{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WK4ZTVJXNRVQ735NXRF2JDD5WX","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":"2237a7f10515007c0d90ad62390462e75b836022f963bdbbdc3804df64484122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-01-15T21:25:09Z","title_canon_sha256":"029d14535185c7884a7522968b648dc30853fc7c5e65ff6cbbb2a9331605183b"},"schema_version":"1.0","source":{"id":"1601.04081","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04081","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04081v2","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04081","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"WK4ZTVJXNRVQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WK4ZTVJXNRVQ735N","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WK4ZTVJX","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:fe9fa063e9d39833aa8f4ef7073bac15a4b225d8a5e3158ea56a7d75c5601fb4","target":"graph","created_at":"2026-05-18T00:05:34Z","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 space is reversible if every continuous bijection of the space onto itself is a homeomorphism. In this paper we study the question of which countable spaces with a unique non-isolated point are reversible. By Stone duality, these spaces correspond to closed subsets in the \\v{C}ech-Stone compactification of the natural numbers $\\beta\\omega$. From this, the following natural problem arises: given a space $X$ that is embeddable in $\\beta\\omega$, is it possible to embed $X$ in such a way that the associated filter of neighborhoods defines a reversible (or non-reversible) space? We give the solut","authors_text":"Alan Dow, Rodrigo Hern\\'andez-Guti\\'errez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-01-15T21:25:09Z","title":"Reversible filters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04081","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:f80c02d8911642cc0edbeb904088cf71a8efb9ef53e0756894f1a1faf19d9dfd","target":"record","created_at":"2026-05-18T00:05:34Z","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":"2237a7f10515007c0d90ad62390462e75b836022f963bdbbdc3804df64484122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-01-15T21:25:09Z","title_canon_sha256":"029d14535185c7884a7522968b648dc30853fc7c5e65ff6cbbb2a9331605183b"},"schema_version":"1.0","source":{"id":"1601.04081","kind":"arxiv","version":2}},"canonical_sha256":"b2b999d5376c6b0fefadbc4ba48c7db5d3104670e18ed6d79239685e04ca6988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2b999d5376c6b0fefadbc4ba48c7db5d3104670e18ed6d79239685e04ca6988","first_computed_at":"2026-05-18T00:05:34.801862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:34.801862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VV1ByEK7AfECSZPv5PUwXTpAMDUiPg6ocxS48ln0kJH88YQ54SDkIkv7Kx8vgCwamlZVt/nUbkxYAH+kUUfqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:34.802379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04081","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f80c02d8911642cc0edbeb904088cf71a8efb9ef53e0756894f1a1faf19d9dfd","sha256:fe9fa063e9d39833aa8f4ef7073bac15a4b225d8a5e3158ea56a7d75c5601fb4"],"state_sha256":"e68d3fe656e8c7caf157e32311dd6daa151891a196a9c15aa87336a3c9225928"}