{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GNS3BEQMVCCFZMLFID2OMRDFTP","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":"9fd4d4fea329421d398be6fd4b23f462f6fed93d2c6c858988bdab946ce5a66b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-05T19:05:20Z","title_canon_sha256":"cfb1606ed2b0885a54dbf47b24444d105fd681cc6b9dbfb49145dcd47a09054b"},"schema_version":"1.0","source":{"id":"1708.01808","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01808","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01808v3","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01808","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"pith_short_12","alias_value":"GNS3BEQMVCCF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GNS3BEQMVCCFZMLF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GNS3BEQM","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:87fe17c2dc0a5d80a02b8e60cc62165330f40cd2db89b872860193928c8f133c","target":"graph","created_at":"2026-05-18T00:09:42Z","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 study the transition to chaos for the restriction to the real and imaginary axes of the tangent family $\\{ T_t(z)=i t\\tan z\\}_{0< t\\leq \\pi}$. Because tangent maps have no critical points but have an essential singularity at infinity and two symmetric asymptotic values, there are new phenomena: as $t$ increases we find single instances of \"period quadrupling\", \"period splitting\" and standard \"period doubling\"; there follows a general pattern of \"period merging\" where two attracting cycles of period $2^n$ \"merge\" into one attracting cycle of period $2^{n+1}$, and \"cycle doublin","authors_text":"Linda Keen, Tao Chen, Yunping Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-05T19:05:20Z","title":"Cycle Doubling, Merging And Renormalization in the Tangent Family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01808","kind":"arxiv","version":3},"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:e431d7b59042430b25a9451eb67271d822449e85794862d844c0c4e42f0f698f","target":"record","created_at":"2026-05-18T00:09:42Z","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":"9fd4d4fea329421d398be6fd4b23f462f6fed93d2c6c858988bdab946ce5a66b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-05T19:05:20Z","title_canon_sha256":"cfb1606ed2b0885a54dbf47b24444d105fd681cc6b9dbfb49145dcd47a09054b"},"schema_version":"1.0","source":{"id":"1708.01808","kind":"arxiv","version":3}},"canonical_sha256":"3365b0920ca8845cb16540f4e644659bf7a1dbe3d3823abaeffd3e3e62d190eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3365b0920ca8845cb16540f4e644659bf7a1dbe3d3823abaeffd3e3e62d190eb","first_computed_at":"2026-05-18T00:09:42.175179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:42.175179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tukt/KNg0/9lxj4dXAHwdV5TZPZprF7MtDtj0Mgx2Hr10SPp2mhufpCjey/OzoIpiW5iPiFJVnE+9ufwy/1DAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:42.175913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01808","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e431d7b59042430b25a9451eb67271d822449e85794862d844c0c4e42f0f698f","sha256:87fe17c2dc0a5d80a02b8e60cc62165330f40cd2db89b872860193928c8f133c"],"state_sha256":"f214943e84951aad65645578720d66b595037827134669fbac079d050676ea7f"}