{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3ZBB6U2C2ABZ62H4WGD4C5WRJW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c01a1df0966d92516eab515a6eb5f4a1340d4a07ffcca66c1439dda1f46c3a43","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-16T14:30:04Z","title_canon_sha256":"e8d132977232933c894d7bd57e3dcd21fc77df6c2278b42a7e0bd09631b030f4"},"schema_version":"1.0","source":{"id":"1308.3640","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3640","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3640v3","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3640","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"3ZBB6U2C2ABZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3ZBB6U2C2ABZ62H4","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3ZBB6U2C","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:f8f2b5f42d890ecc4c1d27aaf363dda1b910487fde0ab9deee5d986e7ec87155","target":"graph","created_at":"2026-05-18T02:41:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study isomorphic universality of Banach spaces of a given density and a number of pairwise non-isomorphic models in the same class. We show that in the Cohen model the isomorphic universality number for Banach spaces of density $\\aleph_1$ is $\\aleph_2$, and analogous results are true for other cardinals (Theorem 1.2(1)) and that adding just one Cohen real to any model destroys the old universality of Banach spaces of density $\\aleph_1$ (Theorem 1.5). Moreover, adding one Cohen real adds a weakly compactly generated Banach space of density $\\aleph_1$ which does not embed into any Banach spac","authors_text":"Mirna D\\v{z}amonja","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-16T14:30:04Z","title":"Isomorphic universality and the number of pairwise non-isomorphic models in the class of Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3640","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:417a9cb8e8e85f63a34bfb9ede11d25473a9b66044befc7dffc0287d37e1035b","target":"record","created_at":"2026-05-18T02:41:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c01a1df0966d92516eab515a6eb5f4a1340d4a07ffcca66c1439dda1f46c3a43","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-08-16T14:30:04Z","title_canon_sha256":"e8d132977232933c894d7bd57e3dcd21fc77df6c2278b42a7e0bd09631b030f4"},"schema_version":"1.0","source":{"id":"1308.3640","kind":"arxiv","version":3}},"canonical_sha256":"de421f5342d0039f68fcb187c176d14daeba2ce648222979e33a2b5a85989381","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de421f5342d0039f68fcb187c176d14daeba2ce648222979e33a2b5a85989381","first_computed_at":"2026-05-18T02:41:52.153339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.153339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/z54SPoueybUVS9xxDCU7qWMeiGPdo4hk6UAMvgwVsz7foffLgoLXVwLj+4Ts9dk+5pbQGgVNxQZLZeQbpYjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.153844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3640","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:417a9cb8e8e85f63a34bfb9ede11d25473a9b66044befc7dffc0287d37e1035b","sha256:f8f2b5f42d890ecc4c1d27aaf363dda1b910487fde0ab9deee5d986e7ec87155"],"state_sha256":"fc125a46291ed6215920d815dde25885d767eb01820de40cb4222751b4626878"}