{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PJGOHGGPVHNTEHNNLDLRFH6J4R","short_pith_number":"pith:PJGOHGGP","canonical_record":{"source":{"id":"1405.6981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-27T17:24:32Z","cross_cats_sorted":[],"title_canon_sha256":"30e41735eebe516655cb9c22e8da3e6793153135654f626f86118ecdff93e1e5","abstract_canon_sha256":"5282676b0000eb82912a98dc20deedcfba69401c71fd8875c23d783edf6823e5"},"schema_version":"1.0"},"canonical_sha256":"7a4ce398cfa9db321dad58d7129fc9e44895652b28ac5d22f5262568cce6d3dd","source":{"kind":"arxiv","id":"1405.6981","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6981","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6981v1","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6981","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"PJGOHGGPVHNT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJGOHGGPVHNTEHNN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJGOHGGP","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PJGOHGGPVHNTEHNNLDLRFH6J4R","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-27T17:24:32Z","cross_cats_sorted":[],"title_canon_sha256":"30e41735eebe516655cb9c22e8da3e6793153135654f626f86118ecdff93e1e5","abstract_canon_sha256":"5282676b0000eb82912a98dc20deedcfba69401c71fd8875c23d783edf6823e5"},"schema_version":"1.0"},"canonical_sha256":"7a4ce398cfa9db321dad58d7129fc9e44895652b28ac5d22f5262568cce6d3dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:15.584362Z","signature_b64":"3/EBFoR7e83JVUxomKdmum/NRmf4+X88QBg43egB4zVSjgtS5LGrs92zVX71gVMbAp2ymHn3S69c56ibjpF9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4ce398cfa9db321dad58d7129fc9e44895652b28ac5d22f5262568cce6d3dd","last_reissued_at":"2026-05-18T01:36:15.583827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:15.583827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6981","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":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mq/YKKUlZHJSiK6Zrd1uQF4dq6EqA/KGRV5vHDUJHbl7ovEmn3DVgP7sJqybzNDaGIzh/HuKdTFEAqlhdn4kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:47:23.785158Z"},"content_sha256":"81c352e513729638cf1419ce1170973bf7735b902ab084993862521cfda46dc0","schema_version":"1.0","event_id":"sha256:81c352e513729638cf1419ce1170973bf7735b902ab084993862521cfda46dc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PJGOHGGPVHNTEHNNLDLRFH6J4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stretched-exponential mixing for $\\mathscr{C}^{1+\\alpha}$ skew products with discontinuities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Peyman Eslami","submitted_at":"2014-05-27T17:24:32Z","abstract_excerpt":"Consider the skew product $F:\\mathbb{T}^2 \\to \\mathbb{T}^2$, $F(x,y)= (f(x),y+\\tau(x))$, where $f:\\mathbb{T}^1\\to \\mathbb{T}^1$ is a piecewise $\\mathscr{C}^{1+\\alpha}$ expanding map on a countable partition and $\\tau:\\mathbb{T}^1 \\to \\mathbb{R}$ is piecewise $\\mathscr{C}^1$. It is shown that if $\\tau$ is not Lipschitz-cohomologous to a piecewise constant function on the joint partition of $\\tau$ and $f$, then $F$ is mixing at a stretched-exponential rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6981","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":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUjQwq1ELI8Y/PpI6X2EvsAccnTrj/0o04WxtaLzdQGyH7gRp8IIkH6uWsirX/7712G/0ldg8c/1eJjxCVe2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:47:23.785519Z"},"content_sha256":"4a19fd512ee27a8c0af2e88c9e44bd36625b01e2c283b5608496e79d8079307c","schema_version":"1.0","event_id":"sha256:4a19fd512ee27a8c0af2e88c9e44bd36625b01e2c283b5608496e79d8079307c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R/bundle.json","state_url":"https://pith.science/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R/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":"2026-06-24T01:47:23Z","links":{"resolver":"https://pith.science/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R","bundle":"https://pith.science/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R/bundle.json","state":"https://pith.science/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJGOHGGPVHNTEHNNLDLRFH6J4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PJGOHGGPVHNTEHNNLDLRFH6J4R","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":"5282676b0000eb82912a98dc20deedcfba69401c71fd8875c23d783edf6823e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-27T17:24:32Z","title_canon_sha256":"30e41735eebe516655cb9c22e8da3e6793153135654f626f86118ecdff93e1e5"},"schema_version":"1.0","source":{"id":"1405.6981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6981","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6981v1","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6981","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"PJGOHGGPVHNT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJGOHGGPVHNTEHNN","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJGOHGGP","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:4a19fd512ee27a8c0af2e88c9e44bd36625b01e2c283b5608496e79d8079307c","target":"graph","created_at":"2026-05-18T01:36:15Z","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":"Consider the skew product $F:\\mathbb{T}^2 \\to \\mathbb{T}^2$, $F(x,y)= (f(x),y+\\tau(x))$, where $f:\\mathbb{T}^1\\to \\mathbb{T}^1$ is a piecewise $\\mathscr{C}^{1+\\alpha}$ expanding map on a countable partition and $\\tau:\\mathbb{T}^1 \\to \\mathbb{R}$ is piecewise $\\mathscr{C}^1$. It is shown that if $\\tau$ is not Lipschitz-cohomologous to a piecewise constant function on the joint partition of $\\tau$ and $f$, then $F$ is mixing at a stretched-exponential rate.","authors_text":"Peyman Eslami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-27T17:24:32Z","title":"Stretched-exponential mixing for $\\mathscr{C}^{1+\\alpha}$ skew products with discontinuities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6981","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":"sha256:81c352e513729638cf1419ce1170973bf7735b902ab084993862521cfda46dc0","target":"record","created_at":"2026-05-18T01:36:15Z","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":"5282676b0000eb82912a98dc20deedcfba69401c71fd8875c23d783edf6823e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-27T17:24:32Z","title_canon_sha256":"30e41735eebe516655cb9c22e8da3e6793153135654f626f86118ecdff93e1e5"},"schema_version":"1.0","source":{"id":"1405.6981","kind":"arxiv","version":1}},"canonical_sha256":"7a4ce398cfa9db321dad58d7129fc9e44895652b28ac5d22f5262568cce6d3dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4ce398cfa9db321dad58d7129fc9e44895652b28ac5d22f5262568cce6d3dd","first_computed_at":"2026-05-18T01:36:15.583827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:15.583827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3/EBFoR7e83JVUxomKdmum/NRmf4+X88QBg43egB4zVSjgtS5LGrs92zVX71gVMbAp2ymHn3S69c56ibjpF9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:15.584362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81c352e513729638cf1419ce1170973bf7735b902ab084993862521cfda46dc0","sha256:4a19fd512ee27a8c0af2e88c9e44bd36625b01e2c283b5608496e79d8079307c"],"state_sha256":"60923c39d3213928370b7c1ad5c4964b814b70d81292a66bde1236bc1458eb2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BF/F6KXhFi5aqBg4OLgkcwNyE1yZaNJd+6QzRoy7x9TJItn2E/319I1dgOEiqNgNNEit7/xSENOVAssaq15QBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T01:47:23.787415Z","bundle_sha256":"6a91cf5596eb538e46732cd3d38ad09a3742e1abff880dafd2c8859b21a00501"}}