{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I7GEWXAMLM4JOOHRCSFV54TYQ4","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":"9968c305f631d4fe09cb5b3df8ebab375d55d35358dddc472d3bfaf1856bd39b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-26T01:33:17Z","title_canon_sha256":"c2ca687391af3c496dd1882e6ea6219691de07164e3a948095a27516db01a5cf"},"schema_version":"1.0","source":{"id":"1803.09381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09381","created_at":"2026-05-18T00:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09381v1","created_at":"2026-05-18T00:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09381","created_at":"2026-05-18T00:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"I7GEWXAMLM4J","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I7GEWXAMLM4JOOHR","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I7GEWXAM","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:59948833f0a8f4dc971cfba026ff66ac3e9ed4c75732dd2e753888478032bdf9","target":"graph","created_at":"2026-05-18T00:20:11Z","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 purpose of this article is to investigate geometric properties of the parameter locus of the H\\'enon family where the uniform hyperbolicity of a horseshoe breaks down. As an application, we obtain a variational characterization of equilibrium measures \"at temperature zero\" for the corresponding non-uniformly hyperbolic H\\'enon maps. The method of the proof also yields that the boundary of the hyperbolic horseshoe locus in the parameter space consists of two monotone pieces, which confirms a conjecture in [AI]. The proofs of these results are based on the machinery developed in [AI] which e","authors_text":"Hiroki Takahasi, Yutaka Ishii, Zin Arai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-26T01:33:17Z","title":"Boundary of the horseshoe locus for the H\\'enon family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09381","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":"sha256:6a7983cfceb3d17fc6bc691e8bc4f6fcbbe59daa724386bfe90b68ded3888ab5","target":"record","created_at":"2026-05-18T00:20:11Z","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":"9968c305f631d4fe09cb5b3df8ebab375d55d35358dddc472d3bfaf1856bd39b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-26T01:33:17Z","title_canon_sha256":"c2ca687391af3c496dd1882e6ea6219691de07164e3a948095a27516db01a5cf"},"schema_version":"1.0","source":{"id":"1803.09381","kind":"arxiv","version":1}},"canonical_sha256":"47cc4b5c0c5b389738f1148b5ef278871a7b48113f4421332a74ec3b44a620f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47cc4b5c0c5b389738f1148b5ef278871a7b48113f4421332a74ec3b44a620f0","first_computed_at":"2026-05-18T00:20:11.792707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:11.792707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VOtrzmRLN1k5TSiKk8UKImKYKkKf8VX2xq4x2jzaeZexzeDpd3jLZSqTnBdvL0vhG30osSb7GCADgaChYYsKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:11.793382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.09381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a7983cfceb3d17fc6bc691e8bc4f6fcbbe59daa724386bfe90b68ded3888ab5","sha256:59948833f0a8f4dc971cfba026ff66ac3e9ed4c75732dd2e753888478032bdf9"],"state_sha256":"8b74c8f8970b2dcd8f36899f356401af5b33ed7018637a50a375616ef5c69ca5"}