{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:54X2L4FXCRDQO45TUNT2236Y46","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":"b72e952c410fbc84344f6182cc8956f62ab4919518c32329f102fa92849cdaf2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-05-29T01:06:06Z","title_canon_sha256":"301f576cddde769d54b3e6e8d620dc9e26a0b5f3100174f71e25e536b0a0a0cb"},"schema_version":"1.0","source":{"id":"0705.4125","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.4125","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"0705.4125v3","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.4125","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"54X2L4FXCRDQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"54X2L4FXCRDQO45T","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"54X2L4FX","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:b411cdb43a5ff8931b4cd9b5f69bea12ea181b7603fb9b7aa586d43862774251","target":"graph","created_at":"2026-05-18T04:42:23Z","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":"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","authors_text":"N. Chernov, N. Simanyi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-05-29T01:06:06Z","title":"Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4125","kind":"arxiv","version":3},"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":"sha256:04208a75800cf7f46af0b165dd172a7acaa8209be233759bddfbcf6b284f0944","target":"record","created_at":"2026-05-18T04:42:23Z","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":"b72e952c410fbc84344f6182cc8956f62ab4919518c32329f102fa92849cdaf2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-05-29T01:06:06Z","title_canon_sha256":"301f576cddde769d54b3e6e8d620dc9e26a0b5f3100174f71e25e536b0a0a0cb"},"schema_version":"1.0","source":{"id":"0705.4125","kind":"arxiv","version":3}},"canonical_sha256":"ef2fa5f0b714470773b3a367ad6fd8e780c4d6ccbec0d4879f8d4d10dc394b36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef2fa5f0b714470773b3a367ad6fd8e780c4d6ccbec0d4879f8d4d10dc394b36","first_computed_at":"2026-05-18T04:42:23.282803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:23.282803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SYjkZFDhk5MuPg7LcwVg1fcpFmFgYsvizUyHHaGYRRcsKV4WOzmrGQ83aknZCv+PyKmXUYP5BqMqe5z467BjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:23.283485Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.4125","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04208a75800cf7f46af0b165dd172a7acaa8209be233759bddfbcf6b284f0944","sha256:b411cdb43a5ff8931b4cd9b5f69bea12ea181b7603fb9b7aa586d43862774251"],"state_sha256":"e22eb35723cbee6c7743faa34b07388e740ea41ce735e602dfd0d64c35eaf558"}