{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L3M3WDMMHMCBQUW3PGPZ7J2WKL","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":"7f3059f0c7a39a0c7f28350f102b56a23270bbf2d0ca1c44bbc26074eb048176","cross_cats_sorted":["math.DS","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-13T13:44:49Z","title_canon_sha256":"8bb77f13b7acc1b4dc671c864fa7be40367bb2cd4591c66d5f534ffb3e938394"},"schema_version":"1.0","source":{"id":"1302.3087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3087","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3087v2","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3087","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"L3M3WDMMHMCB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L3M3WDMMHMCBQUW3","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L3M3WDMM","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:7368d813e4496ff597886602d081d5e9e4f28db6506e7e4e4d43c990bb067db5","target":"graph","created_at":"2026-05-18T01:30:26Z","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 consider a simple model of an open partially expanding map. Its trapped set K in phase space is a fractal set. We first show that there is a well defined discrete spectrum of Ruelle resonances which describes the asymptotics of correlation functions for large time and which is parametrized by the Fourier component \\nu on the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call \"minimal captivity\". This hypothesis is stable under perturbations and means that the dynamics is univalued on a neighborhood of K. Under this hypothesis we show the exist","authors_text":"Fr\\'ed\\'eric Faure (IF), Jean-Fran\\c{c}ois Arnoldi (IF), Tobias Weich","cross_cats":["math.DS","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-13T13:44:49Z","title":"Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3087","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":"sha256:9079e05b60ab4efb2226fcc43153f17b0c20f86a9a6777ecfbff788b92a596d9","target":"record","created_at":"2026-05-18T01:30:26Z","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":"7f3059f0c7a39a0c7f28350f102b56a23270bbf2d0ca1c44bbc26074eb048176","cross_cats_sorted":["math.DS","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-13T13:44:49Z","title_canon_sha256":"8bb77f13b7acc1b4dc671c864fa7be40367bb2cd4591c66d5f534ffb3e938394"},"schema_version":"1.0","source":{"id":"1302.3087","kind":"arxiv","version":2}},"canonical_sha256":"5ed9bb0d8c3b041852db799f9fa75652cfc4be9ee4cf650e14aadf45e7b72cbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ed9bb0d8c3b041852db799f9fa75652cfc4be9ee4cf650e14aadf45e7b72cbd","first_computed_at":"2026-05-18T01:30:26.122499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:26.122499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wScKvqoogFsVz3oeHFchzIV8GGN9WwfVvqa/1O+r+lkeVL9+HUmXwEvUOnEUhRLgyXfygRdk3mfKypuf3dyZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:26.123167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9079e05b60ab4efb2226fcc43153f17b0c20f86a9a6777ecfbff788b92a596d9","sha256:7368d813e4496ff597886602d081d5e9e4f28db6506e7e4e4d43c990bb067db5"],"state_sha256":"c382d49ec656bc3eedabb459be4ed532dcc0a5f076cd8bbcae1de6bc6c9b6ed4"}