{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C5PCP32TU7WQ5HRW5LQE4ERWKR","short_pith_number":"pith:C5PCP32T","canonical_record":{"source":{"id":"1512.01080","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-03T14:10:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d5b2c428fcfcab7848df7c22667d11302b251ee42805332a209a3677d745f94f","abstract_canon_sha256":"2c4d8443d2bd094c8aa10c8ded1385aaa6b17dd58c192d5c100bc4f34e0c5717"},"schema_version":"1.0"},"canonical_sha256":"175e27ef53a7ed0e9e36eae04e12365477f4b5d5aba00a1675637f328f0f660e","source":{"kind":"arxiv","id":"1512.01080","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01080","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01080v3","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01080","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"C5PCP32TU7WQ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C5PCP32TU7WQ5HRW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C5PCP32T","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C5PCP32TU7WQ5HRW5LQE4ERWKR","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01080","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-03T14:10:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d5b2c428fcfcab7848df7c22667d11302b251ee42805332a209a3677d745f94f","abstract_canon_sha256":"2c4d8443d2bd094c8aa10c8ded1385aaa6b17dd58c192d5c100bc4f34e0c5717"},"schema_version":"1.0"},"canonical_sha256":"175e27ef53a7ed0e9e36eae04e12365477f4b5d5aba00a1675637f328f0f660e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:17.893853Z","signature_b64":"DFojtjqlGv+P9oR1zc/FVwF4jZzcteblWv+JmBaMPafBjZwSV2SNJTyucQYF3kU8AZPsH3MbXXt6mpbXvFgsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"175e27ef53a7ed0e9e36eae04e12365477f4b5d5aba00a1675637f328f0f660e","last_reissued_at":"2026-05-18T01:11:17.893348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:17.893348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01080","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":"2026-05-18T01:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsR34TrQ8WaqlKYf5JorlUR6ozC6CX6yyQWTiBNePDxOco7d8bAhPwHRCrQni7e8o+pK7aHDVrXeS1JHk44VCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:19:49.743365Z"},"content_sha256":"2c8b0ef3081c32cfc5de44173a4da9483debdabadaa193cbd0f206109233a245","schema_version":"1.0","event_id":"sha256:2c8b0ef3081c32cfc5de44173a4da9483debdabadaa193cbd0f206109233a245"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C5PCP32TU7WQ5HRW5LQE4ERWKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear response in the intermittent family: differentiation in a weighted $C^0$-norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Beno\\^it Saussol, Wael Bahsoun","submitted_at":"2015-12-03T14:10:54Z","abstract_excerpt":"We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing how the linear response formula of the non-uniformly expanding system is inherited from the linear response formula of the induced one. We apply this general technique to interval maps with a neutral fixed point (Pomeau-Manneville maps) to prove differentiability of the corresponding SRB measure. Our work covers systems that admit a finite SRB measure and it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01080","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":"2026-05-18T01:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KwxJOsRpOwGZ2TdodIrkLmMncEQMDFXlMQWUbOWo7GhFJsTIhngBtK0O//jl+Zb0mzQAh89rNr1q1nvEJiJeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:19:49.743711Z"},"content_sha256":"fffca969380fcce850170276133042633d7c29fe03ab11706f8587fbee8993fc","schema_version":"1.0","event_id":"sha256:fffca969380fcce850170276133042633d7c29fe03ab11706f8587fbee8993fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR/bundle.json","state_url":"https://pith.science/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR/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":"2026-06-01T18:19:49Z","links":{"resolver":"https://pith.science/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR","bundle":"https://pith.science/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR/bundle.json","state":"https://pith.science/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5PCP32TU7WQ5HRW5LQE4ERWKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C5PCP32TU7WQ5HRW5LQE4ERWKR","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":"2c4d8443d2bd094c8aa10c8ded1385aaa6b17dd58c192d5c100bc4f34e0c5717","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-03T14:10:54Z","title_canon_sha256":"d5b2c428fcfcab7848df7c22667d11302b251ee42805332a209a3677d745f94f"},"schema_version":"1.0","source":{"id":"1512.01080","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01080","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01080v3","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01080","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"C5PCP32TU7WQ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C5PCP32TU7WQ5HRW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C5PCP32T","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:fffca969380fcce850170276133042633d7c29fe03ab11706f8587fbee8993fc","target":"graph","created_at":"2026-05-18T01:11:17Z","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 provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing how the linear response formula of the non-uniformly expanding system is inherited from the linear response formula of the induced one. We apply this general technique to interval maps with a neutral fixed point (Pomeau-Manneville maps) to prove differentiability of the corresponding SRB measure. Our work covers systems that admit a finite SRB measure and it ","authors_text":"Beno\\^it Saussol, Wael Bahsoun","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-03T14:10:54Z","title":"Linear response in the intermittent family: differentiation in a weighted $C^0$-norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01080","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":"sha256:2c8b0ef3081c32cfc5de44173a4da9483debdabadaa193cbd0f206109233a245","target":"record","created_at":"2026-05-18T01:11:17Z","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":"2c4d8443d2bd094c8aa10c8ded1385aaa6b17dd58c192d5c100bc4f34e0c5717","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-03T14:10:54Z","title_canon_sha256":"d5b2c428fcfcab7848df7c22667d11302b251ee42805332a209a3677d745f94f"},"schema_version":"1.0","source":{"id":"1512.01080","kind":"arxiv","version":3}},"canonical_sha256":"175e27ef53a7ed0e9e36eae04e12365477f4b5d5aba00a1675637f328f0f660e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"175e27ef53a7ed0e9e36eae04e12365477f4b5d5aba00a1675637f328f0f660e","first_computed_at":"2026-05-18T01:11:17.893348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:17.893348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DFojtjqlGv+P9oR1zc/FVwF4jZzcteblWv+JmBaMPafBjZwSV2SNJTyucQYF3kU8AZPsH3MbXXt6mpbXvFgsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:17.893853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01080","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c8b0ef3081c32cfc5de44173a4da9483debdabadaa193cbd0f206109233a245","sha256:fffca969380fcce850170276133042633d7c29fe03ab11706f8587fbee8993fc"],"state_sha256":"42a0102a3c3520a6aca62c96ec2929cad76508ccffc1cda77778f5a2f3781953"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JAwhPL9rbBgnhR7NAoka527Ekleb/u+HcjArE1x+UOztYzrRtCJHFaKt2kJPfaZnaHBRLiskq/DpkokjoziTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:19:49.745589Z","bundle_sha256":"086d8797ae75f32c5fa84dbe94c12a91c9cb6d88689355199b7f153cb15d0b91"}}