{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:M2ALAZPVSQRAE5EOTJGL2BSRUY","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":"9acfc6ffeebdd1c042890ca41d07a78a8d33528185df686b9b257ce5bb80c356","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-15T21:40:41Z","title_canon_sha256":"d3a05cbd4533e8926c4bda43451933b0dc6cf33db8aef9b60867828b17b0cdca"},"schema_version":"1.0","source":{"id":"1908.05776","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05776","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05776v4","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05776","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"M2ALAZPVSQRA","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"pith_short_16","alias_value":"M2ALAZPVSQRAE5EO","created_at":"2026-07-05T01:59:09Z"},{"alias_kind":"pith_short_8","alias_value":"M2ALAZPV","created_at":"2026-07-05T01:59:09Z"}],"graph_snapshots":[{"event_id":"sha256:933e25c11ea903d2b4582580349d1d806e147de806931b2853e542c5707c8b47","target":"graph","created_at":"2026-07-05T01:59:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A subset $X$ of a Polish group $G$ is \\emph{Haar null} if there exists a Borel probability measure $\\mu$ and a Borel set $B$ containing $X$ such that $\\mu(gBh)=0$ for every $g,h \\in G$. A set $X$ is \\emph{Haar meager} if there exists a compact metric space $K$, a continuous function $f : K \\to G$ and a Borel set $B$ containing $X$ such that $f^{-1}(gBh)$ is meager in $K$ for every $g,h \\in G$. We calculate (in $ZFC$) the four cardinal invariants ($\\rm add$, $\\rm cov$, $\\rm non$, $\\rm cof$) of these two $\\sigma$-ideals for the simplest non-locally compact Polish group, namely in the case $G = \\","authors_text":"M\\'ark Po\\'or, M\\'arton Elekes","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-15T21:40:41Z","title":"Cardinal invariants of Haar null and Haar meager sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05776","kind":"arxiv","version":4},"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:f2cfa061260d3a596b77e41258a9f4ca3fc4834acb23bf80e54f3bc35af13c2d","target":"record","created_at":"2026-07-05T01:59:09Z","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":"9acfc6ffeebdd1c042890ca41d07a78a8d33528185df686b9b257ce5bb80c356","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-08-15T21:40:41Z","title_canon_sha256":"d3a05cbd4533e8926c4bda43451933b0dc6cf33db8aef9b60867828b17b0cdca"},"schema_version":"1.0","source":{"id":"1908.05776","kind":"arxiv","version":4}},"canonical_sha256":"6680b065f5942202748e9a4cbd0651a6245b6bd69fad2687b0e917828e0ae48d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6680b065f5942202748e9a4cbd0651a6245b6bd69fad2687b0e917828e0ae48d","first_computed_at":"2026-07-05T01:59:09.480222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:59:09.480222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a29S4yVokI/xAA/eCMFgferBX6lF/uPH/QJTf406Ysm4ZQt2vavwdNl/VFEyMutPeVVj3hnqS2MKNLCN7ANgDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:59:09.480623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05776","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2cfa061260d3a596b77e41258a9f4ca3fc4834acb23bf80e54f3bc35af13c2d","sha256:933e25c11ea903d2b4582580349d1d806e147de806931b2853e542c5707c8b47"],"state_sha256":"faaf0287075a21c24346b66ae7e6e81ce81afea60684b78acafd50140e2a835d"}