{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:ELTIVHPUQQAAZOEETKQAJTES3J","short_pith_number":"pith:ELTIVHPU","schema_version":"1.0","canonical_sha256":"22e68a9df484000cb8849aa004cc92da6b0a547ec5f739612dbba904ffb6aed2","source":{"kind":"arxiv","id":"math/0311015","version":1},"attestation_state":"computed","paper":{"title":"A compact group which is not Valdivia compact","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Vladimir Uspenskij, Wieslaw Kubi\\'s","submitted_at":"2003-11-03T03:28:15Z","abstract_excerpt":"A compact space $K$ is {\\em Valdivia compact} if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\\cap\\Sigma$ is dense in $K$, where $\\Sigma$ is the sigma-product (= the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight $\\o_1$ which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps."},"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":"math/0311015","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2003-11-03T03:28:15Z","cross_cats_sorted":[],"title_canon_sha256":"56c2d77b0145256d15e59c1f9b937248e18adcea95c93c727cdb1c546c16103e","abstract_canon_sha256":"1b4f57ef54db8885b91c1d998b64ac3b8a52a2800755dc563e1c2b5fde3c6f15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:34.355167Z","signature_b64":"QXaBwKRjccexDPwhDUdcry4r5OJqXe6Crfmm5IAd/ZvRite3hUktWGDojxgKm9GSmTXiw3DDf7+EO4rdIyeEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e68a9df484000cb8849aa004cc92da6b0a547ec5f739612dbba904ffb6aed2","last_reissued_at":"2026-05-18T03:42:34.354569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:34.354569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A compact group which is not Valdivia compact","license":"","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Vladimir Uspenskij, Wieslaw Kubi\\'s","submitted_at":"2003-11-03T03:28:15Z","abstract_excerpt":"A compact space $K$ is {\\em Valdivia compact} if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\\cap\\Sigma$ is dense in $K$, where $\\Sigma$ is the sigma-product (= the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight $\\o_1$ which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311015","kind":"arxiv","version":1},"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":"math/0311015","created_at":"2026-05-18T03:42:34.354635+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0311015v1","created_at":"2026-05-18T03:42:34.354635+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311015","created_at":"2026-05-18T03:42:34.354635+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELTIVHPUQQAA","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELTIVHPUQQAAZOEE","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELTIVHPU","created_at":"2026-05-18T12:25:51.375804+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/ELTIVHPUQQAAZOEETKQAJTES3J","json":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J.json","graph_json":"https://pith.science/api/pith-number/ELTIVHPUQQAAZOEETKQAJTES3J/graph.json","events_json":"https://pith.science/api/pith-number/ELTIVHPUQQAAZOEETKQAJTES3J/events.json","paper":"https://pith.science/paper/ELTIVHPU"},"agent_actions":{"view_html":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J","download_json":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J.json","view_paper":"https://pith.science/paper/ELTIVHPU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0311015&json=true","fetch_graph":"https://pith.science/api/pith-number/ELTIVHPUQQAAZOEETKQAJTES3J/graph.json","fetch_events":"https://pith.science/api/pith-number/ELTIVHPUQQAAZOEETKQAJTES3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J/action/storage_attestation","attest_author":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J/action/author_attestation","sign_citation":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J/action/citation_signature","submit_replication":"https://pith.science/pith/ELTIVHPUQQAAZOEETKQAJTES3J/action/replication_record"}},"created_at":"2026-05-18T03:42:34.354635+00:00","updated_at":"2026-05-18T03:42:34.354635+00:00"}