{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GWNJIH674MS5EQ3A7QJSRZFW2C","short_pith_number":"pith:GWNJIH67","schema_version":"1.0","canonical_sha256":"359a941fdfe325d24360fc1328e4b6d083b65840a896d81833f750d7f89e4365","source":{"kind":"arxiv","id":"1502.01875","version":1},"attestation_state":"computed","paper":{"title":"Extension operators on balls and on spaces of finite sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Witold Marciszewski","submitted_at":"2015-02-06T12:58:07Z","abstract_excerpt":"We study extension operators between spaces $\\sigma_n(2^X)$ of subsets of $X$ of cardinality at most $n$. As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$, equipped with the weak topology, then, for any $0<\\lambda<\\mu$, there is no extension operator $T: C(\\lambda B_H)\\to C(\\mu B_H)$."},"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":"1502.01875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-06T12:58:07Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"ccedc066beeeb2ae64c13a2afbb53ebbfa99955c9e9d0f60dc78b6df58ac6c54","abstract_canon_sha256":"6d53028f1446b08a067fa1945fb1b11d7bd8c27d10970f01390e4a547d3cc6f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:50.500090Z","signature_b64":"t3qTCJgY4P7bXckxiL/xuNyoVvU4lXPB0ItYzkMVmwpZv0eQ1CyOQ79Fh8X0hLnbB8fJcH5r65brQeWJ8npqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"359a941fdfe325d24360fc1328e4b6d083b65840a896d81833f750d7f89e4365","last_reissued_at":"2026-05-18T02:27:50.499707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:50.499707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension operators on balls and on spaces of finite sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Witold Marciszewski","submitted_at":"2015-02-06T12:58:07Z","abstract_excerpt":"We study extension operators between spaces $\\sigma_n(2^X)$ of subsets of $X$ of cardinality at most $n$. As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$, equipped with the weak topology, then, for any $0<\\lambda<\\mu$, there is no extension operator $T: C(\\lambda B_H)\\to C(\\mu B_H)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01875","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":"1502.01875","created_at":"2026-05-18T02:27:50.499770+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.01875v1","created_at":"2026-05-18T02:27:50.499770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01875","created_at":"2026-05-18T02:27:50.499770+00:00"},{"alias_kind":"pith_short_12","alias_value":"GWNJIH674MS5","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GWNJIH674MS5EQ3A","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GWNJIH67","created_at":"2026-05-18T12:29:22.688609+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/GWNJIH674MS5EQ3A7QJSRZFW2C","json":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C.json","graph_json":"https://pith.science/api/pith-number/GWNJIH674MS5EQ3A7QJSRZFW2C/graph.json","events_json":"https://pith.science/api/pith-number/GWNJIH674MS5EQ3A7QJSRZFW2C/events.json","paper":"https://pith.science/paper/GWNJIH67"},"agent_actions":{"view_html":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C","download_json":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C.json","view_paper":"https://pith.science/paper/GWNJIH67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.01875&json=true","fetch_graph":"https://pith.science/api/pith-number/GWNJIH674MS5EQ3A7QJSRZFW2C/graph.json","fetch_events":"https://pith.science/api/pith-number/GWNJIH674MS5EQ3A7QJSRZFW2C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C/action/storage_attestation","attest_author":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C/action/author_attestation","sign_citation":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C/action/citation_signature","submit_replication":"https://pith.science/pith/GWNJIH674MS5EQ3A7QJSRZFW2C/action/replication_record"}},"created_at":"2026-05-18T02:27:50.499770+00:00","updated_at":"2026-05-18T02:27:50.499770+00:00"}