{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:WJACSN6CVDFOCNV4JWT2FQYYBG","short_pith_number":"pith:WJACSN6C","canonical_record":{"source":{"id":"0706.4422","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-06-29T14:00:43Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"e3d87afd93ec3db3721849739076196e9d90d55578cd99cc0776ceb294cad14f","abstract_canon_sha256":"978cc42114c6d364581d630fa54b997fbbaed14d763e8847726d1fc4f64cf422"},"schema_version":"1.0"},"canonical_sha256":"b2402937c2a8cae136bc4da7a2c31809aeca0d8dab8d111782286f55f520a13e","source":{"kind":"arxiv","id":"0706.4422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.4422","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"0706.4422v1","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.4422","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"WJACSN6CVDFO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WJACSN6CVDFOCNV4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WJACSN6C","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:WJACSN6CVDFOCNV4JWT2FQYYBG","target":"record","payload":{"canonical_record":{"source":{"id":"0706.4422","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-06-29T14:00:43Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"e3d87afd93ec3db3721849739076196e9d90d55578cd99cc0776ceb294cad14f","abstract_canon_sha256":"978cc42114c6d364581d630fa54b997fbbaed14d763e8847726d1fc4f64cf422"},"schema_version":"1.0"},"canonical_sha256":"b2402937c2a8cae136bc4da7a2c31809aeca0d8dab8d111782286f55f520a13e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:51.380468Z","signature_b64":"ygCKYge2P4747NRigbwlZ8nbR5yeeN8Z85nSK6/74oMxTbsZtyS9o1lZ9IcNrnkeNRl2Owc4f6JKNLL8WXYMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2402937c2a8cae136bc4da7a2c31809aeca0d8dab8d111782286f55f520a13e","last_reissued_at":"2026-05-18T03:24:51.379745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:51.379745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.4422","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":"2026-05-18T03:24:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MAv7SIWYg70vPZx43sej6U/COyG6wZqQriWSQWtYq/XWy/JF+d81gZXGuiH0lUprDzU+9tJnpZ+nxdo5QZ45DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:39:11.560858Z"},"content_sha256":"2933864280f44bde7f2a7f3dbaef8510c0260a233d1578d3b7de085ead2254bb","schema_version":"1.0","event_id":"sha256:2933864280f44bde7f2a7f3dbaef8510c0260a233d1578d3b7de085ead2254bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:WJACSN6CVDFOCNV4JWT2FQYYBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics towards the Feigenbaum attractor","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Robledo, L. G. Moyano","submitted_at":"2007-06-29T14:00:43Z","abstract_excerpt":"We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4422","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":"2026-05-18T03:24:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cT5EhzFs21vZNvmyyz0BZq3YOwWpE6qOC+QnYnaReMVsyap9YoGtifl00DHtOp5lTOBOxbVzB2r56jt17rwmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:39:11.561206Z"},"content_sha256":"347548e1c480ba2e3281bdb24ffe9186c11cba735d3d2bde035e485dc58c6620","schema_version":"1.0","event_id":"sha256:347548e1c480ba2e3281bdb24ffe9186c11cba735d3d2bde035e485dc58c6620"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJACSN6CVDFOCNV4JWT2FQYYBG/bundle.json","state_url":"https://pith.science/pith/WJACSN6CVDFOCNV4JWT2FQYYBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJACSN6CVDFOCNV4JWT2FQYYBG/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":"2026-06-22T20:39:11Z","links":{"resolver":"https://pith.science/pith/WJACSN6CVDFOCNV4JWT2FQYYBG","bundle":"https://pith.science/pith/WJACSN6CVDFOCNV4JWT2FQYYBG/bundle.json","state":"https://pith.science/pith/WJACSN6CVDFOCNV4JWT2FQYYBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJACSN6CVDFOCNV4JWT2FQYYBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WJACSN6CVDFOCNV4JWT2FQYYBG","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":"978cc42114c6d364581d630fa54b997fbbaed14d763e8847726d1fc4f64cf422","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-06-29T14:00:43Z","title_canon_sha256":"e3d87afd93ec3db3721849739076196e9d90d55578cd99cc0776ceb294cad14f"},"schema_version":"1.0","source":{"id":"0706.4422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.4422","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"0706.4422v1","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.4422","created_at":"2026-05-18T03:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"WJACSN6CVDFO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WJACSN6CVDFOCNV4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WJACSN6C","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:347548e1c480ba2e3281bdb24ffe9186c11cba735d3d2bde035e485dc58c6620","target":"graph","created_at":"2026-05-18T03:24:51Z","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 expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families o","authors_text":"A. Robledo, L. G. Moyano","cross_cats":["nlin.CD"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-06-29T14:00:43Z","title":"Dynamics towards the Feigenbaum attractor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4422","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":"sha256:2933864280f44bde7f2a7f3dbaef8510c0260a233d1578d3b7de085ead2254bb","target":"record","created_at":"2026-05-18T03:24:51Z","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":"978cc42114c6d364581d630fa54b997fbbaed14d763e8847726d1fc4f64cf422","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-06-29T14:00:43Z","title_canon_sha256":"e3d87afd93ec3db3721849739076196e9d90d55578cd99cc0776ceb294cad14f"},"schema_version":"1.0","source":{"id":"0706.4422","kind":"arxiv","version":1}},"canonical_sha256":"b2402937c2a8cae136bc4da7a2c31809aeca0d8dab8d111782286f55f520a13e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2402937c2a8cae136bc4da7a2c31809aeca0d8dab8d111782286f55f520a13e","first_computed_at":"2026-05-18T03:24:51.379745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:51.379745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ygCKYge2P4747NRigbwlZ8nbR5yeeN8Z85nSK6/74oMxTbsZtyS9o1lZ9IcNrnkeNRl2Owc4f6JKNLL8WXYMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:51.380468Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.4422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2933864280f44bde7f2a7f3dbaef8510c0260a233d1578d3b7de085ead2254bb","sha256:347548e1c480ba2e3281bdb24ffe9186c11cba735d3d2bde035e485dc58c6620"],"state_sha256":"16722369d27978713d854dcac37431a8a16bc407c8909b81c91dfa134a33de3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25hWSMe1az4dUeNo5AUvVF0W2Wxp2lbEB0GhEIxl1N93b/b5ul5sEkWI8DeosigiO1tv70plFiuTKMtyUhqRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:39:11.563196Z","bundle_sha256":"a133ccd16e38375a81936a3fe7595cae574a62a7754a291a8021a4b435707652"}}