{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BYJTVLJADDZ6YZBP6TD42IV6ZS","short_pith_number":"pith:BYJTVLJA","canonical_record":{"source":{"id":"1103.6110","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-31T07:26:11Z","cross_cats_sorted":[],"title_canon_sha256":"af3685a572b10b28bd775653476cdaec3bc6843408d472a6ed2fb63c0961f6ce","abstract_canon_sha256":"2a5d1f8c2800db3ba21c9019dffc7f0ee1e9520365ca3187c9c1b0802ced845c"},"schema_version":"1.0"},"canonical_sha256":"0e133aad2018f3ec642ff4c7cd22becc92c91895f1be97eb4227590cab88e735","source":{"kind":"arxiv","id":"1103.6110","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6110","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6110v3","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6110","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"BYJTVLJADDZ6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BYJTVLJADDZ6YZBP","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BYJTVLJA","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BYJTVLJADDZ6YZBP6TD42IV6ZS","target":"record","payload":{"canonical_record":{"source":{"id":"1103.6110","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-31T07:26:11Z","cross_cats_sorted":[],"title_canon_sha256":"af3685a572b10b28bd775653476cdaec3bc6843408d472a6ed2fb63c0961f6ce","abstract_canon_sha256":"2a5d1f8c2800db3ba21c9019dffc7f0ee1e9520365ca3187c9c1b0802ced845c"},"schema_version":"1.0"},"canonical_sha256":"0e133aad2018f3ec642ff4c7cd22becc92c91895f1be97eb4227590cab88e735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:03.656530Z","signature_b64":"gbtkaerhB6Mncz+InXylxTrU7IvwTQnLioO4ipnpoEM7HeA2CKcEmggOzEBt4uYZLOr9c7xN04iyIdIMYtXbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e133aad2018f3ec642ff4c7cd22becc92c91895f1be97eb4227590cab88e735","last_reissued_at":"2026-05-18T03:34:03.655918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:03.655918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.6110","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mcZM3CxsmdfjMg1ZM+47BOQhroz4lqwLmVOWufHF0Uo4Dkzb/MyKWYhpfVrHbLYpxRoEn2g8tgi4AziH5BJnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:52:33.069790Z"},"content_sha256":"e8f09486794b68fe6828bc098f7ae457fd39f19f2b5f6885a97095b2aea12dc7","schema_version":"1.0","event_id":"sha256:e8f09486794b68fe6828bc098f7ae457fd39f19f2b5f6885a97095b2aea12dc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BYJTVLJADDZ6YZBP6TD42IV6ZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"CPT, IML), Marco Lenci, Serge Troubetzkoy (FRUMAM","submitted_at":"2011-03-31T07:26:11Z","abstract_excerpt":"We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincar\\'e) recurrent, uniformly hyperbolic, ergodic, and the first-return map to any scatterer is $K$-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (\\emph{ensembles}) for which the above properties occur with probability 1. In the case of the Lorentz gases in the plane, we define families, endowed with a natural metric, within which the set of all chaotic dynamical systems is unco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6110","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evkwP7bIb85Ufb0iQPQgaKB3CfBiZb/HahWpu/8B7HkwKHrLUZUxQBEP27DbjrIqKesw4LzOSyk1/p0e0sRMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:52:33.070455Z"},"content_sha256":"5cf3f91fa00386e1049b0f4983f7042bf50b24d24aacb1c53430bc8b1143c06f","schema_version":"1.0","event_id":"sha256:5cf3f91fa00386e1049b0f4983f7042bf50b24d24aacb1c53430bc8b1143c06f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS/bundle.json","state_url":"https://pith.science/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T06:52:33Z","links":{"resolver":"https://pith.science/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS","bundle":"https://pith.science/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS/bundle.json","state":"https://pith.science/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYJTVLJADDZ6YZBP6TD42IV6ZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BYJTVLJADDZ6YZBP6TD42IV6ZS","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":"2a5d1f8c2800db3ba21c9019dffc7f0ee1e9520365ca3187c9c1b0802ced845c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-31T07:26:11Z","title_canon_sha256":"af3685a572b10b28bd775653476cdaec3bc6843408d472a6ed2fb63c0961f6ce"},"schema_version":"1.0","source":{"id":"1103.6110","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6110","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6110v3","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6110","created_at":"2026-05-18T03:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"BYJTVLJADDZ6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BYJTVLJADDZ6YZBP","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BYJTVLJA","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:5cf3f91fa00386e1049b0f4983f7042bf50b24d24aacb1c53430bc8b1143c06f","target":"graph","created_at":"2026-05-18T03:34:03Z","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 construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincar\\'e) recurrent, uniformly hyperbolic, ergodic, and the first-return map to any scatterer is $K$-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (\\emph{ensembles}) for which the above properties occur with probability 1. In the case of the Lorentz gases in the plane, we define families, endowed with a natural metric, within which the set of all chaotic dynamical systems is unco","authors_text":"CPT, IML), Marco Lenci, Serge Troubetzkoy (FRUMAM","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-31T07:26:11Z","title":"Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6110","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:e8f09486794b68fe6828bc098f7ae457fd39f19f2b5f6885a97095b2aea12dc7","target":"record","created_at":"2026-05-18T03:34:03Z","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":"2a5d1f8c2800db3ba21c9019dffc7f0ee1e9520365ca3187c9c1b0802ced845c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-31T07:26:11Z","title_canon_sha256":"af3685a572b10b28bd775653476cdaec3bc6843408d472a6ed2fb63c0961f6ce"},"schema_version":"1.0","source":{"id":"1103.6110","kind":"arxiv","version":3}},"canonical_sha256":"0e133aad2018f3ec642ff4c7cd22becc92c91895f1be97eb4227590cab88e735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e133aad2018f3ec642ff4c7cd22becc92c91895f1be97eb4227590cab88e735","first_computed_at":"2026-05-18T03:34:03.655918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:03.655918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gbtkaerhB6Mncz+InXylxTrU7IvwTQnLioO4ipnpoEM7HeA2CKcEmggOzEBt4uYZLOr9c7xN04iyIdIMYtXbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:03.656530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.6110","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8f09486794b68fe6828bc098f7ae457fd39f19f2b5f6885a97095b2aea12dc7","sha256:5cf3f91fa00386e1049b0f4983f7042bf50b24d24aacb1c53430bc8b1143c06f"],"state_sha256":"a99f0f7fd19d9023e3753e1db4d4713a95d4bfab8d43ecf2ee57df1fa3130da7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LqfBGgX3ykZtDgogTj94chBAP62VFD73a2pepwN0SZRiQhKtfwkcJuw46fGS2FuM8Jjl9outYeVTRYVZmeXhAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:52:33.073875Z","bundle_sha256":"a2e63959c7b7e5205479328a7354be8ef34c0324ff4171fc688598c707036a52"}}