{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XVOGUTRKDIYA4KGMHTZVG6Q25Z","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":"5760e5297c7d38c8e9dcb5d5f982e81bf4beaec00110293d268ad9230e05e8ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-02T18:51:58Z","title_canon_sha256":"cec06786de825daed1fede23c64429b921ef960d4ef74248eac7d72e266be55e"},"schema_version":"1.0","source":{"id":"1801.00770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00770","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00770v1","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00770","created_at":"2026-05-18T00:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"XVOGUTRKDIYA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XVOGUTRKDIYA4KGM","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XVOGUTRK","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:6ee83a07d3a5685aa9b10737d19ab62915b6cc8ec52cf4e552efae79bb0f606b","target":"graph","created_at":"2026-05-18T00:26:52Z","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 show that the set of not uniquely ergodic d-IETs has Hausdorff dimension d-3/2 (in the (d-1)-dimension space of d-IETs) for d>4. For d=4 this was shown by Athreya-Chaika and for d=2,3 the set is known to have dimension d-2.","authors_text":"Howard Masur, Jon Chaika","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-02T18:51:58Z","title":"The set of non-uniquely ergodic d-IETs has Hausdorff codimension 1/2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00770","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:f7ac61c3e0fcf6904e141322ff48356fa9342688500e693e2ed01e4b677a3536","target":"record","created_at":"2026-05-18T00:26:52Z","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":"5760e5297c7d38c8e9dcb5d5f982e81bf4beaec00110293d268ad9230e05e8ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-02T18:51:58Z","title_canon_sha256":"cec06786de825daed1fede23c64429b921ef960d4ef74248eac7d72e266be55e"},"schema_version":"1.0","source":{"id":"1801.00770","kind":"arxiv","version":1}},"canonical_sha256":"bd5c6a4e2a1a300e28cc3cf3537a1aee7ae42dfec526510a5ef9e63ee18c406a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd5c6a4e2a1a300e28cc3cf3537a1aee7ae42dfec526510a5ef9e63ee18c406a","first_computed_at":"2026-05-18T00:26:52.388741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:52.388741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNsIiKlgGZuKtfKMWrbSdR+aGUDn2PEZWv+LP4qr2LeA9LQCV19Qvm3nvvK8Eo257JIb7Tf+MfLUtWUPoU7eDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:52.389472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ac61c3e0fcf6904e141322ff48356fa9342688500e693e2ed01e4b677a3536","sha256:6ee83a07d3a5685aa9b10737d19ab62915b6cc8ec52cf4e552efae79bb0f606b"],"state_sha256":"74a908d7cfe34b92e7fee85938a02d37889a003d094c37cdfae44029fc678910"}