{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OV2NNSACGQ3UQMYGCM3Y6OPBNH","short_pith_number":"pith:OV2NNSAC","schema_version":"1.0","canonical_sha256":"7574d6c802343748330613378f39e169d5cf291739e90a4dc0a196ab6c88899c","source":{"kind":"arxiv","id":"1302.4091","version":2},"attestation_state":"computed","paper":{"title":"SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Artur Avila, Carlos Matheus, Jean-Christophe Yoccoz","submitted_at":"2013-02-17T17:14:01Z","abstract_excerpt":"In the moduli space $H_g$ of normalized translation surfaces of genus $g$, consider, for a small parameter $\\rho >0$, those translation surfaces which have two non-parallel saddle-connections of length $\\leq \\rho$. We prove that this subset of $H_g$ has measure $o(\\rho^2)$ w.r.t. any probability measure on $H_g$ which is invariant under the natural action of $SL(2,R)$. This implies that any such probability measure is regular, a property which is important in relation with the recent fundamental work of Eskin-Kontsevich-Zorich on the Lyapunov exponents of the KZ-cocycle."},"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":"1302.4091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-17T17:14:01Z","cross_cats_sorted":[],"title_canon_sha256":"4bdab2d636794e5e25a9cf8dd831b8088d57d5a0e498bbf3504fb840bad27106","abstract_canon_sha256":"4f7e6c20c57b2ceae235cb477ddb9890ef405d0c66c7ca4e6b8f933e9e24a5f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:35.681416Z","signature_b64":"B3P0Hv6lkt90ehTNSZbIFchy+rpd3qBKPaY8FQrmNOTOGh1LSgG8WHqQso7GhFQ24x5cHK9xrVXxmiuzexcwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7574d6c802343748330613378f39e169d5cf291739e90a4dc0a196ab6c88899c","last_reissued_at":"2026-05-18T03:05:35.681000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:35.681000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Artur Avila, Carlos Matheus, Jean-Christophe Yoccoz","submitted_at":"2013-02-17T17:14:01Z","abstract_excerpt":"In the moduli space $H_g$ of normalized translation surfaces of genus $g$, consider, for a small parameter $\\rho >0$, those translation surfaces which have two non-parallel saddle-connections of length $\\leq \\rho$. We prove that this subset of $H_g$ has measure $o(\\rho^2)$ w.r.t. any probability measure on $H_g$ which is invariant under the natural action of $SL(2,R)$. This implies that any such probability measure is regular, a property which is important in relation with the recent fundamental work of Eskin-Kontsevich-Zorich on the Lyapunov exponents of the KZ-cocycle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4091","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":"1302.4091","created_at":"2026-05-18T03:05:35.681058+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4091v2","created_at":"2026-05-18T03:05:35.681058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4091","created_at":"2026-05-18T03:05:35.681058+00:00"},{"alias_kind":"pith_short_12","alias_value":"OV2NNSACGQ3U","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OV2NNSACGQ3UQMYG","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OV2NNSAC","created_at":"2026-05-18T12:27:54.935989+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/OV2NNSACGQ3UQMYGCM3Y6OPBNH","json":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH.json","graph_json":"https://pith.science/api/pith-number/OV2NNSACGQ3UQMYGCM3Y6OPBNH/graph.json","events_json":"https://pith.science/api/pith-number/OV2NNSACGQ3UQMYGCM3Y6OPBNH/events.json","paper":"https://pith.science/paper/OV2NNSAC"},"agent_actions":{"view_html":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH","download_json":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH.json","view_paper":"https://pith.science/paper/OV2NNSAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4091&json=true","fetch_graph":"https://pith.science/api/pith-number/OV2NNSACGQ3UQMYGCM3Y6OPBNH/graph.json","fetch_events":"https://pith.science/api/pith-number/OV2NNSACGQ3UQMYGCM3Y6OPBNH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH/action/storage_attestation","attest_author":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH/action/author_attestation","sign_citation":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH/action/citation_signature","submit_replication":"https://pith.science/pith/OV2NNSACGQ3UQMYGCM3Y6OPBNH/action/replication_record"}},"created_at":"2026-05-18T03:05:35.681058+00:00","updated_at":"2026-05-18T03:05:35.681058+00:00"}