{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UVCDMKSZEE7LZCOYH3Y5SCXWEP","short_pith_number":"pith:UVCDMKSZ","schema_version":"1.0","canonical_sha256":"a544362a59213ebc89d83ef1d90af623e1aa2eb957105719d6f6746a830d5a42","source":{"kind":"arxiv","id":"1805.02228","version":1},"attestation_state":"computed","paper":{"title":"On the tightness of $G_\\delta$-modifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alan Dow, Istv\\'an Juh\\'asz, Lajos Soukup, William Weiss, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2018-05-06T15:12:55Z","abstract_excerpt":"The $G_\\delta$-modification $X_\\delta$ of a topological space $X$ is the space on the same underlying set generated by, i.e. having as a basis, the collection of all $G_\\delta$ subsets of $X$. Bella and Spadaro recently investigated the connection between the values of various cardinal functions taken on $X$ and $X_\\delta$, respectively. In their paper, as Question 2, they raised the following problem: Is $t(X_\\delta) \\le 2^{t(X)}$ true for every (compact) $T_2$ space $X$? Note that this is actually two questions.\n  In this note we answer both questions: In the compact case affirmatively and i"},"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":"1805.02228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-05-06T15:12:55Z","cross_cats_sorted":[],"title_canon_sha256":"9c3c75dbe309064513039530a7230937938c33547b539a3c5b7902c2b0aa78e7","abstract_canon_sha256":"113727ef61edd7a315349cef5efa9a7a865abc40b712aaa74c99bd5bf8a4cedb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:40.513219Z","signature_b64":"l32aXBtU9wAv6YQIozeoVDDgD9OzmFhtJr8iQBGqD8LUUwKBRaGdJM2iy+7L/S3h913+kMegy2Wpnwaa+2CxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a544362a59213ebc89d83ef1d90af623e1aa2eb957105719d6f6746a830d5a42","last_reissued_at":"2026-05-18T00:16:40.512498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:40.512498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the tightness of $G_\\delta$-modifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alan Dow, Istv\\'an Juh\\'asz, Lajos Soukup, William Weiss, Zolt\\'an Szentmikl\\'ossy","submitted_at":"2018-05-06T15:12:55Z","abstract_excerpt":"The $G_\\delta$-modification $X_\\delta$ of a topological space $X$ is the space on the same underlying set generated by, i.e. having as a basis, the collection of all $G_\\delta$ subsets of $X$. Bella and Spadaro recently investigated the connection between the values of various cardinal functions taken on $X$ and $X_\\delta$, respectively. In their paper, as Question 2, they raised the following problem: Is $t(X_\\delta) \\le 2^{t(X)}$ true for every (compact) $T_2$ space $X$? Note that this is actually two questions.\n  In this note we answer both questions: In the compact case affirmatively and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02228","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":"1805.02228","created_at":"2026-05-18T00:16:40.512618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.02228v1","created_at":"2026-05-18T00:16:40.512618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02228","created_at":"2026-05-18T00:16:40.512618+00:00"},{"alias_kind":"pith_short_12","alias_value":"UVCDMKSZEE7L","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UVCDMKSZEE7LZCOY","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UVCDMKSZ","created_at":"2026-05-18T12:32:56.356000+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/UVCDMKSZEE7LZCOYH3Y5SCXWEP","json":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP.json","graph_json":"https://pith.science/api/pith-number/UVCDMKSZEE7LZCOYH3Y5SCXWEP/graph.json","events_json":"https://pith.science/api/pith-number/UVCDMKSZEE7LZCOYH3Y5SCXWEP/events.json","paper":"https://pith.science/paper/UVCDMKSZ"},"agent_actions":{"view_html":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP","download_json":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP.json","view_paper":"https://pith.science/paper/UVCDMKSZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.02228&json=true","fetch_graph":"https://pith.science/api/pith-number/UVCDMKSZEE7LZCOYH3Y5SCXWEP/graph.json","fetch_events":"https://pith.science/api/pith-number/UVCDMKSZEE7LZCOYH3Y5SCXWEP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP/action/storage_attestation","attest_author":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP/action/author_attestation","sign_citation":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP/action/citation_signature","submit_replication":"https://pith.science/pith/UVCDMKSZEE7LZCOYH3Y5SCXWEP/action/replication_record"}},"created_at":"2026-05-18T00:16:40.512618+00:00","updated_at":"2026-05-18T00:16:40.512618+00:00"}