{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7PPJ5LPB6QLAWTQ4LHH5D4S2VT","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":"cdb06fb269e9504f35609e081553b5d5fdcc8af04187088327010fce94048614","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-09T18:00:33Z","title_canon_sha256":"74d37312de461986ac0d57d655eb268c65643ae3cb88c846c9e10e6954cc4d56"},"schema_version":"1.0","source":{"id":"1509.02874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02874","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02874v1","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02874","created_at":"2026-05-18T01:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"7PPJ5LPB6QLA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7PPJ5LPB6QLAWTQ4","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7PPJ5LPB","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:47c88dd34d0f771383e9f752adc8fa8221850308eb68841e59536dc7706d9839","target":"graph","created_at":"2026-05-18T01:33:33Z","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 show that if $Y$ is a dense subspace of a Tychonoff space $X$, then $w(X)\\leq nw(Y)^{Nag(Y)}$, where $Nag(Y)$ is the Nagami number of $Y$. In particular, if $Y$ is a Lindel\\\"of $\\Sigma$-space, then $w(X)\\leq nw(Y)^\\omega\\leq nw(X)^\\omega$.\n  Better upper bounds for the weight of topological groups are given. For example, if a topological group $H$ contains a dense subgroup $G$ such that $G$ is a Lindel\\\"of $\\Sigma$-space, then $w(H)=w(G)\\leq \\psi(G)^\\omega$. Further, if a Lindel\\\"of $\\Sigma$-space $X$ generates a dense subgroup of a topological group $H$, then $w(H)\\leq 2^{\\psi(X)}$.\n  Seve","authors_text":"Mikhail G. Tkachenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-09T18:00:33Z","title":"The weight and Lindel\\\"of property in spaces and topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02874","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:b1c9c0a6e4299db1b6ffc28c68b672b8d4a53d40bb43cde304b28feed6ac3741","target":"record","created_at":"2026-05-18T01:33:33Z","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":"cdb06fb269e9504f35609e081553b5d5fdcc8af04187088327010fce94048614","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-09T18:00:33Z","title_canon_sha256":"74d37312de461986ac0d57d655eb268c65643ae3cb88c846c9e10e6954cc4d56"},"schema_version":"1.0","source":{"id":"1509.02874","kind":"arxiv","version":1}},"canonical_sha256":"fbde9eade1f4160b4e1c59cfd1f25aacca90c09a9561a999cf38864d085e3674","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbde9eade1f4160b4e1c59cfd1f25aacca90c09a9561a999cf38864d085e3674","first_computed_at":"2026-05-18T01:33:33.047172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:33.047172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A0k962x56RsjQ4osx69VmsJ08OTW88GkH6dC8/YeevKGulrYod2k+JtltORuQgs7twcdLa1uGqgrSGI1e0XpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:33.047881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1c9c0a6e4299db1b6ffc28c68b672b8d4a53d40bb43cde304b28feed6ac3741","sha256:47c88dd34d0f771383e9f752adc8fa8221850308eb68841e59536dc7706d9839"],"state_sha256":"9b52d519b519a9aec63e493ff76ec3f40e1940fab5a1449601aa56c4f430238a"}