{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:522OSNRS3VJEBB4QRJOHQ2DXVP","short_pith_number":"pith:522OSNRS","schema_version":"1.0","canonical_sha256":"eeb4e93632dd524087908a5c786877abf50fc4c8b7fef136d5e33f727e0846dc","source":{"kind":"arxiv","id":"2305.00527","version":3},"attestation_state":"computed","paper":{"title":"Exponential Mixing Via Additive Combinatorics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CO"],"primary_cat":"math.DS","authors_text":"Osama Khalil","submitted_at":"2023-04-30T16:53:08Z","abstract_excerpt":"We prove that the geodesic flow on a geometrically finite locally symmetric space of negative curvature is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure. The approach is based on constructing a suitable anisotropic Banach space on which the infinitesimal generator of the flow admits an essential spectral gap. A key step in the proof involves estimating certain oscillatory integrals against the Patterson-Sullivan measure. For this purpose, we prove a general result of independent interest asserting that the Fourier transform of measures on $\\mathbb{R}^d$ that do not c"},"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":"2305.00527","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-04-30T16:53:08Z","cross_cats_sorted":["math.CA","math.CO"],"title_canon_sha256":"e6cd676bab8ea5ad98e3a5618bd1ccc0ff7b599bfc949de972a75bbd312e5b55","abstract_canon_sha256":"9a847e6cac185f23a091a79e9143cf5229f5c9f4f27213feeec4593ad8167597"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:42.621787Z","signature_b64":"vuRmr/bO6pYdvHBYPqDcQqnG2abXd/TPZCNNyj+5McFDt/fx41YmvYRkPT1eIFfAG4H/7hE2GlY9AhiPDaIqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeb4e93632dd524087908a5c786877abf50fc4c8b7fef136d5e33f727e0846dc","last_reissued_at":"2026-07-05T09:54:42.621337Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:42.621337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential Mixing Via Additive Combinatorics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CO"],"primary_cat":"math.DS","authors_text":"Osama Khalil","submitted_at":"2023-04-30T16:53:08Z","abstract_excerpt":"We prove that the geodesic flow on a geometrically finite locally symmetric space of negative curvature is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure. The approach is based on constructing a suitable anisotropic Banach space on which the infinitesimal generator of the flow admits an essential spectral gap. A key step in the proof involves estimating certain oscillatory integrals against the Patterson-Sullivan measure. For this purpose, we prove a general result of independent interest asserting that the Fourier transform of measures on $\\mathbb{R}^d$ that do not c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00527","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.00527/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":"2305.00527","created_at":"2026-07-05T09:54:42.621398+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.00527v3","created_at":"2026-07-05T09:54:42.621398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.00527","created_at":"2026-07-05T09:54:42.621398+00:00"},{"alias_kind":"pith_short_12","alias_value":"522OSNRS3VJE","created_at":"2026-07-05T09:54:42.621398+00:00"},{"alias_kind":"pith_short_16","alias_value":"522OSNRS3VJEBB4Q","created_at":"2026-07-05T09:54:42.621398+00:00"},{"alias_kind":"pith_short_8","alias_value":"522OSNRS","created_at":"2026-07-05T09:54:42.621398+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.23731","citing_title":"Fourier decay of equilibrium states and the Fibonacci Hamiltonian","ref_index":1995,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP","json":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP.json","graph_json":"https://pith.science/api/pith-number/522OSNRS3VJEBB4QRJOHQ2DXVP/graph.json","events_json":"https://pith.science/api/pith-number/522OSNRS3VJEBB4QRJOHQ2DXVP/events.json","paper":"https://pith.science/paper/522OSNRS"},"agent_actions":{"view_html":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP","download_json":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP.json","view_paper":"https://pith.science/paper/522OSNRS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.00527&json=true","fetch_graph":"https://pith.science/api/pith-number/522OSNRS3VJEBB4QRJOHQ2DXVP/graph.json","fetch_events":"https://pith.science/api/pith-number/522OSNRS3VJEBB4QRJOHQ2DXVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP/action/storage_attestation","attest_author":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP/action/author_attestation","sign_citation":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP/action/citation_signature","submit_replication":"https://pith.science/pith/522OSNRS3VJEBB4QRJOHQ2DXVP/action/replication_record"}},"created_at":"2026-07-05T09:54:42.621398+00:00","updated_at":"2026-07-05T09:54:42.621398+00:00"}