{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FLDBDNJSGVGIZCTZC2IIWMDR2U","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":"d0dfa4a969f796ced690efc5f849e738812b4b1d0b6998611597d7fd19ac306a","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-20T18:47:12Z","title_canon_sha256":"57172560cc936efde28f1263969cd30a053c96aa15d6c730a6fec60e77c86650"},"schema_version":"1.0","source":{"id":"1702.06105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06105","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06105v2","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06105","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"FLDBDNJSGVGI","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLDBDNJSGVGIZCTZ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLDBDNJS","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:dd95c32a0f9896f4589d95bf20d4382530414c0502aef6a8d689c69da6ab59c4","target":"graph","created_at":"2026-05-18T00:45:01Z","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 study feebly compact topologies $\\tau$ on the semilattice $\\left(\\exp_n\\lambda,\\cap\\right)$ such that $\\left(\\exp_n\\lambda,\\tau\\right)$ is a semitopological semilattice and prove that for any shift-continuous $T_1$-topology $\\tau$ on $\\exp_n\\lambda$ the following conditions are equivalent: $(i)$~$\\tau$ is countably pracompact; $(ii)$ $\\tau$ is feebly compact; $(iii)$ $\\tau$ is $d$-feebly compact; $(iv)$ $\\left(\\exp_n\\lambda,\\tau\\right)$ is an $H$-closed space.","authors_text":"Oleg Gutik, Oleksandra Sobol","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-20T18:47:12Z","title":"On feebly compact shift-continuous topologies on the semilattice $\\exp_n\\lambda$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06105","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":"sha256:7aab04278de927bdab0d074333d8b17e945ca4bbb092ae5230d05c1ab25afdb8","target":"record","created_at":"2026-05-18T00:45:01Z","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":"d0dfa4a969f796ced690efc5f849e738812b4b1d0b6998611597d7fd19ac306a","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-20T18:47:12Z","title_canon_sha256":"57172560cc936efde28f1263969cd30a053c96aa15d6c730a6fec60e77c86650"},"schema_version":"1.0","source":{"id":"1702.06105","kind":"arxiv","version":2}},"canonical_sha256":"2ac611b532354c8c8a7916908b3071d50889b33ebd32700fbe8f675bd3bf6514","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ac611b532354c8c8a7916908b3071d50889b33ebd32700fbe8f675bd3bf6514","first_computed_at":"2026-05-18T00:45:01.217259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:01.217259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VS/qe7UCkobCdk4GsRa3vaf1y8nd42S3PGZOOXieYY3rut7V4nQK8IA12vKIYqpy2fPoxfbr4akjIGiKDfqoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:01.217735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aab04278de927bdab0d074333d8b17e945ca4bbb092ae5230d05c1ab25afdb8","sha256:dd95c32a0f9896f4589d95bf20d4382530414c0502aef6a8d689c69da6ab59c4"],"state_sha256":"b47651fa14f87166cd61447b3bd48a31026be8735f6119a8f8b7b867350fe7b6"}