{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:O6TYPVJDAGP37DMUYKXTHBYGPA","short_pith_number":"pith:O6TYPVJD","schema_version":"1.0","canonical_sha256":"77a787d523019fbf8d94c2af33870678148d7f2e752ebdacff8d473091383763","source":{"kind":"arxiv","id":"1904.00322","version":2},"attestation_state":"computed","paper":{"title":"A note on the tightness of $G_\\delta$-modifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Toshimichi Usuba","submitted_at":"2019-03-31T02:10:05Z","abstract_excerpt":"We construct a normal countably tight $T_1$ space $X$ with $t(X_\\delta) >2^\\omega$. This is an answer to the question posed by Dow-Juh\\'asz-Soukup-Szentmikl\\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_\\delta$-modifications of countably tight spaces can be arbitrary large up to the least $\\omega_1$-strongly compact cardinal."},"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":"1904.00322","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-31T02:10:05Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"4e6ebdd691e36801eb18102cbea6d4132a5e992e92c79a5d5a3a25d5c4807ba4","abstract_canon_sha256":"a0fd45fae2016e6a7d24d7ef3fdbe91222440a189ac68fc319a1a75565a07d24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:38.906926Z","signature_b64":"EjjI6FAqQFhOT8lELeYibca/YaU3TMtN4M0f8kjGOn2MGNkpUv6347mRgIDpyc3LvtkGWoMqD0dDbnkm715SAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77a787d523019fbf8d94c2af33870678148d7f2e752ebdacff8d473091383763","last_reissued_at":"2026-05-17T23:40:38.906377Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:38.906377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the tightness of $G_\\delta$-modifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Toshimichi Usuba","submitted_at":"2019-03-31T02:10:05Z","abstract_excerpt":"We construct a normal countably tight $T_1$ space $X$ with $t(X_\\delta) >2^\\omega$. This is an answer to the question posed by Dow-Juh\\'asz-Soukup-Szentmikl\\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_\\delta$-modifications of countably tight spaces can be arbitrary large up to the least $\\omega_1$-strongly compact cardinal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00322","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":"1904.00322","created_at":"2026-05-17T23:40:38.906460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.00322v2","created_at":"2026-05-17T23:40:38.906460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00322","created_at":"2026-05-17T23:40:38.906460+00:00"},{"alias_kind":"pith_short_12","alias_value":"O6TYPVJDAGP3","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"O6TYPVJDAGP37DMU","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"O6TYPVJD","created_at":"2026-05-18T12:33:24.271573+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/O6TYPVJDAGP37DMUYKXTHBYGPA","json":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA.json","graph_json":"https://pith.science/api/pith-number/O6TYPVJDAGP37DMUYKXTHBYGPA/graph.json","events_json":"https://pith.science/api/pith-number/O6TYPVJDAGP37DMUYKXTHBYGPA/events.json","paper":"https://pith.science/paper/O6TYPVJD"},"agent_actions":{"view_html":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA","download_json":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA.json","view_paper":"https://pith.science/paper/O6TYPVJD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.00322&json=true","fetch_graph":"https://pith.science/api/pith-number/O6TYPVJDAGP37DMUYKXTHBYGPA/graph.json","fetch_events":"https://pith.science/api/pith-number/O6TYPVJDAGP37DMUYKXTHBYGPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA/action/storage_attestation","attest_author":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA/action/author_attestation","sign_citation":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA/action/citation_signature","submit_replication":"https://pith.science/pith/O6TYPVJDAGP37DMUYKXTHBYGPA/action/replication_record"}},"created_at":"2026-05-17T23:40:38.906460+00:00","updated_at":"2026-05-17T23:40:38.906460+00:00"}