{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XKXEH67U5FJ7PDH73LIQRTJ24W","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":"997c84127447ef17949a3428c94911e8c0e6f1b136aa11b061000143f002e885","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-21T21:43:16Z","title_canon_sha256":"38b68db4783e9bb5a8652be6dbae1971d3d912fa472d6af51f98129134a2e8f5"},"schema_version":"1.0","source":{"id":"1305.4971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4971","created_at":"2026-05-18T03:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4971v1","created_at":"2026-05-18T03:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4971","created_at":"2026-05-18T03:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"XKXEH67U5FJ7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XKXEH67U5FJ7PDH7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XKXEH67U","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3fd2f4f822a94dc78b0195e4038ecc81e459977478a837359876939ddf8d16ba","target":"graph","created_at":"2026-05-18T03:25:13Z","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 give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, near the phase transition these functions behave as $x \\mapsto \\exp (- 1 / x^2)$ near $x = 0$, before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.","authors_text":"Daniel Coronel, Juan Rivera-Letelier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-21T21:43:16Z","title":"High-order phase transitions in the quadratic family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4971","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":"sha256:4b14d9877ae376982ac953275440aaa828bf1bd21217a9a29ceacb0603713db3","target":"record","created_at":"2026-05-18T03:25:13Z","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":"997c84127447ef17949a3428c94911e8c0e6f1b136aa11b061000143f002e885","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-21T21:43:16Z","title_canon_sha256":"38b68db4783e9bb5a8652be6dbae1971d3d912fa472d6af51f98129134a2e8f5"},"schema_version":"1.0","source":{"id":"1305.4971","kind":"arxiv","version":1}},"canonical_sha256":"baae43fbf4e953f78cffdad108cd3ae5814ab4993f86857b29475fc76b01de02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baae43fbf4e953f78cffdad108cd3ae5814ab4993f86857b29475fc76b01de02","first_computed_at":"2026-05-18T03:25:13.847028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:13.847028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wxGkfZx/NXclVFq1x8D4hpgzgMUOGCvBFVdSigc3jGyIp2FbxhijRADdJF/Ukk3FjI/3cJv+8n6HHwhKFx1IAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:13.847747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b14d9877ae376982ac953275440aaa828bf1bd21217a9a29ceacb0603713db3","sha256:3fd2f4f822a94dc78b0195e4038ecc81e459977478a837359876939ddf8d16ba"],"state_sha256":"dd8a69f2a99284cfbc533cf445c48973e354b386ef9f76d9874a5079aa502eb6"}