{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LDLBEITHNWMZQZRFNXKIGERDBK","short_pith_number":"pith:LDLBEITH","canonical_record":{"source":{"id":"1202.2162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-10T00:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"637848f78e6f1b949548f87509344fc3b67c4fc8628b291f4f33a638c83edd2b","abstract_canon_sha256":"62e7bba0777988c5d8e0cfeb1a04fbc2837ded2b24fb9ab331ee43c1d79c9dfd"},"schema_version":"1.0"},"canonical_sha256":"58d61222676d999866256dd48312230a9a8f9967ec98b44da6e441b028b45a53","source":{"kind":"arxiv","id":"1202.2162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2162","created_at":"2026-05-18T01:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2162v1","created_at":"2026-05-18T01:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2162","created_at":"2026-05-18T01:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"LDLBEITHNWMZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LDLBEITHNWMZQZRF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LDLBEITH","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LDLBEITHNWMZQZRFNXKIGERDBK","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-10T00:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"637848f78e6f1b949548f87509344fc3b67c4fc8628b291f4f33a638c83edd2b","abstract_canon_sha256":"62e7bba0777988c5d8e0cfeb1a04fbc2837ded2b24fb9ab331ee43c1d79c9dfd"},"schema_version":"1.0"},"canonical_sha256":"58d61222676d999866256dd48312230a9a8f9967ec98b44da6e441b028b45a53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:31.457814Z","signature_b64":"x+J9PtDwuACn20CqEOn6+dolsUXcGL7lk5jjxKoRC5wTseuIsoVhMZmFa4J3Bfo2AHKk48CBC4ud1cmo85HbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d61222676d999866256dd48312230a9a8f9967ec98b44da6e441b028b45a53","last_reissued_at":"2026-05-18T01:58:31.457262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:31.457262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2162","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03iMoRTPHFDUZMWLf2JrDKq7BwxtsNw7oUt5+XlbNQUOsDI6wrQLDvnFw6HiiGzV9J5cq45fSgs2QDfvkxq5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:31:52.689839Z"},"content_sha256":"e936f140eff0e831aba043809d0476db43da49cf1091020c41f799e2f0e3794b","schema_version":"1.0","event_id":"sha256:e936f140eff0e831aba043809d0476db43da49cf1091020c41f799e2f0e3794b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LDLBEITHNWMZQZRFNXKIGERDBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential speed of mixing for skew-products with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J. Vieitez, M. J. Pacifico, R. Markarian","submitted_at":"2012-02-10T00:41:45Z","abstract_excerpt":"Let $f: [0,1]\\times [0,1] \\setminus {1/2} \\to [0,1]\\times [0,1]$ be the $C^\\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2162","kind":"arxiv","version":1},"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":"2026-05-18T01:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aIqyYRTMVUY1Pao9B9Z4L9KPtDt71t8/uddklY/zqoGCVV1tNQnVhL0n90ZwIy+M8/T1cMbv31SeBAqTBQu9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:31:52.690618Z"},"content_sha256":"cace2ea83acd48b1a66f7c6adea1db71d528332354565f7a22de32df3070121a","schema_version":"1.0","event_id":"sha256:cace2ea83acd48b1a66f7c6adea1db71d528332354565f7a22de32df3070121a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDLBEITHNWMZQZRFNXKIGERDBK/bundle.json","state_url":"https://pith.science/pith/LDLBEITHNWMZQZRFNXKIGERDBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDLBEITHNWMZQZRFNXKIGERDBK/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":"2026-06-01T06:31:52Z","links":{"resolver":"https://pith.science/pith/LDLBEITHNWMZQZRFNXKIGERDBK","bundle":"https://pith.science/pith/LDLBEITHNWMZQZRFNXKIGERDBK/bundle.json","state":"https://pith.science/pith/LDLBEITHNWMZQZRFNXKIGERDBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDLBEITHNWMZQZRFNXKIGERDBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LDLBEITHNWMZQZRFNXKIGERDBK","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":"62e7bba0777988c5d8e0cfeb1a04fbc2837ded2b24fb9ab331ee43c1d79c9dfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-10T00:41:45Z","title_canon_sha256":"637848f78e6f1b949548f87509344fc3b67c4fc8628b291f4f33a638c83edd2b"},"schema_version":"1.0","source":{"id":"1202.2162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2162","created_at":"2026-05-18T01:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2162v1","created_at":"2026-05-18T01:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2162","created_at":"2026-05-18T01:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"LDLBEITHNWMZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LDLBEITHNWMZQZRF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LDLBEITH","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:cace2ea83acd48b1a66f7c6adea1db71d528332354565f7a22de32df3070121a","target":"graph","created_at":"2026-05-18T01:58:31Z","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":"Let $f: [0,1]\\times [0,1] \\setminus {1/2} \\to [0,1]\\times [0,1]$ be the $C^\\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.","authors_text":"J. Vieitez, M. J. Pacifico, R. Markarian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-10T00:41:45Z","title":"Exponential speed of mixing for skew-products with singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2162","kind":"arxiv","version":1},"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:e936f140eff0e831aba043809d0476db43da49cf1091020c41f799e2f0e3794b","target":"record","created_at":"2026-05-18T01:58:31Z","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":"62e7bba0777988c5d8e0cfeb1a04fbc2837ded2b24fb9ab331ee43c1d79c9dfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-10T00:41:45Z","title_canon_sha256":"637848f78e6f1b949548f87509344fc3b67c4fc8628b291f4f33a638c83edd2b"},"schema_version":"1.0","source":{"id":"1202.2162","kind":"arxiv","version":1}},"canonical_sha256":"58d61222676d999866256dd48312230a9a8f9967ec98b44da6e441b028b45a53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58d61222676d999866256dd48312230a9a8f9967ec98b44da6e441b028b45a53","first_computed_at":"2026-05-18T01:58:31.457262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:31.457262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+J9PtDwuACn20CqEOn6+dolsUXcGL7lk5jjxKoRC5wTseuIsoVhMZmFa4J3Bfo2AHKk48CBC4ud1cmo85HbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:31.457814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e936f140eff0e831aba043809d0476db43da49cf1091020c41f799e2f0e3794b","sha256:cace2ea83acd48b1a66f7c6adea1db71d528332354565f7a22de32df3070121a"],"state_sha256":"5a3ef2adb83148d94de9009ac0538d3e1a462caa823ea81ec341b7efc0e3b32a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzrAGkRTYwqSVAlxD4sJLAIkLHGuTIzgQ9pOYxXerCAyb/44AS0wuMZZuU1ghOQ5la7qww1cYd3eRo3CVglrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:31:52.694260Z","bundle_sha256":"88b6cbe772ad11cf9b3fe3c79d053742bbb538265a887908e665f334bd454fa6"}}