{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:LATVECEMRGEQZ5KUCI3E6YVX4K","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":"e8fc13ac3ecc52132ee101b7817f4e00d75ad5b067e402982d7c8a07f17163ed","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2007-10-02T22:51:02Z","title_canon_sha256":"f12a2709de3233a0f41ba424066400fc729c3e03ff3273359e52876d39dd590f"},"schema_version":"1.0","source":{"id":"0710.0667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0667","created_at":"2026-07-04T15:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0667v1","created_at":"2026-07-04T15:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0667","created_at":"2026-07-04T15:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"LATVECEMRGEQ","created_at":"2026-07-04T15:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"LATVECEMRGEQZ5KU","created_at":"2026-07-04T15:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"LATVECEM","created_at":"2026-07-04T15:04:39Z"}],"graph_snapshots":[{"event_id":"sha256:88e88a5ae872294e026fe2857a7206ad8664714f039ede45d6ae0ae7f71b001d","target":"graph","created_at":"2026-07-04T15:04:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0710.0667/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The period doubling renormalization operator was introduced by M. Feigenbaum and by P. Coullet and C. Tresser in the nineteen-seventieth to study the asymptotic small scale geometry of the attractor of one-dimensional systems which are at the transition from simple to chaotic dynamics. This geometry turns out to not depend on the choice of the map under rather mild smoothness conditions. The existence of a unique renormalization fixed point which is also hyperbolic among generic smooth enough maps plays a crucial role in the corresponding renormalization theory. The uniqueness and hyperbolicit","authors_text":"C.P. Tresser, M. Martens, V.V.M.S. Chandramouli, W. de Melo","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2007-10-02T22:51:02Z","title":"Chaotic Period Doubling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0667","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:f64a3c739c2fefe0da033ce619b8c75619a3efe39d819115acdcb0b76b917059","target":"record","created_at":"2026-07-04T15:04:39Z","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":"e8fc13ac3ecc52132ee101b7817f4e00d75ad5b067e402982d7c8a07f17163ed","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2007-10-02T22:51:02Z","title_canon_sha256":"f12a2709de3233a0f41ba424066400fc729c3e03ff3273359e52876d39dd590f"},"schema_version":"1.0","source":{"id":"0710.0667","kind":"arxiv","version":1}},"canonical_sha256":"582752088c89890cf55412364f62b7e2bcfe9533eb30a6d77adc922cbc6614cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"582752088c89890cf55412364f62b7e2bcfe9533eb30a6d77adc922cbc6614cc","first_computed_at":"2026-07-04T15:04:39.237907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:04:39.237907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vP9oLsfgLoDpXsvm6P4o9jGVvUKslk1aP32TrYhSdNuzhYoxEK9kZavTCskhymrLvlvgirgcZL5yFxf+H5CHDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:04:39.238267Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.0667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f64a3c739c2fefe0da033ce619b8c75619a3efe39d819115acdcb0b76b917059","sha256:88e88a5ae872294e026fe2857a7206ad8664714f039ede45d6ae0ae7f71b001d"],"state_sha256":"84c0ce43ac5ff9606c7d4ac757955e6aa8994f390a21d8718da7a200db122a8d"}