{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KE7Q4A2S7L23NHQL3GULMR3FWH","short_pith_number":"pith:KE7Q4A2S","schema_version":"1.0","canonical_sha256":"513f0e0352faf5b69e0bd9a8b64765b1d7abbc533a1520e18cd16dbc1c61d066","source":{"kind":"arxiv","id":"1404.4657","version":2},"attestation_state":"computed","paper":{"title":"The Hausdorff Dimension of Non-Uniquely Ergodic directions in $\\mathcal{H}(2)$ is almost everywhere $1/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jayadev S. Athreya, Jon Chaika","submitted_at":"2014-04-17T21:36:39Z","abstract_excerpt":"We show that for almost every (with respect to Masur-Veech measure) $\\omega \\in \\mathcal{H}(2)$, the set of angles $\\theta \\in [0, 2\\pi)$ so that $e^{i\\theta}\\omega$ has non-uniquely ergodic vertical foliation has Hausdorff dimension (and codimension) $1/2$."},"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":"1404.4657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-17T21:36:39Z","cross_cats_sorted":[],"title_canon_sha256":"0c63699dd5845fba19aeb40b0cfa32a18264b1ff8727b20d73f6a9002dc18bf8","abstract_canon_sha256":"8406da2c9d1c192c3b78e2645a40538920b0bd6ee7d50298b90af96559c63672"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:24.088224Z","signature_b64":"x1/aZ3aA66/m6KxD3GL8lBqIkrWV+8I3w93QUrAEFutyHZd8hMLlz/0atwFewnU9nnx1dLAQnnK5fYSgegsIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"513f0e0352faf5b69e0bd9a8b64765b1d7abbc533a1520e18cd16dbc1c61d066","last_reissued_at":"2026-05-18T01:22:24.087418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:24.087418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hausdorff Dimension of Non-Uniquely Ergodic directions in $\\mathcal{H}(2)$ is almost everywhere $1/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jayadev S. Athreya, Jon Chaika","submitted_at":"2014-04-17T21:36:39Z","abstract_excerpt":"We show that for almost every (with respect to Masur-Veech measure) $\\omega \\in \\mathcal{H}(2)$, the set of angles $\\theta \\in [0, 2\\pi)$ so that $e^{i\\theta}\\omega$ has non-uniquely ergodic vertical foliation has Hausdorff dimension (and codimension) $1/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4657","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":"1404.4657","created_at":"2026-05-18T01:22:24.087541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4657v2","created_at":"2026-05-18T01:22:24.087541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4657","created_at":"2026-05-18T01:22:24.087541+00:00"},{"alias_kind":"pith_short_12","alias_value":"KE7Q4A2S7L23","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KE7Q4A2S7L23NHQL","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KE7Q4A2S","created_at":"2026-05-18T12:28:35.611951+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/KE7Q4A2S7L23NHQL3GULMR3FWH","json":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH.json","graph_json":"https://pith.science/api/pith-number/KE7Q4A2S7L23NHQL3GULMR3FWH/graph.json","events_json":"https://pith.science/api/pith-number/KE7Q4A2S7L23NHQL3GULMR3FWH/events.json","paper":"https://pith.science/paper/KE7Q4A2S"},"agent_actions":{"view_html":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH","download_json":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH.json","view_paper":"https://pith.science/paper/KE7Q4A2S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4657&json=true","fetch_graph":"https://pith.science/api/pith-number/KE7Q4A2S7L23NHQL3GULMR3FWH/graph.json","fetch_events":"https://pith.science/api/pith-number/KE7Q4A2S7L23NHQL3GULMR3FWH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH/action/storage_attestation","attest_author":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH/action/author_attestation","sign_citation":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH/action/citation_signature","submit_replication":"https://pith.science/pith/KE7Q4A2S7L23NHQL3GULMR3FWH/action/replication_record"}},"created_at":"2026-05-18T01:22:24.087541+00:00","updated_at":"2026-05-18T01:22:24.087541+00:00"}