{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CJY5VDPNALGLTAXZYLTVCQECX2","short_pith_number":"pith:CJY5VDPN","schema_version":"1.0","canonical_sha256":"1271da8ded02ccb982f9c2e7514082bebf59034a1360b46b062019e25d953bbe","source":{"kind":"arxiv","id":"1906.10832","version":2},"attestation_state":"computed","paper":{"title":"Existence of well-filterifications of $T_0$ topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dongsheng Zhao, Guohua Wu, Xiaoquan Xu, Xiaoyong Xi","submitted_at":"2019-06-26T03:52:12Z","abstract_excerpt":"We prove that for every $T_0$ space $X$, there is a well-filtered space $W(X)$ and a continuous mapping $\\eta_X: X\\lra W(X)$ such that for any well-filtered space $Y$ and any continuous mapping $f: X\\lra Y$ there is a unique continuous mapping $\\hat{f}: W(X)\\lra Y$ such that $f=\\hat{f}\\circ \\eta_X$. Such a space $W(X)$ will be called the well-filterification of $X$. This result gives a positive answer to one of the major open problems on well-filtered spaces. Another result on well-filtered spaces we will prove is that the product of two well-filtered spaces is well-filtered."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.10832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-06-26T03:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"fe94643ffccb14a662f11b0e1c3adfcbcc821e3477d74ad40559fa1945a822dd","abstract_canon_sha256":"4253bd7defa1cb995218ef6e26fe838ac0fa29830e74e3978ff2317081e72286"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:38.621816Z","signature_b64":"xVPelfJstP0EfYISVFi/oz1cOq7pOafLAhStFmUKXc0Dp64gLgNNxsmQm3l7S5937M6frnditlNMavYyQTDQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1271da8ded02ccb982f9c2e7514082bebf59034a1360b46b062019e25d953bbe","last_reissued_at":"2026-05-17T23:40:38.621424Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:38.621424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of well-filterifications of $T_0$ topological spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dongsheng Zhao, Guohua Wu, Xiaoquan Xu, Xiaoyong Xi","submitted_at":"2019-06-26T03:52:12Z","abstract_excerpt":"We prove that for every $T_0$ space $X$, there is a well-filtered space $W(X)$ and a continuous mapping $\\eta_X: X\\lra W(X)$ such that for any well-filtered space $Y$ and any continuous mapping $f: X\\lra Y$ there is a unique continuous mapping $\\hat{f}: W(X)\\lra Y$ such that $f=\\hat{f}\\circ \\eta_X$. Such a space $W(X)$ will be called the well-filterification of $X$. This result gives a positive answer to one of the major open problems on well-filtered spaces. Another result on well-filtered spaces we will prove is that the product of two well-filtered spaces is well-filtered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10832","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.10832","created_at":"2026-05-17T23:40:38.621480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.10832v2","created_at":"2026-05-17T23:40:38.621480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10832","created_at":"2026-05-17T23:40:38.621480+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJY5VDPNALGL","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJY5VDPNALGLTAXZ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJY5VDPN","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2","json":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2.json","graph_json":"https://pith.science/api/pith-number/CJY5VDPNALGLTAXZYLTVCQECX2/graph.json","events_json":"https://pith.science/api/pith-number/CJY5VDPNALGLTAXZYLTVCQECX2/events.json","paper":"https://pith.science/paper/CJY5VDPN"},"agent_actions":{"view_html":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2","download_json":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2.json","view_paper":"https://pith.science/paper/CJY5VDPN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.10832&json=true","fetch_graph":"https://pith.science/api/pith-number/CJY5VDPNALGLTAXZYLTVCQECX2/graph.json","fetch_events":"https://pith.science/api/pith-number/CJY5VDPNALGLTAXZYLTVCQECX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2/action/storage_attestation","attest_author":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2/action/author_attestation","sign_citation":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2/action/citation_signature","submit_replication":"https://pith.science/pith/CJY5VDPNALGLTAXZYLTVCQECX2/action/replication_record"}},"created_at":"2026-05-17T23:40:38.621480+00:00","updated_at":"2026-05-17T23:40:38.621480+00:00"}