{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YOSWXEJZ35ZXKO6GORJJSEF3KT","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":"539c4a1e63d8b84bcd4bab9349536c60b58e9372ca2a60eb67ae9f8dc643c7d9","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-15T14:51:52Z","title_canon_sha256":"fa69396d419f64b033b55853a48cb9f35d8b6c1adb5ff0b46221f92bbcc4564b"},"schema_version":"1.0","source":{"id":"1705.05276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05276","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05276v2","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05276","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"YOSWXEJZ35ZX","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YOSWXEJZ35ZXKO6G","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YOSWXEJZ","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:fe4bb8425cf4bae790a700654af76e96be43c113c9311290678bf13c97da2132","target":"graph","created_at":"2026-05-18T00:44:22Z","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":"Let $\\Lambda$ be a quasi-projective variety and assume that, either $\\Lambda$ is a subvariety of the moduli space $\\mathcal{M}_d$ of degree $d$ rational maps, or $\\Lambda$ parametrizes an algebraic family $(f_\\lambda)_{\\lambda\\in\\Lambda}$ of degree $d$ rational maps on $\\mathbb{P}^1$. We prove the equidistribution of parameters having $p$ distinct neutral cycles towards the $p$-th bifurcation current letting the periods of the cycles go to $\\infty$, with an exponential speed of convergence. We deduce several fundamental consequences of this result on equidistribution and counting of hyperbolic","authors_text":"Gabriel Vigny, Thomas Gauthier, Y\\^usuke Okuyama","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-15T14:51:52Z","title":"Hyperbolic components of rational maps: Quantitative equidistribution and counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05276","kind":"arxiv","version":2},"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":"sha256:3e2f6223db11dd5aa7bf859fcb9aef857f73147adb600b6c59faaca1c1fe9f19","target":"record","created_at":"2026-05-18T00:44:22Z","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":"539c4a1e63d8b84bcd4bab9349536c60b58e9372ca2a60eb67ae9f8dc643c7d9","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-15T14:51:52Z","title_canon_sha256":"fa69396d419f64b033b55853a48cb9f35d8b6c1adb5ff0b46221f92bbcc4564b"},"schema_version":"1.0","source":{"id":"1705.05276","kind":"arxiv","version":2}},"canonical_sha256":"c3a56b9139df73753bc674529910bb54fe071858425a86b2f8d5e967084462fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3a56b9139df73753bc674529910bb54fe071858425a86b2f8d5e967084462fc","first_computed_at":"2026-05-18T00:44:22.854267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:22.854267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g4omHkpRaaRYkMaADHmxgXTscvxxw5hLY8vCn/k7wM4e3QQECXt/fc17tlKNgtwU+l2qHAU0BO7a6eV9Q6zMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:22.854707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e2f6223db11dd5aa7bf859fcb9aef857f73147adb600b6c59faaca1c1fe9f19","sha256:fe4bb8425cf4bae790a700654af76e96be43c113c9311290678bf13c97da2132"],"state_sha256":"55d50e66700887f7a2a99d5bdf5cb67c790f9466ff7ff20466718eba7deca9f0"}