{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WNYOM6UKD4FWWJVT4V4VDFVNKA","short_pith_number":"pith:WNYOM6UK","canonical_record":{"source":{"id":"1603.09690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-31T17:20:02Z","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"title_canon_sha256":"f414fbd3d2ce1a1a4d3120220ed6fabad01ab9a54aa680c007e13f51816825ca","abstract_canon_sha256":"c821bd736d79e1bbac1d4f1c323fd00c2d4b0966fa33a43fe695b5472cd7d88e"},"schema_version":"1.0"},"canonical_sha256":"b370e67a8a1f0b6b26b3e5795196ad503881e5f9d9e06cd7713d050bd3126fa6","source":{"kind":"arxiv","id":"1603.09690","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09690","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09690v3","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09690","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"WNYOM6UKD4FW","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WNYOM6UKD4FWWJVT","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WNYOM6UK","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WNYOM6UKD4FWWJVT4V4VDFVNKA","target":"record","payload":{"canonical_record":{"source":{"id":"1603.09690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-31T17:20:02Z","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"title_canon_sha256":"f414fbd3d2ce1a1a4d3120220ed6fabad01ab9a54aa680c007e13f51816825ca","abstract_canon_sha256":"c821bd736d79e1bbac1d4f1c323fd00c2d4b0966fa33a43fe695b5472cd7d88e"},"schema_version":"1.0"},"canonical_sha256":"b370e67a8a1f0b6b26b3e5795196ad503881e5f9d9e06cd7713d050bd3126fa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:58.462641Z","signature_b64":"8EY29YfeHi/lqaKAnFRWmv7t923zMfZoY4QodGLGwh/d/rWNMe/nVPLWdrf//9DY29dD6VzSXGB2UKds25CIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b370e67a8a1f0b6b26b3e5795196ad503881e5f9d9e06cd7713d050bd3126fa6","last_reissued_at":"2026-05-18T00:41:58.462057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:58.462057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.09690","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":"2026-05-18T00:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q65CwEPRvtPize24a+WYYXn+lEnbdd/u+jIoEL7mUd00RKd6gffRyhjQbVbJMOEr+FOCi13l4Cqd8ZnTdGmMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:38:43.949017Z"},"content_sha256":"31e2641941f0a2126b93494ca59613ebcfff3e0db4cedc52ed93ed6fd0cda3aa","schema_version":"1.0","event_id":"sha256:31e2641941f0a2126b93494ca59613ebcfff3e0db4cedc52ed93ed6fd0cda3aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WNYOM6UKD4FWWJVT4V4VDFVNKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CD"],"primary_cat":"math.DS","authors_text":"Tobias Kuna, Valerio Lucarini, Viviane Baladi","submitted_at":"2016-03-31T17:20:02Z","abstract_excerpt":"We consider a smooth one-parameter family $t \\to f_t$ of diffeomorphisms with compact transitive Axiom A attractors. Our first result (corrected) is that for any function $G$ in the Sobolev space $H^r_p$, with $p>1$ and $0<r<1/p$, the map $R(t)$ sending $t$ to the average of $G$ with respect to the SRB measure of $f_t$ is $\\alpha$-H\\\"older continuous for all $\\alpha <r- |log \\mathcal J|/(p|log \\nu_s|$) where $\\mathcal J\\le 1$ is the strongest volume contraction and $\\nu_s<1$ is the weakest contraction. This applies to $\\theta(x)=h(x)\\Theta(g(x)-a)$ (for all $\\alpha <1- |log \\mathcal J|/|log \\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09690","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":"2026-05-18T00:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ThQLmrKeT5xTalRj4LTvnuJRLs4kB080Xnu0CWeym3a1Iykp6BtTQLRTwRvYra7hlBJgCrmRL/Be3SIblxoUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:38:43.949686Z"},"content_sha256":"f9ad0e7dc9d256a665ee9639871f9cb779ff014a0a78bb2e0430eb8946f20559","schema_version":"1.0","event_id":"sha256:f9ad0e7dc9d256a665ee9639871f9cb779ff014a0a78bb2e0430eb8946f20559"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA/bundle.json","state_url":"https://pith.science/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA/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":"2026-06-06T20:38:43Z","links":{"resolver":"https://pith.science/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA","bundle":"https://pith.science/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA/bundle.json","state":"https://pith.science/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNYOM6UKD4FWWJVT4V4VDFVNKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WNYOM6UKD4FWWJVT4V4VDFVNKA","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":"c821bd736d79e1bbac1d4f1c323fd00c2d4b0966fa33a43fe695b5472cd7d88e","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-31T17:20:02Z","title_canon_sha256":"f414fbd3d2ce1a1a4d3120220ed6fabad01ab9a54aa680c007e13f51816825ca"},"schema_version":"1.0","source":{"id":"1603.09690","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09690","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09690v3","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09690","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"WNYOM6UKD4FW","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WNYOM6UKD4FWWJVT","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WNYOM6UK","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:f9ad0e7dc9d256a665ee9639871f9cb779ff014a0a78bb2e0430eb8946f20559","target":"graph","created_at":"2026-05-18T00:41:58Z","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 consider a smooth one-parameter family $t \\to f_t$ of diffeomorphisms with compact transitive Axiom A attractors. Our first result (corrected) is that for any function $G$ in the Sobolev space $H^r_p$, with $p>1$ and $0<r<1/p$, the map $R(t)$ sending $t$ to the average of $G$ with respect to the SRB measure of $f_t$ is $\\alpha$-H\\\"older continuous for all $\\alpha <r- |log \\mathcal J|/(p|log \\nu_s|$) where $\\mathcal J\\le 1$ is the strongest volume contraction and $\\nu_s<1$ is the weakest contraction. This applies to $\\theta(x)=h(x)\\Theta(g(x)-a)$ (for all $\\alpha <1- |log \\mathcal J|/|log \\n","authors_text":"Tobias Kuna, Valerio Lucarini, Viviane Baladi","cross_cats":["math-ph","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-31T17:20:02Z","title":"Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09690","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":"sha256:31e2641941f0a2126b93494ca59613ebcfff3e0db4cedc52ed93ed6fd0cda3aa","target":"record","created_at":"2026-05-18T00:41:58Z","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":"c821bd736d79e1bbac1d4f1c323fd00c2d4b0966fa33a43fe695b5472cd7d88e","cross_cats_sorted":["math-ph","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-31T17:20:02Z","title_canon_sha256":"f414fbd3d2ce1a1a4d3120220ed6fabad01ab9a54aa680c007e13f51816825ca"},"schema_version":"1.0","source":{"id":"1603.09690","kind":"arxiv","version":3}},"canonical_sha256":"b370e67a8a1f0b6b26b3e5795196ad503881e5f9d9e06cd7713d050bd3126fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b370e67a8a1f0b6b26b3e5795196ad503881e5f9d9e06cd7713d050bd3126fa6","first_computed_at":"2026-05-18T00:41:58.462057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:58.462057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8EY29YfeHi/lqaKAnFRWmv7t923zMfZoY4QodGLGwh/d/rWNMe/nVPLWdrf//9DY29dD6VzSXGB2UKds25CIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:58.462641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.09690","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31e2641941f0a2126b93494ca59613ebcfff3e0db4cedc52ed93ed6fd0cda3aa","sha256:f9ad0e7dc9d256a665ee9639871f9cb779ff014a0a78bb2e0430eb8946f20559"],"state_sha256":"aeda492bd5661980afda3440eedb537e338e7d18e41b2ce417d3549a57ca39c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G79UrJwpCjgesrFkphKyrFqU9mPMdgo4TM2iMzp+uLgG5zhpj/yFlVX7mwJM8B/FdxxCVL/r3QHxQkpSUmziDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:38:43.952983Z","bundle_sha256":"5c35068fcfd329f4bbb3b82c58cf644089a67881bf1cbcb883a3b2a3ac3d470d"}}