{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:UGHRHNJTM7S6NSNSJKCFH3VCMZ","short_pith_number":"pith:UGHRHNJT","schema_version":"1.0","canonical_sha256":"a18f13b53367e5e6c9b24a8453eea2667bfaa6a45d22bef38ceef78d2c1c45f3","source":{"kind":"arxiv","id":"2102.11196","version":4},"attestation_state":"computed","paper":{"title":"Micro-local analysis of contact Anosov flows and band structure of the Ruelle spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Faure, Masato Tsujii","submitted_at":"2021-02-22T17:19:33Z","abstract_excerpt":"We develop a geometrical micro-local analysis of contact Anosov flow, such as geodesic flow on negatively curved manifold. This micro-local analysis is based on wave-packet transform discussed in arXiv:1706.09307. The main result is that the transfer operator is well approximated (in the high frequency limit) by the quantization of the Hamiltonian flow naturally defined from the contact Anosov flow and extended to some vector bundle over the symplectization set. This gives a few important consequences: the discrete eigenvalues of the generator of transfer operators, called Ruelle spectrum, are"},"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":"2102.11196","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-02-22T17:19:33Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"3761fcfdcb53b027b5f25b3e9f524573ad78482e7d9a149fed5e225385fcadfd","abstract_canon_sha256":"04a6237a8ac78fe0119f2209ea5c6c8b1e76dcd520515b667d73e49ebaa47239"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:02.150027Z","signature_b64":"PpKi9vgiDvfl0zNkPPXOV6oZ7dNMvg2XmdLA4C7nCgZSEOfa+KRErmAbm/9+t3xXN7n+AjqWTjM8N2ubq/A5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a18f13b53367e5e6c9b24a8453eea2667bfaa6a45d22bef38ceef78d2c1c45f3","last_reissued_at":"2026-07-05T10:27:02.149193Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:02.149193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Micro-local analysis of contact Anosov flows and band structure of the Ruelle spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Faure, Masato Tsujii","submitted_at":"2021-02-22T17:19:33Z","abstract_excerpt":"We develop a geometrical micro-local analysis of contact Anosov flow, such as geodesic flow on negatively curved manifold. This micro-local analysis is based on wave-packet transform discussed in arXiv:1706.09307. The main result is that the transfer operator is well approximated (in the high frequency limit) by the quantization of the Hamiltonian flow naturally defined from the contact Anosov flow and extended to some vector bundle over the symplectization set. This gives a few important consequences: the discrete eigenvalues of the generator of transfer operators, called Ruelle spectrum, are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11196","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.11196/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2102.11196","created_at":"2026-07-05T10:27:02.149308+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.11196v4","created_at":"2026-07-05T10:27:02.149308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11196","created_at":"2026-07-05T10:27:02.149308+00:00"},{"alias_kind":"pith_short_12","alias_value":"UGHRHNJTM7S6","created_at":"2026-07-05T10:27:02.149308+00:00"},{"alias_kind":"pith_short_16","alias_value":"UGHRHNJTM7S6NSNS","created_at":"2026-07-05T10:27:02.149308+00:00"},{"alias_kind":"pith_short_8","alias_value":"UGHRHNJT","created_at":"2026-07-05T10:27:02.149308+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.04320","citing_title":"Egorov's theorem in the Weyl--H\\\"ormander calculus","ref_index":2023,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ","json":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ.json","graph_json":"https://pith.science/api/pith-number/UGHRHNJTM7S6NSNSJKCFH3VCMZ/graph.json","events_json":"https://pith.science/api/pith-number/UGHRHNJTM7S6NSNSJKCFH3VCMZ/events.json","paper":"https://pith.science/paper/UGHRHNJT"},"agent_actions":{"view_html":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ","download_json":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ.json","view_paper":"https://pith.science/paper/UGHRHNJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.11196&json=true","fetch_graph":"https://pith.science/api/pith-number/UGHRHNJTM7S6NSNSJKCFH3VCMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UGHRHNJTM7S6NSNSJKCFH3VCMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ/action/storage_attestation","attest_author":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ/action/author_attestation","sign_citation":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ/action/citation_signature","submit_replication":"https://pith.science/pith/UGHRHNJTM7S6NSNSJKCFH3VCMZ/action/replication_record"}},"created_at":"2026-07-05T10:27:02.149308+00:00","updated_at":"2026-07-05T10:27:02.149308+00:00"}