{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2F43Q5GL4PGVGEUTC4A4WDTOH6","short_pith_number":"pith:2F43Q5GL","schema_version":"1.0","canonical_sha256":"d179b874cbe3cd5312931701cb0e6e3faa73aeba9a95bb057ce771fe9ad63f1e","source":{"kind":"arxiv","id":"1512.00836","version":2},"attestation_state":"computed","paper":{"title":"Improved fractal Weyl bounds for hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"David Borthwick, Semyon Dyatlov, Tobias Weich","submitted_at":"2015-12-02T20:38:55Z","abstract_excerpt":"We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension $\\delta$ of its limit set. More precisely, we show that as $R\\to\\infty$, the number of resonances in the box $[R,R+1]+i[-\\beta,0]$ is $O(R^{m(\\beta,\\delta)+})$, where the exponent $m(\\beta,\\delta)=\\min(2\\delta+2\\beta+1-n,\\delta)$ changes its behavior at $\\beta=(n-1-\\delta)/2$. In the case $\\delta<(n-1)/2$, we also give an improved resolvent upper bound in the standard resonance free strip $\\{\\mathrm{Im}\\ \\lambda\\ > \\delta-(n-1)/2\\}$. Bo"},"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":"1512.00836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-02T20:38:55Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"65129e2465ba724422df644780726b4a04deaf3a7d46e42ca63e8f56fa4e5af7","abstract_canon_sha256":"f0680f2ae47ff00999aec8eb69e5910abd4d74101a5b5bd5c34a9a9358a44a34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.183973Z","signature_b64":"/4Dp5mQwFu8D8/RLXKxJv1QBfqIgefst+jwm6QJTiDTqxxCV9KK3CZVJUxnT8duDMeiwHv2PxOsJhCnSYncSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d179b874cbe3cd5312931701cb0e6e3faa73aeba9a95bb057ce771fe9ad63f1e","last_reissued_at":"2026-05-17T23:54:27.183355Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.183355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved fractal Weyl bounds for hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"David Borthwick, Semyon Dyatlov, Tobias Weich","submitted_at":"2015-12-02T20:38:55Z","abstract_excerpt":"We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension $\\delta$ of its limit set. More precisely, we show that as $R\\to\\infty$, the number of resonances in the box $[R,R+1]+i[-\\beta,0]$ is $O(R^{m(\\beta,\\delta)+})$, where the exponent $m(\\beta,\\delta)=\\min(2\\delta+2\\beta+1-n,\\delta)$ changes its behavior at $\\beta=(n-1-\\delta)/2$. In the case $\\delta<(n-1)/2$, we also give an improved resolvent upper bound in the standard resonance free strip $\\{\\mathrm{Im}\\ \\lambda\\ > \\delta-(n-1)/2\\}$. Bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00836","kind":"arxiv","version":2},"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":"1512.00836","created_at":"2026-05-17T23:54:27.183456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00836v2","created_at":"2026-05-17T23:54:27.183456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00836","created_at":"2026-05-17T23:54:27.183456+00:00"},{"alias_kind":"pith_short_12","alias_value":"2F43Q5GL4PGV","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2F43Q5GL4PGVGEUT","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2F43Q5GL","created_at":"2026-05-18T12:28:59.999130+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/2F43Q5GL4PGVGEUTC4A4WDTOH6","json":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6.json","graph_json":"https://pith.science/api/pith-number/2F43Q5GL4PGVGEUTC4A4WDTOH6/graph.json","events_json":"https://pith.science/api/pith-number/2F43Q5GL4PGVGEUTC4A4WDTOH6/events.json","paper":"https://pith.science/paper/2F43Q5GL"},"agent_actions":{"view_html":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6","download_json":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6.json","view_paper":"https://pith.science/paper/2F43Q5GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00836&json=true","fetch_graph":"https://pith.science/api/pith-number/2F43Q5GL4PGVGEUTC4A4WDTOH6/graph.json","fetch_events":"https://pith.science/api/pith-number/2F43Q5GL4PGVGEUTC4A4WDTOH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6/action/storage_attestation","attest_author":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6/action/author_attestation","sign_citation":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6/action/citation_signature","submit_replication":"https://pith.science/pith/2F43Q5GL4PGVGEUTC4A4WDTOH6/action/replication_record"}},"created_at":"2026-05-17T23:54:27.183456+00:00","updated_at":"2026-05-17T23:54:27.183456+00:00"}