{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:TL4KA2M2OMGDSXW76ZVALHCNW7","short_pith_number":"pith:TL4KA2M2","schema_version":"1.0","canonical_sha256":"9af8a0699a730c395edff66a059c4db7d9dacb3a36f21164e6de827836d2ba2d","source":{"kind":"arxiv","id":"math/0509369","version":3},"attestation_state":"computed","paper":{"title":"Spectra of differentiable hyperbolic maps","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Masato Tsujii, Viviane Baladi","submitted_at":"2005-09-16T08:53:49Z","abstract_excerpt":"This note is about the spectral properties of transfer operators associated to smooth hyperbolic dynamics. In the first two sections (written in 2006), we state our new results relating such spectra with dynamical determinants, first announced at the conference ``Traces in Geometry, Number Theory and Quantum Fields\" at the Max Planck Institute, Bonn, October 2005. In the last two sections, we give a reader-friendly presentation of some key ideas in our work in the simplest possible settings, including a new proof of a result of Ruelle on expanding endomorphisms. (These last two sections are a "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0509369","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-09-16T08:53:49Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a02b0d63c5f7a2eef385279e56e5b4460520cdfdc5f20497596fdbbcef7fa1e9","abstract_canon_sha256":"eb7bc0f78afd411aa5b19424ff3e1f475a8ba67204595f515b68fa996b85103a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:23.145536Z","signature_b64":"DsH8YsVLb8atuTWQrMYIJqkeWnr1Z97MLZl0viQRFNzZ/33cW6CbA6TcocwUjr8BI3dlgoDoAcJAXeXzEQ5OAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9af8a0699a730c395edff66a059c4db7d9dacb3a36f21164e6de827836d2ba2d","last_reissued_at":"2026-05-18T01:05:23.145031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:23.145031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectra of differentiable hyperbolic maps","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Masato Tsujii, Viviane Baladi","submitted_at":"2005-09-16T08:53:49Z","abstract_excerpt":"This note is about the spectral properties of transfer operators associated to smooth hyperbolic dynamics. In the first two sections (written in 2006), we state our new results relating such spectra with dynamical determinants, first announced at the conference ``Traces in Geometry, Number Theory and Quantum Fields\" at the Max Planck Institute, Bonn, October 2005. In the last two sections, we give a reader-friendly presentation of some key ideas in our work in the simplest possible settings, including a new proof of a result of Ruelle on expanding endomorphisms. (These last two sections are a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509369","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0509369","created_at":"2026-05-18T01:05:23.145107+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0509369v3","created_at":"2026-05-18T01:05:23.145107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509369","created_at":"2026-05-18T01:05:23.145107+00:00"},{"alias_kind":"pith_short_12","alias_value":"TL4KA2M2OMGD","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"TL4KA2M2OMGDSXW7","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"TL4KA2M2","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7","json":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7.json","graph_json":"https://pith.science/api/pith-number/TL4KA2M2OMGDSXW76ZVALHCNW7/graph.json","events_json":"https://pith.science/api/pith-number/TL4KA2M2OMGDSXW76ZVALHCNW7/events.json","paper":"https://pith.science/paper/TL4KA2M2"},"agent_actions":{"view_html":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7","download_json":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7.json","view_paper":"https://pith.science/paper/TL4KA2M2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0509369&json=true","fetch_graph":"https://pith.science/api/pith-number/TL4KA2M2OMGDSXW76ZVALHCNW7/graph.json","fetch_events":"https://pith.science/api/pith-number/TL4KA2M2OMGDSXW76ZVALHCNW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7/action/storage_attestation","attest_author":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7/action/author_attestation","sign_citation":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7/action/citation_signature","submit_replication":"https://pith.science/pith/TL4KA2M2OMGDSXW76ZVALHCNW7/action/replication_record"}},"created_at":"2026-05-18T01:05:23.145107+00:00","updated_at":"2026-05-18T01:05:23.145107+00:00"}