF","created_at":"2026-05-18T12:30:53.716459+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/ZDB5M6KFSJFHHSX2UCFOF4GCCC","json":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC.json","graph_json":"https://pith.science/api/pith-number/ZDB5M6KFSJFHHSX2UCFOF4GCCC/graph.json","events_json":"https://pith.science/api/pith-number/ZDB5M6KFSJFHHSX2UCFOF4GCCC/events.json","paper":"https://pith.science/paper/ZDB5M6KF"},"agent_actions":{"view_html":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC","download_json":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC.json","view_paper":"https://pith.science/paper/ZDB5M6KF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.01969&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDB5M6KFSJFHHSX2UCFOF4GCCC/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDB5M6KFSJFHHSX2UCFOF4GCCC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC/action/storage_attestation","attest_author":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC/action/author_attestation","sign_citation":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC/action/citation_signature","submit_replication":"https://pith.science/pith/ZDB5M6KFSJFHHSX2UCFOF4GCCC/action/replication_record"}},"created_at":"2026-05-18T01:15:30.788574+00:00","updated_at":"2026-05-18T01:15:30.788574+00:00"}