{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V4XAHSVMN2A3VU3M3PYSMUNCV2","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":"31af77967b63de7cef5386ac5f1a0888dd3553f28d954c99a585726547aedeae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-01-20T18:06:00Z","title_canon_sha256":"4c4d4e7d831b1f09c15bce4606b56ec3b4c2d21ca4d3c587963e474852c96aca"},"schema_version":"1.0","source":{"id":"1501.04900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04900","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04900v2","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04900","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"V4XAHSVMN2A3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V4XAHSVMN2A3VU3M","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V4XAHSVM","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:50a2578675a46826be2acb8d32f74901a05149f83319778210a5b28eaa5063c5","target":"graph","created_at":"2026-05-18T02:28:41Z","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":"In this paper we consider a notion of $\\mathcal{I}$-Luzin set which generalizes the classical notion of Luzin set and Sierpi{\\'n}ski set on Euclidean spaces. We show that there is a translation invariant $\\sigma$-ideal $\\mathcal{I}$ with Borel base for which $\\mathcal{I}$-Luzin set can be $\\mathcal{I}$-measurable. If we additionally assume that $\\mathcal{I}$ has Smital property (or its weaker version) then $\\mathcal{I}$-Luzin sets are $\\mathcal{I}$-nonmeasurable. We give some constructions of $\\mathcal{I}$-Luzin sets involving additive structure of $\\mathbb{R}^n$. Moreover, we show that if $L$","authors_text":"Marcin Michalski, Szymon \\.Zeberski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-01-20T18:06:00Z","title":"Some properties of $\\mathcal{I}$-Luzin sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04900","kind":"arxiv","version":2},"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":"sha256:8ae89ad493c5940e34d2f7021639a3a7e3a794daf4a0df82e230b98abde590d7","target":"record","created_at":"2026-05-18T02:28:41Z","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":"31af77967b63de7cef5386ac5f1a0888dd3553f28d954c99a585726547aedeae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-01-20T18:06:00Z","title_canon_sha256":"4c4d4e7d831b1f09c15bce4606b56ec3b4c2d21ca4d3c587963e474852c96aca"},"schema_version":"1.0","source":{"id":"1501.04900","kind":"arxiv","version":2}},"canonical_sha256":"af2e03caac6e81bad36cdbf12651a2ae8de09c62491dd89b263c851da324cec9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af2e03caac6e81bad36cdbf12651a2ae8de09c62491dd89b263c851da324cec9","first_computed_at":"2026-05-18T02:28:41.156760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:41.156760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sY2a5JiUZZyT3E/54DTX0dgJMyxv06pu/3bE+df6DBeH9a3xc2HMb7wbEgy9Ijm1jw4UEWa50zAiVFNkI+a6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:41.157161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ae89ad493c5940e34d2f7021639a3a7e3a794daf4a0df82e230b98abde590d7","sha256:50a2578675a46826be2acb8d32f74901a05149f83319778210a5b28eaa5063c5"],"state_sha256":"5290e04aea9143413ed35bdc3e8d385377be16512e544c064ff96cfce4d0e8b2"}