{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MALXRYYBVFUSTJI2XPE7ZGZ524","short_pith_number":"pith:MALXRYYB","canonical_record":{"source":{"id":"1812.10166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-25T21:11:39Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"059bc7431c7b0fe6da6b52a562c93606c7bf0ff3d03b50b90694daec0c904dc1","abstract_canon_sha256":"259af0e011f033b9febfc6c7da6034e60df9cdf077ba71ab6d2e2834b6e34082"},"schema_version":"1.0"},"canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","source":{"kind":"arxiv","id":"1812.10166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10166","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10166v2","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10166","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"MALXRYYBVFUS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MALXRYYBVFUSTJI2","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MALXRYYB","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MALXRYYBVFUSTJI2XPE7ZGZ524","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-25T21:11:39Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"059bc7431c7b0fe6da6b52a562c93606c7bf0ff3d03b50b90694daec0c904dc1","abstract_canon_sha256":"259af0e011f033b9febfc6c7da6034e60df9cdf077ba71ab6d2e2834b6e34082"},"schema_version":"1.0"},"canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:52.465997Z","signature_b64":"8YtP7AtV+xli8ena+vdaZn50HeC/ybjhnfjupdsvnqFQViQGioLJGaUILV9NR6yAtMIGqDlR7nKMhw0CxDSUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","last_reissued_at":"2026-05-17T23:56:52.465548Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:52.465548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10166","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jNd9OueW9S967akaTBnPXDLyfrjE9keUFbf1ADWlJw2c5GiDkHujEGZESxGvN08Lnvna4Vj6abBJYVVjL6LVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T19:53:17.357524Z"},"content_sha256":"90650185e1c65de15c83ebe5b1d6c4f8597f228b742413ad4cb87230851c8e53","schema_version":"1.0","event_id":"sha256:90650185e1c65de15c83ebe5b1d6c4f8597f228b742413ad4cb87230851c8e53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MALXRYYBVFUSTJI2XPE7ZGZ524","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $\\kappa$-Fr\\'{e}chet--Urysohn property for locally convex spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"S. Gabriyelyan","submitted_at":"2018-12-25T21:11:39Z","abstract_excerpt":"A topological space $X$ is $\\kappa$-Fr\\'{e}chet--Urysohn if for every open subset $U$ of $X$ and every $x\\in \\overline{U}$ there exists a sequence in $ U$ converging to $x$. We prove that every $\\kappa$-Fr\\'{e}chet--Urysohn Tychonoff space $X$ is Ascoli. We apply this statement and some of known results to characterize the $\\kappa$-Fr\\'echet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that $C_p(X)$ is Ascoli iff $X$ has the property $(\\kappa)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10166","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"napmVn2iMkyJOj5yDm2AmT0oAwhyoiUpFl4bTyBZ1en+iEC9/X5T6EQKO+N7pdWaeD5sxPlYxrOyLYn3KkPcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T19:53:17.357876Z"},"content_sha256":"6fcb1b2468ce59833f02a8e2dbc1a0a120a0214c06f8b765bf2615aee9d6282c","schema_version":"1.0","event_id":"sha256:6fcb1b2468ce59833f02a8e2dbc1a0a120a0214c06f8b765bf2615aee9d6282c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/bundle.json","state_url":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T19:53:17Z","links":{"resolver":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524","bundle":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/bundle.json","state":"https://pith.science/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MALXRYYBVFUSTJI2XPE7ZGZ524/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MALXRYYBVFUSTJI2XPE7ZGZ524","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":"259af0e011f033b9febfc6c7da6034e60df9cdf077ba71ab6d2e2834b6e34082","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-25T21:11:39Z","title_canon_sha256":"059bc7431c7b0fe6da6b52a562c93606c7bf0ff3d03b50b90694daec0c904dc1"},"schema_version":"1.0","source":{"id":"1812.10166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10166","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10166v2","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10166","created_at":"2026-05-17T23:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"MALXRYYBVFUS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MALXRYYBVFUSTJI2","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MALXRYYB","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:6fcb1b2468ce59833f02a8e2dbc1a0a120a0214c06f8b765bf2615aee9d6282c","target":"graph","created_at":"2026-05-17T23:56:52Z","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":"A topological space $X$ is $\\kappa$-Fr\\'{e}chet--Urysohn if for every open subset $U$ of $X$ and every $x\\in \\overline{U}$ there exists a sequence in $ U$ converging to $x$. We prove that every $\\kappa$-Fr\\'{e}chet--Urysohn Tychonoff space $X$ is Ascoli. We apply this statement and some of known results to characterize the $\\kappa$-Fr\\'echet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that $C_p(X)$ is Ascoli iff $X$ has the property $(\\kappa)$.","authors_text":"S. Gabriyelyan","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-25T21:11:39Z","title":"The $\\kappa$-Fr\\'{e}chet--Urysohn property for locally convex spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10166","kind":"arxiv","version":2},"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":"sha256:90650185e1c65de15c83ebe5b1d6c4f8597f228b742413ad4cb87230851c8e53","target":"record","created_at":"2026-05-17T23:56:52Z","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":"259af0e011f033b9febfc6c7da6034e60df9cdf077ba71ab6d2e2834b6e34082","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-12-25T21:11:39Z","title_canon_sha256":"059bc7431c7b0fe6da6b52a562c93606c7bf0ff3d03b50b90694daec0c904dc1"},"schema_version":"1.0","source":{"id":"1812.10166","kind":"arxiv","version":2}},"canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"601778e301a96929a51abbc9fc9b3dd70a34288491fc2fa9e002b85fd60d177a","first_computed_at":"2026-05-17T23:56:52.465548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:52.465548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8YtP7AtV+xli8ena+vdaZn50HeC/ybjhnfjupdsvnqFQViQGioLJGaUILV9NR6yAtMIGqDlR7nKMhw0CxDSUCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:52.465997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90650185e1c65de15c83ebe5b1d6c4f8597f228b742413ad4cb87230851c8e53","sha256:6fcb1b2468ce59833f02a8e2dbc1a0a120a0214c06f8b765bf2615aee9d6282c"],"state_sha256":"222075cb4f79ae6d4209d1509712fcae2d0d8897b9860b8e6947e1e0a7626b47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ljVbxgJ6Bizm+VyitavoGXDPswankOxUeodEMR4faCutHgA45is6zkMVotdGAQ8NUxvL8iaf0f8Oig7wpxeAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T19:53:17.359815Z","bundle_sha256":"d49f7d4b3a2138149911b975e2b42d3279039aa2bdf9d199ba72be0d0be26bd4"}}