{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZF4UYTWIKZLUU6K2SXGM2NDQYH","short_pith_number":"pith:ZF4UYTWI","canonical_record":{"source":{"id":"1205.5226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T17:19:24Z","cross_cats_sorted":["math.CV","nlin.CD"],"title_canon_sha256":"de7422a1467f2ffe524e1e2b91ba7e407d2fe31966da33ba023116d7ffc649f8","abstract_canon_sha256":"edd315fb3092078f65a0e4723942922e3fc01e251be5061d47e14df0d7725731"},"schema_version":"1.0"},"canonical_sha256":"c9794c4ec856574a795a95cccd3470c1c79f3973f086bba8d0bd712b37973d84","source":{"kind":"arxiv","id":"1205.5226","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5226","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5226v2","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5226","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZF4UYTWIKZLU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZF4UYTWIKZLUU6K2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZF4UYTWI","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZF4UYTWIKZLUU6K2SXGM2NDQYH","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5226","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T17:19:24Z","cross_cats_sorted":["math.CV","nlin.CD"],"title_canon_sha256":"de7422a1467f2ffe524e1e2b91ba7e407d2fe31966da33ba023116d7ffc649f8","abstract_canon_sha256":"edd315fb3092078f65a0e4723942922e3fc01e251be5061d47e14df0d7725731"},"schema_version":"1.0"},"canonical_sha256":"c9794c4ec856574a795a95cccd3470c1c79f3973f086bba8d0bd712b37973d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.718638Z","signature_b64":"33Hbhhq32SDlauO+6Bw6/JL9gHzD2iIm6X7ChgY7/ULMOJ5Naq8OHuUvtLlaMYfhD2/kqvideuNtDN/3gamDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9794c4ec856574a795a95cccd3470c1c79f3973f086bba8d0bd712b37973d84","last_reissued_at":"2026-05-17T23:53:18.718053Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.718053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5226","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Pe1GYo3VJmHfyCYBXylCDkFoH0CV0MpWgGaPMj8c9E1rxvCJd1+BpjetnqZPJIEqZu0gsK4GRZSVM/4iwQcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:43:06.593920Z"},"content_sha256":"0ea82da388c15100d5d947a3e1c273b1f82227dc583fe623a2c07b1454e2d3c8","schema_version":"1.0","event_id":"sha256:0ea82da388c15100d5d947a3e1c273b1f82227dc583fe623a2c07b1454e2d3c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZF4UYTWIKZLUU6K2SXGM2NDQYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","nlin.CD"],"primary_cat":"math.DS","authors_text":"David Sauzin, Stefano Marmi, Viviane Baladi","submitted_at":"2012-05-23T17:19:24Z","abstract_excerpt":"We consider the susceptibility function Psi(z) of a piecewise expanding unimodal interval map f with unique acim mu, a perturbation X, and an observable phi. Combining previous results (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer-Simon (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon), we show that density of the postcritical orbit (a generic condition) implies that Psi(z) has a strong natural boundary on the unit circle. The Breuer-Simon method provides uncountably many candidates for the outer functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5226","kind":"arxiv","version":2},"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":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NI4Fb3ASrrE3pewAowPYHdLSQpXzTNtOf6I+HnA1d5Bv0gKq8w7L0nuzo24rfDF9yS6hgPfEZnM6GJBCUMWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:43:06.594262Z"},"content_sha256":"0dacae19b16b0ac70d520947dd531dab79daad9527a4bcb2d6355cf8cdd12ca8","schema_version":"1.0","event_id":"sha256:0dacae19b16b0ac70d520947dd531dab79daad9527a4bcb2d6355cf8cdd12ca8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH/bundle.json","state_url":"https://pith.science/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH/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":"2026-06-24T10:43:06Z","links":{"resolver":"https://pith.science/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH","bundle":"https://pith.science/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH/bundle.json","state":"https://pith.science/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZF4UYTWIKZLUU6K2SXGM2NDQYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZF4UYTWIKZLUU6K2SXGM2NDQYH","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":"edd315fb3092078f65a0e4723942922e3fc01e251be5061d47e14df0d7725731","cross_cats_sorted":["math.CV","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T17:19:24Z","title_canon_sha256":"de7422a1467f2ffe524e1e2b91ba7e407d2fe31966da33ba023116d7ffc649f8"},"schema_version":"1.0","source":{"id":"1205.5226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5226","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5226v2","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5226","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZF4UYTWIKZLU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZF4UYTWIKZLUU6K2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZF4UYTWI","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:0dacae19b16b0ac70d520947dd531dab79daad9527a4bcb2d6355cf8cdd12ca8","target":"graph","created_at":"2026-05-17T23:53:18Z","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 the susceptibility function Psi(z) of a piecewise expanding unimodal interval map f with unique acim mu, a perturbation X, and an observable phi. Combining previous results (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer-Simon (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon), we show that density of the postcritical orbit (a generic condition) implies that Psi(z) has a strong natural boundary on the unit circle. The Breuer-Simon method provides uncountably many candidates for the outer functi","authors_text":"David Sauzin, Stefano Marmi, Viviane Baladi","cross_cats":["math.CV","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T17:19:24Z","title":"Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5226","kind":"arxiv","version":2},"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":"sha256:0ea82da388c15100d5d947a3e1c273b1f82227dc583fe623a2c07b1454e2d3c8","target":"record","created_at":"2026-05-17T23:53:18Z","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":"edd315fb3092078f65a0e4723942922e3fc01e251be5061d47e14df0d7725731","cross_cats_sorted":["math.CV","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T17:19:24Z","title_canon_sha256":"de7422a1467f2ffe524e1e2b91ba7e407d2fe31966da33ba023116d7ffc649f8"},"schema_version":"1.0","source":{"id":"1205.5226","kind":"arxiv","version":2}},"canonical_sha256":"c9794c4ec856574a795a95cccd3470c1c79f3973f086bba8d0bd712b37973d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9794c4ec856574a795a95cccd3470c1c79f3973f086bba8d0bd712b37973d84","first_computed_at":"2026-05-17T23:53:18.718053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.718053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33Hbhhq32SDlauO+6Bw6/JL9gHzD2iIm6X7ChgY7/ULMOJ5Naq8OHuUvtLlaMYfhD2/kqvideuNtDN/3gamDCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.718638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ea82da388c15100d5d947a3e1c273b1f82227dc583fe623a2c07b1454e2d3c8","sha256:0dacae19b16b0ac70d520947dd531dab79daad9527a4bcb2d6355cf8cdd12ca8"],"state_sha256":"b2ebe94cfdf9f528006d6e97fa3b37d6d32b251d4085da7a79a17a376e220725"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ie7We4ZavSWPukPGhJeS4NmOKrx4jHZMVIf7ZO7eNYvkojVhxmvkNaCU8kl0WRBx12jexBuSXnyjkxOrsS4SCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:43:06.596171Z","bundle_sha256":"222ca9f2b543bedffde595c65bbfa82d1ad6cc1a06e0903191f2fd5b0311b88a"}}