{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QXZJKD6KSNZQFXMI47PEMMNRT6","short_pith_number":"pith:QXZJKD6K","schema_version":"1.0","canonical_sha256":"85f2950fca937302dd88e7de4631b19f9fc7309124584ba4b23a00fe3ffe5af2","source":{"kind":"arxiv","id":"1006.2672","version":1},"attestation_state":"computed","paper":{"title":"On strictly singular operators between separable Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Beanland, Pandelis Dodos","submitted_at":"2010-06-14T11:18:07Z","abstract_excerpt":"Let $X$ and $Y$ be separable Banach spaces and denote by $\\sss\\sss(X,Y)$ the subset of $\\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\\sss\\sss(X,Y)$. Our main results are summarized as follows. Firstly, we define a new rank $\\rs$ on $\\sss\\sss(X,Y)$. We show that $\\rs$ is a co-analytic rank and that dominates the rank $\\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\\leq p<+\\infty$ we construct a Banach space $Y_p$ with an unconditional basis such that $\\sss\\sss"},"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":"1006.2672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-06-14T11:18:07Z","cross_cats_sorted":[],"title_canon_sha256":"47fe2afaa899ff247dc12aff480c6c022d2b94e37eab63cab0411da143aa6c17","abstract_canon_sha256":"28fc034179e6dd00a37d4f784d0d2d797358356e25b0734d20e2114964f3e769"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.405594Z","signature_b64":"nbeDieaHPGklzj0hhSXIfLXsLJnA/rjRmifp+6Ti2ktHCNJtxELQ6XTqKLBINFeT6JU7PzahmIdiQnkdMBcqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f2950fca937302dd88e7de4631b19f9fc7309124584ba4b23a00fe3ffe5af2","last_reissued_at":"2026-05-18T03:02:44.404958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.404958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On strictly singular operators between separable Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kevin Beanland, Pandelis Dodos","submitted_at":"2010-06-14T11:18:07Z","abstract_excerpt":"Let $X$ and $Y$ be separable Banach spaces and denote by $\\sss\\sss(X,Y)$ the subset of $\\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\\sss\\sss(X,Y)$. Our main results are summarized as follows. Firstly, we define a new rank $\\rs$ on $\\sss\\sss(X,Y)$. We show that $\\rs$ is a co-analytic rank and that dominates the rank $\\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\\leq p<+\\infty$ we construct a Banach space $Y_p$ with an unconditional basis such that $\\sss\\sss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2672","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":"1006.2672","created_at":"2026-05-18T03:02:44.405058+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.2672v1","created_at":"2026-05-18T03:02:44.405058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2672","created_at":"2026-05-18T03:02:44.405058+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXZJKD6KSNZQ","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXZJKD6KSNZQFXMI","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXZJKD6K","created_at":"2026-05-18T12:26:13.927090+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/QXZJKD6KSNZQFXMI47PEMMNRT6","json":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6.json","graph_json":"https://pith.science/api/pith-number/QXZJKD6KSNZQFXMI47PEMMNRT6/graph.json","events_json":"https://pith.science/api/pith-number/QXZJKD6KSNZQFXMI47PEMMNRT6/events.json","paper":"https://pith.science/paper/QXZJKD6K"},"agent_actions":{"view_html":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6","download_json":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6.json","view_paper":"https://pith.science/paper/QXZJKD6K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.2672&json=true","fetch_graph":"https://pith.science/api/pith-number/QXZJKD6KSNZQFXMI47PEMMNRT6/graph.json","fetch_events":"https://pith.science/api/pith-number/QXZJKD6KSNZQFXMI47PEMMNRT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6/action/storage_attestation","attest_author":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6/action/author_attestation","sign_citation":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6/action/citation_signature","submit_replication":"https://pith.science/pith/QXZJKD6KSNZQFXMI47PEMMNRT6/action/replication_record"}},"created_at":"2026-05-18T03:02:44.405058+00:00","updated_at":"2026-05-18T03:02:44.405058+00:00"}