{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UABDGX24F6TPE235ICFKSOA6BP","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":"1a19a38fbb10506522c67c8ff02aecc8ea8fd03e24578e7b6dee1df79c765a3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-29T09:57:31Z","title_canon_sha256":"17b19981c968eccdabd7743d04ffccb8a727bd7133e6bceb510ddb8406278e2e"},"schema_version":"1.0","source":{"id":"1603.08699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08699","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08699v1","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08699","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"UABDGX24F6TP","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UABDGX24F6TPE235","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UABDGX24","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:05c181ad6c7e0f35ea448a9a605ece8be737a0dd9e4d6d6f20d027b6042a2e15","target":"graph","created_at":"2026-05-18T01:18:05Z","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":"We study ideals $\\mathcal{I}$ on $\\mathbb{N}$ satisfying the following Baire-type property: if $X$ is a complete metric space and $\\{X_{A} \\colon A \\in \\mathcal{I} \\}$ is a family of nowhere dense subsets of $X$ with $X_{A} \\subset X_{B}$ whenever $A \\subset B$, then $\\bigcup_{A \\in \\mathcal{I}}{X_{A}} \\neq X$. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of $X$.","authors_text":"A. Avil\\'es, A. P\\'erez, S. Solecki, V. Kadets","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-29T09:57:31Z","title":"Baire theorem for ideals of sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08699","kind":"arxiv","version":1},"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":"sha256:3e8ca23e824245643ea845e817671ad7bf1a5208aeba4b3a59051321bc6b1305","target":"record","created_at":"2026-05-18T01:18:05Z","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":"1a19a38fbb10506522c67c8ff02aecc8ea8fd03e24578e7b6dee1df79c765a3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-29T09:57:31Z","title_canon_sha256":"17b19981c968eccdabd7743d04ffccb8a727bd7133e6bceb510ddb8406278e2e"},"schema_version":"1.0","source":{"id":"1603.08699","kind":"arxiv","version":1}},"canonical_sha256":"a002335f5c2fa6f26b7d408aa9381e0bccc80bdefa8d69f643b25a2d9d3200b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a002335f5c2fa6f26b7d408aa9381e0bccc80bdefa8d69f643b25a2d9d3200b8","first_computed_at":"2026-05-18T01:18:05.583713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:05.583713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WU7/1c+mJbEh0eh+Te0qXfakC88PsooR54YV3v6j2gLlgP208AgEKHk7EgnJfCmAMDvCXT7H4lK9o1GkeTPhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:05.584464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e8ca23e824245643ea845e817671ad7bf1a5208aeba4b3a59051321bc6b1305","sha256:05c181ad6c7e0f35ea448a9a605ece8be737a0dd9e4d6d6f20d027b6042a2e15"],"state_sha256":"28d90c04ea3142c4ac724dfea6cc4fd1b0ad6fc0cdd59ee559514d14a6b81197"}