{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:U64MICUFRCXTNT5XTDCGDMMWX7","short_pith_number":"pith:U64MICUF","canonical_record":{"source":{"id":"1701.06418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-23T14:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"02431d4d931448a4d68a940cdcb05bc99f3418e1aefceab94c68c1d9682a03ee","abstract_canon_sha256":"e8f55dbec2734678d96186d42ca3017af99624c15d8ea3efd3732ab4fdc40f11"},"schema_version":"1.0"},"canonical_sha256":"a7b8c40a8588af36cfb798c461b196bfe284a53e9511afd50d6026afb35ce1b9","source":{"kind":"arxiv","id":"1701.06418","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06418","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06418v1","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06418","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"U64MICUFRCXT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U64MICUFRCXTNT5X","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U64MICUF","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:U64MICUFRCXTNT5XTDCGDMMWX7","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-23T14:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"02431d4d931448a4d68a940cdcb05bc99f3418e1aefceab94c68c1d9682a03ee","abstract_canon_sha256":"e8f55dbec2734678d96186d42ca3017af99624c15d8ea3efd3732ab4fdc40f11"},"schema_version":"1.0"},"canonical_sha256":"a7b8c40a8588af36cfb798c461b196bfe284a53e9511afd50d6026afb35ce1b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:18.477702Z","signature_b64":"4bwEIIuqu0Z36D0EQQrHX9jCuFztOoXpFkZkR1Jyok7sfkWIlB9MtebiQak2Km6l7TYQZ4vznrP/HhSKlmj5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7b8c40a8588af36cfb798c461b196bfe284a53e9511afd50d6026afb35ce1b9","last_reissued_at":"2026-05-18T00:52:18.477067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:18.477067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06418","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":"2026-05-18T00:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJ/gvIewTLoNLmerlJsQUP6eRZ+UCd2lggsgfl9PCAG5lYRTjsb+uAacERrkX2OLPIEjbGw7tWQYI6G1y5QvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:04:55.693652Z"},"content_sha256":"37857b6707b42beb7ee06feee9c2064ceafc69336679b6827153ce7b60cd43cb","schema_version":"1.0","event_id":"sha256:37857b6707b42beb7ee06feee9c2064ceafc69336679b6827153ce7b60cd43cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:U64MICUFRCXTNT5XTDCGDMMWX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the invariant Cantor sets of period doubling type of infinitely renormalizable area-preserving maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dan Str\\\"angberg","submitted_at":"2017-01-23T14:39:22Z","abstract_excerpt":"In this paper we show that the invariant Cantor set of period doubling type of any infinitely renormalizable area-preserving map in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point is always contained in a Lipschitz curve but never contained in a smooth curve. This extends previous results by de Carvalho, Lyubich and Martens about strongly dissipative maps of the plane close to unimodal maps to the area-preserving setting. The method used for constructing the Lipschitz curve is very similar to the method used in the dissipative case but proving the nonexistence of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06418","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":"2026-05-18T00:52:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bXbfN690+M9AV68xccT8bjlfr3ryAGumZbyyLKZzcHTrpcvYn7RdKj1IVx90lKK8NfuUdOkLL0wtX+O8awjvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:04:55.693997Z"},"content_sha256":"ac6e6ab29d09031919a839b07e709c9134931f791c5934a54c3454924d84e3b9","schema_version":"1.0","event_id":"sha256:ac6e6ab29d09031919a839b07e709c9134931f791c5934a54c3454924d84e3b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U64MICUFRCXTNT5XTDCGDMMWX7/bundle.json","state_url":"https://pith.science/pith/U64MICUFRCXTNT5XTDCGDMMWX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U64MICUFRCXTNT5XTDCGDMMWX7/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":"2026-06-29T14:04:55Z","links":{"resolver":"https://pith.science/pith/U64MICUFRCXTNT5XTDCGDMMWX7","bundle":"https://pith.science/pith/U64MICUFRCXTNT5XTDCGDMMWX7/bundle.json","state":"https://pith.science/pith/U64MICUFRCXTNT5XTDCGDMMWX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U64MICUFRCXTNT5XTDCGDMMWX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:U64MICUFRCXTNT5XTDCGDMMWX7","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":"e8f55dbec2734678d96186d42ca3017af99624c15d8ea3efd3732ab4fdc40f11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-23T14:39:22Z","title_canon_sha256":"02431d4d931448a4d68a940cdcb05bc99f3418e1aefceab94c68c1d9682a03ee"},"schema_version":"1.0","source":{"id":"1701.06418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06418","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06418v1","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06418","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"U64MICUFRCXT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U64MICUFRCXTNT5X","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U64MICUF","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:ac6e6ab29d09031919a839b07e709c9134931f791c5934a54c3454924d84e3b9","target":"graph","created_at":"2026-05-18T00:52:18Z","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":"In this paper we show that the invariant Cantor set of period doubling type of any infinitely renormalizable area-preserving map in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point is always contained in a Lipschitz curve but never contained in a smooth curve. This extends previous results by de Carvalho, Lyubich and Martens about strongly dissipative maps of the plane close to unimodal maps to the area-preserving setting. The method used for constructing the Lipschitz curve is very similar to the method used in the dissipative case but proving the nonexistence of","authors_text":"Dan Str\\\"angberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-23T14:39:22Z","title":"On the invariant Cantor sets of period doubling type of infinitely renormalizable area-preserving maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06418","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":"sha256:37857b6707b42beb7ee06feee9c2064ceafc69336679b6827153ce7b60cd43cb","target":"record","created_at":"2026-05-18T00:52:18Z","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":"e8f55dbec2734678d96186d42ca3017af99624c15d8ea3efd3732ab4fdc40f11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-23T14:39:22Z","title_canon_sha256":"02431d4d931448a4d68a940cdcb05bc99f3418e1aefceab94c68c1d9682a03ee"},"schema_version":"1.0","source":{"id":"1701.06418","kind":"arxiv","version":1}},"canonical_sha256":"a7b8c40a8588af36cfb798c461b196bfe284a53e9511afd50d6026afb35ce1b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7b8c40a8588af36cfb798c461b196bfe284a53e9511afd50d6026afb35ce1b9","first_computed_at":"2026-05-18T00:52:18.477067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:18.477067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4bwEIIuqu0Z36D0EQQrHX9jCuFztOoXpFkZkR1Jyok7sfkWIlB9MtebiQak2Km6l7TYQZ4vznrP/HhSKlmj5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:18.477702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37857b6707b42beb7ee06feee9c2064ceafc69336679b6827153ce7b60cd43cb","sha256:ac6e6ab29d09031919a839b07e709c9134931f791c5934a54c3454924d84e3b9"],"state_sha256":"8f4729f3225d5e7033ca47dbad29118d3e4e5deb51a207a58b8bebf2425a3fe7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5CKQ839O/enFy+PS0H1px4ItJEzSD8MX8jTOeu3PIQOWeH9sFlfw7E4fF3tXVK/3rhydmSleI5hP+EN2pqODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:04:55.695931Z","bundle_sha256":"afbfd5c9f8aee1c1dc61a83686ba40ca29c0595bdc449b4237f76a5e3c4b106a"}}