{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AZ5PEOAZZUJFBT6MQ45BU3QSMO","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":"9e2d6397d409edebd766d3843a286c2e473b37e8ee85293dfc02b7fee10f65f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-21T09:19:31Z","title_canon_sha256":"08a39eafb063342a38f10d0aabd951d066eeeefd6b1ac2ba050e8f279cec06ef"},"schema_version":"1.0","source":{"id":"1603.06361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06361","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06361v1","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06361","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"AZ5PEOAZZUJF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AZ5PEOAZZUJFBT6M","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AZ5PEOAZ","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:fa687138cf4c7d1dd1d3d38ff864aa53fe701f5642c65fd61c2578102d95f480","target":"graph","created_at":"2026-05-18T00:52:50Z","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":"The Gurari\\u{\\i} space is the unique separable Banach space $\\mathbb{G}$ which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every $\\varepsilon>0$, for all finite-dimensional normed spaces $E \\subseteq F$, for every isometric embedding ${e}\\colon{E}\\to{\\mathbb{G}}$ there exists an $\\varepsilon$-isometric embedding ${f}\\colon{F}\\to{\\mathbb{G}}$ such that $f \\restriction E = e$.\n  We show that $\\mathbb{G}^{\\mathbb{N}}$ with a special sequence of semi-norms is of almost universal disposition for finite-dimensional graded Fr\\'echet spaces. The constr","authors_text":"C. Bargetz, J. Kakol, W. Kubi\\'s","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-21T09:19:31Z","title":"A separable Fr\\'echet space of almost universal disposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06361","kind":"arxiv","version":1},"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":"sha256:43e67c43beeb6745db9f2c19ec90080c8ae2bf92163383b9e85312526c9c8735","target":"record","created_at":"2026-05-18T00:52:50Z","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":"9e2d6397d409edebd766d3843a286c2e473b37e8ee85293dfc02b7fee10f65f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-21T09:19:31Z","title_canon_sha256":"08a39eafb063342a38f10d0aabd951d066eeeefd6b1ac2ba050e8f279cec06ef"},"schema_version":"1.0","source":{"id":"1603.06361","kind":"arxiv","version":1}},"canonical_sha256":"067af23819cd1250cfcc873a1a6e1263b7f34ef427ae44960a168326cf82a14f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"067af23819cd1250cfcc873a1a6e1263b7f34ef427ae44960a168326cf82a14f","first_computed_at":"2026-05-18T00:52:50.446619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:50.446619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iNZT+8NhE3+Uysba4RCgmsA8k29ZhcbVIdCxWR+kvSQiIdKui2ruOHRcLBd5UquZgBjPAVWdftsgl32d6mLDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:50.447235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43e67c43beeb6745db9f2c19ec90080c8ae2bf92163383b9e85312526c9c8735","sha256:fa687138cf4c7d1dd1d3d38ff864aa53fe701f5642c65fd61c2578102d95f480"],"state_sha256":"65d5d71716ef0939b1997a98f255b9a3c5cd2df7c6a5d93e62570ff53b1d8b8a"}