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These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square.\n  We show that every separable space containing"},"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":"1402.0818","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-04T18:22:38Z","cross_cats_sorted":[],"title_canon_sha256":"047e38c283c51f39bd02e58a596ebad66d3865f9332dbed7c745bf7f1afdcf63","abstract_canon_sha256":"0b1d8f770d2e9be5f525965489d7aef9028c272f7cc2a9177186e85324c7b4cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:55.634764Z","signature_b64":"RRpU2E5x8ENxMR5TyO2p4d0tSPFmevsK0VU1bghNzPEFrus0THB9dYH9L4NoDg4yYOxaQTdWofjZTzn5kq0LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12829ecd55046881bab21add2121b724adefcf6500cac1f01430b23dcbc9f4f7","last_reissued_at":"2026-05-18T01:34:55.634221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:55.634221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost square Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Johann Langemets, Trond A. 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We prove that non-reflexive spaces which are M-ideals in their biduals are almost square.\n  We show that every separable space containing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0818","kind":"arxiv","version":2},"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":"1402.0818","created_at":"2026-05-18T01:34:55.634295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0818v2","created_at":"2026-05-18T01:34:55.634295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0818","created_at":"2026-05-18T01:34:55.634295+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKBJ5TKVARUI","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKBJ5TKVARUIDOVS","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKBJ5TKV","created_at":"2026-05-18T12:28:22.404517+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/CKBJ5TKVARUIDOVSDLOSCINXES","json":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES.json","graph_json":"https://pith.science/api/pith-number/CKBJ5TKVARUIDOVSDLOSCINXES/graph.json","events_json":"https://pith.science/api/pith-number/CKBJ5TKVARUIDOVSDLOSCINXES/events.json","paper":"https://pith.science/paper/CKBJ5TKV"},"agent_actions":{"view_html":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES","download_json":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES.json","view_paper":"https://pith.science/paper/CKBJ5TKV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0818&json=true","fetch_graph":"https://pith.science/api/pith-number/CKBJ5TKVARUIDOVSDLOSCINXES/graph.json","fetch_events":"https://pith.science/api/pith-number/CKBJ5TKVARUIDOVSDLOSCINXES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES/action/storage_attestation","attest_author":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES/action/author_attestation","sign_citation":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES/action/citation_signature","submit_replication":"https://pith.science/pith/CKBJ5TKVARUIDOVSDLOSCINXES/action/replication_record"}},"created_at":"2026-05-18T01:34:55.634295+00:00","updated_at":"2026-05-18T01:34:55.634295+00:00"}