{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:Z6ATRTOGY5XZ5F676ZXKQOCJ6F","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":"e1de4f769646e03a80c2c695b44108e2b87eb0bd61601fc705fe09382e3f1c03","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1997-09-12T15:27:29Z","title_canon_sha256":"4e7b20ad1d523d9ca0c223720e81d62f91093c24ea99c428df640cb6297ac5e4"},"schema_version":"1.0","source":{"id":"chao-dyn/9709018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9709018","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9709018v1","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9709018","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"Z6ATRTOGY5XZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"Z6ATRTOGY5XZ5F67","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"Z6ATRTOG","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:1992fb3c94df000ada48cfac7ece3f297af59490eaa7b8cf79a698c058ec7fd1","target":"graph","created_at":"2026-05-18T01:40:11Z","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":"The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a turning point which represents a local minimum or maximum of the trajectory. Following we investigate the highly organized and structured distribution of turning points. The turning point dynamics is discussed and the corresponding turning point map which possesses an appealing asymptotic scaling property is investigated. Strong correlations are shown to exist fo","authors_text":"F. K. Diakonos, P. Schmelcher","cross_cats":["nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1997-09-12T15:27:29Z","title":"A turning point analysis of the ergodic dynamics of iterative maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9709018","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":"sha256:377e45e79b6c70b0aaca6416f7e97de1c9b018628a4190ce0fe3a133868c44bb","target":"record","created_at":"2026-05-18T01:40:11Z","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":"e1de4f769646e03a80c2c695b44108e2b87eb0bd61601fc705fe09382e3f1c03","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1997-09-12T15:27:29Z","title_canon_sha256":"4e7b20ad1d523d9ca0c223720e81d62f91093c24ea99c428df640cb6297ac5e4"},"schema_version":"1.0","source":{"id":"chao-dyn/9709018","kind":"arxiv","version":1}},"canonical_sha256":"cf8138cdc6c76f9e97dff66ea83849f1667f1120e1fe6f805548922bccd0314b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8138cdc6c76f9e97dff66ea83849f1667f1120e1fe6f805548922bccd0314b","first_computed_at":"2026-05-18T01:40:11.755225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:11.755225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ha5fIdxK4KgQezl1qu3urpMSc6xOXJuUqxkCtFZgmwQBAz24d+2FjEO249IURO8pZN95ygcmvU7OwMLE5O2XAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:11.755771Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9709018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:377e45e79b6c70b0aaca6416f7e97de1c9b018628a4190ce0fe3a133868c44bb","sha256:1992fb3c94df000ada48cfac7ece3f297af59490eaa7b8cf79a698c058ec7fd1"],"state_sha256":"6e59e2b088479247846d352d84f467387acef5e6f3cecb282f678dd01b138301"}