{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3DRJRIXJAN6H4E2627FEIK53UH","short_pith_number":"pith:3DRJRIXJ","canonical_record":{"source":{"id":"1701.05253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-18T22:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"40c9c90a6bbe4acec435e5080ab4e248e73e0eff62f55082cfe74605e0049a14","abstract_canon_sha256":"1dbb01e9aa1d1d9174c2bd1239cf3d70ad33febd5328c781a932842bebfa2047"},"schema_version":"1.0"},"canonical_sha256":"d8e298a2e9037c7e135ed7ca442bbba1f1950fe7bed4d4cf76b1061c4c0ed3d6","source":{"kind":"arxiv","id":"1701.05253","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05253","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05253v3","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05253","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"3DRJRIXJAN6H","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3DRJRIXJAN6H4E26","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3DRJRIXJ","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3DRJRIXJAN6H4E2627FEIK53UH","target":"record","payload":{"canonical_record":{"source":{"id":"1701.05253","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-18T22:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"40c9c90a6bbe4acec435e5080ab4e248e73e0eff62f55082cfe74605e0049a14","abstract_canon_sha256":"1dbb01e9aa1d1d9174c2bd1239cf3d70ad33febd5328c781a932842bebfa2047"},"schema_version":"1.0"},"canonical_sha256":"d8e298a2e9037c7e135ed7ca442bbba1f1950fe7bed4d4cf76b1061c4c0ed3d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:14.746091Z","signature_b64":"PuZMP/+ZlDBaP9k8CD/kkuSnVzxKtzgZLxVJWB3ExWBIGaegT99BCefnqme7RiVnXFI81cAbt26nIQ/fpid0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8e298a2e9037c7e135ed7ca442bbba1f1950fe7bed4d4cf76b1061c4c0ed3d6","last_reissued_at":"2026-05-18T00:21:14.745702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:14.745702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.05253","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":"2026-05-18T00:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NinYw5S+uZ40mPEmmZ4Xmvs3BDErBFc1/HArUuT43LHflntxZGnszbNqQtwDIpOsjicfK6cAQVVjhU0zYCTBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:47:57.682114Z"},"content_sha256":"4a51e3b9330e4be3db2ed6327f6f13e0fb31113ea516b1a36bedb1b4e697f285","schema_version":"1.0","event_id":"sha256:4a51e3b9330e4be3db2ed6327f6f13e0fb31113ea516b1a36bedb1b4e697f285"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3DRJRIXJAN6H4E2627FEIK53UH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the smooth dependence of SRB measures for partially hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhiyuan Zhang","submitted_at":"2017-01-18T22:47:48Z","abstract_excerpt":"In this paper, we study the differentiability of SRB measures for partially hyperbolic systems. We show that for any $s \\geq 1$, for any integer $\\ell \\geq 2$, any sufficiently large $r$, any $\\varphi \\in C^{r}(\\T, \\R)$ such that the map $f : \\T^2 \\to \\T^2, f(x,y) = (\\ell x, y + \\varphi(x))$ is $C^r-$stably ergodic, there exists an open neighbourhood of $f$ in $C^r(\\T^2,\\T^2)$ such that any map in this neighbourhood has a unique SRB measure with $C^{s-1}$ density, which depends on the dynamics in a $C^s$ fashion. We also construct a $C^{\\infty}$ mostly contracting partially hyperbolic diffeomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05253","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":"2026-05-18T00:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUG/bxnpAbkSmyYNcypnnwV2RrJW8Wi499unkjh/yObNaexr7Du0reBmqMXoR/h5qD9zXA4qjSTmHuLH4RJrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:47:57.682754Z"},"content_sha256":"8a8e1893d0b29f99aea99ee8e997183c8ed1753ff35017def3164a221ebc0d1a","schema_version":"1.0","event_id":"sha256:8a8e1893d0b29f99aea99ee8e997183c8ed1753ff35017def3164a221ebc0d1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DRJRIXJAN6H4E2627FEIK53UH/bundle.json","state_url":"https://pith.science/pith/3DRJRIXJAN6H4E2627FEIK53UH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DRJRIXJAN6H4E2627FEIK53UH/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":"2026-06-07T20:47:57Z","links":{"resolver":"https://pith.science/pith/3DRJRIXJAN6H4E2627FEIK53UH","bundle":"https://pith.science/pith/3DRJRIXJAN6H4E2627FEIK53UH/bundle.json","state":"https://pith.science/pith/3DRJRIXJAN6H4E2627FEIK53UH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DRJRIXJAN6H4E2627FEIK53UH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3DRJRIXJAN6H4E2627FEIK53UH","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":"1dbb01e9aa1d1d9174c2bd1239cf3d70ad33febd5328c781a932842bebfa2047","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-18T22:47:48Z","title_canon_sha256":"40c9c90a6bbe4acec435e5080ab4e248e73e0eff62f55082cfe74605e0049a14"},"schema_version":"1.0","source":{"id":"1701.05253","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05253","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05253v3","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05253","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"3DRJRIXJAN6H","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3DRJRIXJAN6H4E26","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3DRJRIXJ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:8a8e1893d0b29f99aea99ee8e997183c8ed1753ff35017def3164a221ebc0d1a","target":"graph","created_at":"2026-05-18T00:21:14Z","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":"In this paper, we study the differentiability of SRB measures for partially hyperbolic systems. We show that for any $s \\geq 1$, for any integer $\\ell \\geq 2$, any sufficiently large $r$, any $\\varphi \\in C^{r}(\\T, \\R)$ such that the map $f : \\T^2 \\to \\T^2, f(x,y) = (\\ell x, y + \\varphi(x))$ is $C^r-$stably ergodic, there exists an open neighbourhood of $f$ in $C^r(\\T^2,\\T^2)$ such that any map in this neighbourhood has a unique SRB measure with $C^{s-1}$ density, which depends on the dynamics in a $C^s$ fashion. We also construct a $C^{\\infty}$ mostly contracting partially hyperbolic diffeomo","authors_text":"Zhiyuan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-18T22:47:48Z","title":"On the smooth dependence of SRB measures for partially hyperbolic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05253","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":"sha256:4a51e3b9330e4be3db2ed6327f6f13e0fb31113ea516b1a36bedb1b4e697f285","target":"record","created_at":"2026-05-18T00:21:14Z","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":"1dbb01e9aa1d1d9174c2bd1239cf3d70ad33febd5328c781a932842bebfa2047","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-18T22:47:48Z","title_canon_sha256":"40c9c90a6bbe4acec435e5080ab4e248e73e0eff62f55082cfe74605e0049a14"},"schema_version":"1.0","source":{"id":"1701.05253","kind":"arxiv","version":3}},"canonical_sha256":"d8e298a2e9037c7e135ed7ca442bbba1f1950fe7bed4d4cf76b1061c4c0ed3d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8e298a2e9037c7e135ed7ca442bbba1f1950fe7bed4d4cf76b1061c4c0ed3d6","first_computed_at":"2026-05-18T00:21:14.745702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:14.745702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PuZMP/+ZlDBaP9k8CD/kkuSnVzxKtzgZLxVJWB3ExWBIGaegT99BCefnqme7RiVnXFI81cAbt26nIQ/fpid0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:14.746091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05253","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a51e3b9330e4be3db2ed6327f6f13e0fb31113ea516b1a36bedb1b4e697f285","sha256:8a8e1893d0b29f99aea99ee8e997183c8ed1753ff35017def3164a221ebc0d1a"],"state_sha256":"733ae90b44e636746384c2ee5c062d9cad17408e01b99bef28bf2c8893b506c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zBBgAmT2inRPcBCUp24G1mV0NlyS34DfJiK9tW+mohW1BmEWfFK4tPVGVz7WZUuRfjHV95JtbcX+0uIT9TVlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:47:57.686632Z","bundle_sha256":"b67ae7ecdd9b9aaa5f1395248c65c0508c72df35cd6fc3aad6a7e4ac2ba51db8"}}