{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S25VEMXT3SDUD3ZZNR4AYONPXB","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":"3fda0752c1c5446d0838b92ba8a5e528102426b5e729c12dd05afd08c2b09658","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T23:39:29Z","title_canon_sha256":"38d91881874dafb2d9f209a362281f0bf4e38dd734dc5a411cabfc7c7c44ca01"},"schema_version":"1.0","source":{"id":"1706.02006","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02006","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02006v3","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02006","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"pith_short_12","alias_value":"S25VEMXT3SDU","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S25VEMXT3SDUD3ZZ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S25VEMXT","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:60bccaec1f4721fbd0b9c4227f4221c66afbd1316f567429ba37b0d794b052bf","target":"graph","created_at":"2026-05-18T00:42:04Z","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":"Let $x_\\alpha$ be a net in a locally solid vector lattice $(X,\\tau)$; we say that $x_\\alpha$ is unbounded $\\tau$-convergent to a vector $x\\in X$ if $\\lvert x_\\alpha-x \\rvert\\wedge w \\xrightarrow{\\tau} 0$ for all $w\\in X_+$. In this paper, we study general properties of unbounded $\\tau$-convergence (shortly, $u\\tau$-convergence). $u\\tau$-Convergence generalizes unbounded norm convergence and unbounded absolute weak convergence in normed lattices that have been investigated recently. Besides, we introduce $u\\tau$-topology and study briefly metrizabililty and completeness of this topology.","authors_text":"E. Yu. Emelyanov, M. A. A. Marabeh, Y. A. Dabboorasad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T23:39:29Z","title":"$u\\tau$-Convergence in locally solid vector lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02006","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":"sha256:8a5b40d75b64c862b3e633d052a1e612cb3e7234b18dadf2b9be7ed5816f0587","target":"record","created_at":"2026-05-18T00:42:04Z","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":"3fda0752c1c5446d0838b92ba8a5e528102426b5e729c12dd05afd08c2b09658","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T23:39:29Z","title_canon_sha256":"38d91881874dafb2d9f209a362281f0bf4e38dd734dc5a411cabfc7c7c44ca01"},"schema_version":"1.0","source":{"id":"1706.02006","kind":"arxiv","version":3}},"canonical_sha256":"96bb5232f3dc8741ef396c780c39afb86bcfb11383578dce8453dff1fb43bb33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96bb5232f3dc8741ef396c780c39afb86bcfb11383578dce8453dff1fb43bb33","first_computed_at":"2026-05-18T00:42:04.371759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:04.371759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ZYWZnL3RvcQjEEnx2cui0rtBhoEEbMwqMD0BqTM3An3ymdO2IP3woduaYrBOhFn1QGmKdfPHEKdihlAXoF4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:04.372284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02006","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a5b40d75b64c862b3e633d052a1e612cb3e7234b18dadf2b9be7ed5816f0587","sha256:60bccaec1f4721fbd0b9c4227f4221c66afbd1316f567429ba37b0d794b052bf"],"state_sha256":"f6cffb0d0a8be76c0f5e04a525e2abdb34646f527b058b9d39a26d76f0effa3b"}