{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:54X2L4FXCRDQO45TUNT2236Y46","short_pith_number":"pith:54X2L4FX","schema_version":"1.0","canonical_sha256":"ef2fa5f0b714470773b3a367ad6fd8e780c4d6ccbec0d4879f8d4d10dc394b36","source":{"kind":"arxiv","id":"0705.4125","version":3},"attestation_state":"computed","paper":{"title":"Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"N. Chernov, N. Simanyi","submitted_at":"2007-05-29T01:06:06Z","abstract_excerpt":"The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional bill"},"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":"0705.4125","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-05-29T01:06:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"301f576cddde769d54b3e6e8d620dc9e26a0b5f3100174f71e25e536b0a0a0cb","abstract_canon_sha256":"b72e952c410fbc84344f6182cc8956f62ab4919518c32329f102fa92849cdaf2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:23.283485Z","signature_b64":"SYjkZFDhk5MuPg7LcwVg1fcpFmFgYsvizUyHHaGYRRcsKV4WOzmrGQ83aknZCv+PyKmXUYP5BqMqe5z467BjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef2fa5f0b714470773b3a367ad6fd8e780c4d6ccbec0d4879f8d4d10dc394b36","last_reissued_at":"2026-05-18T04:42:23.282803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:23.282803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"N. Chernov, N. Simanyi","submitted_at":"2007-05-29T01:06:06Z","abstract_excerpt":"The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional bill"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4125","kind":"arxiv","version":3},"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":"0705.4125","created_at":"2026-05-18T04:42:23.282887+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.4125v3","created_at":"2026-05-18T04:42:23.282887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.4125","created_at":"2026-05-18T04:42:23.282887+00:00"},{"alias_kind":"pith_short_12","alias_value":"54X2L4FXCRDQ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"54X2L4FXCRDQO45T","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"54X2L4FX","created_at":"2026-05-18T12:25:55.427421+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/54X2L4FXCRDQO45TUNT2236Y46","json":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46.json","graph_json":"https://pith.science/api/pith-number/54X2L4FXCRDQO45TUNT2236Y46/graph.json","events_json":"https://pith.science/api/pith-number/54X2L4FXCRDQO45TUNT2236Y46/events.json","paper":"https://pith.science/paper/54X2L4FX"},"agent_actions":{"view_html":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46","download_json":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46.json","view_paper":"https://pith.science/paper/54X2L4FX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.4125&json=true","fetch_graph":"https://pith.science/api/pith-number/54X2L4FXCRDQO45TUNT2236Y46/graph.json","fetch_events":"https://pith.science/api/pith-number/54X2L4FXCRDQO45TUNT2236Y46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46/action/storage_attestation","attest_author":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46/action/author_attestation","sign_citation":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46/action/citation_signature","submit_replication":"https://pith.science/pith/54X2L4FXCRDQO45TUNT2236Y46/action/replication_record"}},"created_at":"2026-05-18T04:42:23.282887+00:00","updated_at":"2026-05-18T04:42:23.282887+00:00"}