{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SEFPQ5NLHDCDRGI2M22UHU6NQI","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":"bb1b7bc252dce9514c40cbe7a2521308b8872a7343d50c0385348992c9e2b845","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-08-24T09:41:33Z","title_canon_sha256":"44f95150cdc2ae07a35f920591586684a0c6ba548136508f31bd7c7c7a8647ce"},"schema_version":"1.0","source":{"id":"1908.09115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09115","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09115v1","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09115","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"pith_short_12","alias_value":"SEFPQ5NLHDCD","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"pith_short_16","alias_value":"SEFPQ5NLHDCDRGI2","created_at":"2026-07-04T23:59:36Z"},{"alias_kind":"pith_short_8","alias_value":"SEFPQ5NL","created_at":"2026-07-04T23:59:36Z"}],"graph_snapshots":[{"event_id":"sha256:41d64586c3a7bf271c7a206e1909a0bb4a0416cb22e2a3f860a1c2187139cdc0","target":"graph","created_at":"2026-07-04T23:59:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.09115/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper the weak topology on a normed space is studied from the viewpoint of infinite-dimensional topology. Besides the weak topology on a normed space $X$ (coinciding with the topology of uniform convergence on finite subsets of the dual space $X^*$), we consider the topology $c$ of uniform convergence on compact subsets of $X^*$. It is known that this topology coincides with the weak topology on bounded subsets of $X$, but unlike to the latter has much better topological properties (e.g., is stratifiable).\n  We prove that for normed spaces $X,Y$ with separable duals the spaces $(X,weak","authors_text":"Taras Banakh","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-08-24T09:41:33Z","title":"On topological classification of normed spaces endowed with the weak topology or the topology of compact convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09115","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":"sha256:5561d03bf9d669218dda7d9f05ed3d4fbe96572bb66c254039321a1f7252a399","target":"record","created_at":"2026-07-04T23:59:36Z","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":"bb1b7bc252dce9514c40cbe7a2521308b8872a7343d50c0385348992c9e2b845","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-08-24T09:41:33Z","title_canon_sha256":"44f95150cdc2ae07a35f920591586684a0c6ba548136508f31bd7c7c7a8647ce"},"schema_version":"1.0","source":{"id":"1908.09115","kind":"arxiv","version":1}},"canonical_sha256":"910af875ab38c438991a66b543d3cd822719cb439e23634e0acacd024c0fd6d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"910af875ab38c438991a66b543d3cd822719cb439e23634e0acacd024c0fd6d1","first_computed_at":"2026-07-04T23:59:36.894724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:36.894724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"doYUIx+X/wsdws416udRAOfXvMPK80FyF4O0Vfhitrru7vjqSFlKhB5ciOfmn3pnJbesFxC7UNaySIDoewZ6BA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:36.895074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5561d03bf9d669218dda7d9f05ed3d4fbe96572bb66c254039321a1f7252a399","sha256:41d64586c3a7bf271c7a206e1909a0bb4a0416cb22e2a3f860a1c2187139cdc0"],"state_sha256":"58aac58790693bcc5bc666e55c0c53fba7f29210e404d4a2feeccacec5e9ad37"}