{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZLE2HCTIJ7EJWHYDUICRWLT7MV","short_pith_number":"pith:ZLE2HCTI","canonical_record":{"source":{"id":"1111.5554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-23T17:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"c72873e961a79d8ff00ee5f1a5b5e38f791cafa4ecb57021743f49b7765cd1e0","abstract_canon_sha256":"eeaa359b84b9ed737bb2d8fab372bf569d1b60b8b8bd16c343149d5d0ede035d"},"schema_version":"1.0"},"canonical_sha256":"cac9a38a684fc89b1f03a2051b2e7f6542f2036cd7405d9a1322e1a629679270","source":{"kind":"arxiv","id":"1111.5554","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5554","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5554v1","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5554","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZLE2HCTIJ7EJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZLE2HCTIJ7EJWHYD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZLE2HCTI","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZLE2HCTIJ7EJWHYDUICRWLT7MV","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-23T17:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"c72873e961a79d8ff00ee5f1a5b5e38f791cafa4ecb57021743f49b7765cd1e0","abstract_canon_sha256":"eeaa359b84b9ed737bb2d8fab372bf569d1b60b8b8bd16c343149d5d0ede035d"},"schema_version":"1.0"},"canonical_sha256":"cac9a38a684fc89b1f03a2051b2e7f6542f2036cd7405d9a1322e1a629679270","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:00.141496Z","signature_b64":"MuOQSfRc6B8YYrvh3wbfygXBCRZzdGgsAwuQ0dMOAVjCPDXu9HUVbwQexYJQXTrohcZWFel+iSBQ+zmLtHhPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cac9a38a684fc89b1f03a2051b2e7f6542f2036cd7405d9a1322e1a629679270","last_reissued_at":"2026-05-18T02:58:00.140903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:00.140903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5554","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":"2026-05-18T02:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zY/BXpGR3EUnh4XQlT3m+NzPh6ii0hQOk/6LJ/kI2ih6H2L+RobvzqJgPCEOTDBbSvdokqpnDFa+yy1uWifiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:53:56.997622Z"},"content_sha256":"3b00d76a9a9c165d6463e0a981d551cf7597395d9c8c78d86da0bc76e306a831","schema_version":"1.0","event_id":"sha256:3b00d76a9a9c165d6463e0a981d551cf7597395d9c8c78d86da0bc76e306a831"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZLE2HCTIJ7EJWHYDUICRWLT7MV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explosion of smoothness for conjugacies between multimodal maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alberto A. Pinto, Jose F. Alves, Vilton Pinheiro","submitted_at":"2011-11-23T17:01:43Z","abstract_excerpt":"Let $f$ and $g$ be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy $h$ between $f$ and $g$ is $C^{1}$ at a point in the nearby expanding set of $f$, then $h$ is a smooth diffeomorphism in the basin of attraction of a renormalization interval of $f$. In particular, if $f:I \\to I$ and $g:J \\to J$ are $C^r$ unimodal maps and $h$ is $C^{1}$ at a boundary of $I$ then $h$ is $C^r$ in $I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5554","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":"2026-05-18T02:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3PHzo6RfhPx+xxPwZFi5MuP4t2iaZ2plElrOqRnD/FBzrBxBtUkYmQu/rE78vvUNcGr5Q4my1c4gnCabSxODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:53:56.998280Z"},"content_sha256":"39dca0ed745514b096f94ec5b49dd5c6b2e91626f6322266afe6339eb8ebfa14","schema_version":"1.0","event_id":"sha256:39dca0ed745514b096f94ec5b49dd5c6b2e91626f6322266afe6339eb8ebfa14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV/bundle.json","state_url":"https://pith.science/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV/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":"2026-05-18T21:53:56Z","links":{"resolver":"https://pith.science/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV","bundle":"https://pith.science/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV/bundle.json","state":"https://pith.science/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLE2HCTIJ7EJWHYDUICRWLT7MV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZLE2HCTIJ7EJWHYDUICRWLT7MV","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":"eeaa359b84b9ed737bb2d8fab372bf569d1b60b8b8bd16c343149d5d0ede035d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-23T17:01:43Z","title_canon_sha256":"c72873e961a79d8ff00ee5f1a5b5e38f791cafa4ecb57021743f49b7765cd1e0"},"schema_version":"1.0","source":{"id":"1111.5554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5554","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5554v1","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5554","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZLE2HCTIJ7EJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZLE2HCTIJ7EJWHYD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZLE2HCTI","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:39dca0ed745514b096f94ec5b49dd5c6b2e91626f6322266afe6339eb8ebfa14","target":"graph","created_at":"2026-05-18T02:58:00Z","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":"Let $f$ and $g$ be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy $h$ between $f$ and $g$ is $C^{1}$ at a point in the nearby expanding set of $f$, then $h$ is a smooth diffeomorphism in the basin of attraction of a renormalization interval of $f$. In particular, if $f:I \\to I$ and $g:J \\to J$ are $C^r$ unimodal maps and $h$ is $C^{1}$ at a boundary of $I$ then $h$ is $C^r$ in $I$.","authors_text":"Alberto A. Pinto, Jose F. Alves, Vilton Pinheiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-23T17:01:43Z","title":"Explosion of smoothness for conjugacies between multimodal maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5554","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":"sha256:3b00d76a9a9c165d6463e0a981d551cf7597395d9c8c78d86da0bc76e306a831","target":"record","created_at":"2026-05-18T02:58:00Z","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":"eeaa359b84b9ed737bb2d8fab372bf569d1b60b8b8bd16c343149d5d0ede035d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-23T17:01:43Z","title_canon_sha256":"c72873e961a79d8ff00ee5f1a5b5e38f791cafa4ecb57021743f49b7765cd1e0"},"schema_version":"1.0","source":{"id":"1111.5554","kind":"arxiv","version":1}},"canonical_sha256":"cac9a38a684fc89b1f03a2051b2e7f6542f2036cd7405d9a1322e1a629679270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cac9a38a684fc89b1f03a2051b2e7f6542f2036cd7405d9a1322e1a629679270","first_computed_at":"2026-05-18T02:58:00.140903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.140903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MuOQSfRc6B8YYrvh3wbfygXBCRZzdGgsAwuQ0dMOAVjCPDXu9HUVbwQexYJQXTrohcZWFel+iSBQ+zmLtHhPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.141496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b00d76a9a9c165d6463e0a981d551cf7597395d9c8c78d86da0bc76e306a831","sha256:39dca0ed745514b096f94ec5b49dd5c6b2e91626f6322266afe6339eb8ebfa14"],"state_sha256":"562fc507dd568a596019716f5863cef19748574f82d5d171cc8e65629379dd66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uHnlWWjKMnDxUONMaBYvuwvsYcXdeY4Cb57+twBA6hmU0rDV3AwAs8RIus+mpZgNd7nJCDQxhMSaXrdRUbQcBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T21:53:57.000347Z","bundle_sha256":"28e85349357e8909ac491a32cab4c3319d9db8bdf6c17f22f903c49fb17f6364"}}