{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:A6XKWIFCPSTLBXL3OZZZYGVLMX","short_pith_number":"pith:A6XKWIFC","schema_version":"1.0","canonical_sha256":"07aeab20a27ca6b0dd7b76739c1aab65d657ed708fb8393aabf257627b8c6bcd","source":{"kind":"arxiv","id":"1310.4035","version":3},"attestation_state":"computed","paper":{"title":"Chains of functions in $C(K)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"Richard J. Smith, Tomasz Kania","submitted_at":"2013-10-15T12:42:07Z","abstract_excerpt":"The Bishop property ($\\symbishop$), introduced recently by K.P. Hart, T. Kochanek and the first-named author, was motivated by Pe{\\l}czy{\\'n}ski's classical work on weakly compact operators on $C(K)$-spaces. This property asserts that certain chains of functions in said spaces, with respect to a particular partial ordering, must be countable. There are two versions of ($\\symbishop$): one applies to linear operators on $C(K)$-spaces and the other to the compact Hausdorff spaces themselves.\n  We answer two questions that arose after ($\\symbishop$) was first introduced. We show that if $\\mathscr{"},"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":"1310.4035","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-15T12:42:07Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2354bd4510a1e81b84b543877d2a84b0978b4ec238286d74431439cd072675bb","abstract_canon_sha256":"b6bc1e2ebfaa2577018a8f9d7ef851762ce7e736da5eeb1d20cf0e584c9ca7ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.137536Z","signature_b64":"hIDryBHMpSS3J1eACJ5b0MyWrMxE2t0j2gQNOLVVcQVcClihtlsKEu+ItRxqSt+lAZZWUj6hmyJJbW6PnQ2kBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07aeab20a27ca6b0dd7b76739c1aab65d657ed708fb8393aabf257627b8c6bcd","last_reissued_at":"2026-05-18T01:28:06.136951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.136951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chains of functions in $C(K)$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"Richard J. Smith, Tomasz Kania","submitted_at":"2013-10-15T12:42:07Z","abstract_excerpt":"The Bishop property ($\\symbishop$), introduced recently by K.P. Hart, T. Kochanek and the first-named author, was motivated by Pe{\\l}czy{\\'n}ski's classical work on weakly compact operators on $C(K)$-spaces. This property asserts that certain chains of functions in said spaces, with respect to a particular partial ordering, must be countable. There are two versions of ($\\symbishop$): one applies to linear operators on $C(K)$-spaces and the other to the compact Hausdorff spaces themselves.\n  We answer two questions that arose after ($\\symbishop$) was first introduced. We show that if $\\mathscr{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4035","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":"1310.4035","created_at":"2026-05-18T01:28:06.137044+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4035v3","created_at":"2026-05-18T01:28:06.137044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4035","created_at":"2026-05-18T01:28:06.137044+00:00"},{"alias_kind":"pith_short_12","alias_value":"A6XKWIFCPSTL","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"A6XKWIFCPSTLBXL3","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"A6XKWIFC","created_at":"2026-05-18T12:27:38.830355+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/A6XKWIFCPSTLBXL3OZZZYGVLMX","json":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX.json","graph_json":"https://pith.science/api/pith-number/A6XKWIFCPSTLBXL3OZZZYGVLMX/graph.json","events_json":"https://pith.science/api/pith-number/A6XKWIFCPSTLBXL3OZZZYGVLMX/events.json","paper":"https://pith.science/paper/A6XKWIFC"},"agent_actions":{"view_html":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX","download_json":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX.json","view_paper":"https://pith.science/paper/A6XKWIFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4035&json=true","fetch_graph":"https://pith.science/api/pith-number/A6XKWIFCPSTLBXL3OZZZYGVLMX/graph.json","fetch_events":"https://pith.science/api/pith-number/A6XKWIFCPSTLBXL3OZZZYGVLMX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX/action/storage_attestation","attest_author":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX/action/author_attestation","sign_citation":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX/action/citation_signature","submit_replication":"https://pith.science/pith/A6XKWIFCPSTLBXL3OZZZYGVLMX/action/replication_record"}},"created_at":"2026-05-18T01:28:06.137044+00:00","updated_at":"2026-05-18T01:28:06.137044+00:00"}