{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6WMPFXTVVGNXCQW5N5VJ4SEYOU","short_pith_number":"pith:6WMPFXTV","schema_version":"1.0","canonical_sha256":"f598f2de75a99b7142dd6f6a9e48987510ee45699fa64a7ffc0914d86d3a3062","source":{"kind":"arxiv","id":"1203.4378","version":1},"attestation_state":"computed","paper":{"title":"Density and localization of resonances for convex co-compact hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fr\\'ed\\'eric Naud (LANLG)","submitted_at":"2012-03-20T10:38:16Z","abstract_excerpt":"Let $X$ be a convex co-compact hyperbolic surface and let $\\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips ${\\sigma\\leq \\re(s) \\leq \\delta}$ with $|\\im(s)| \\leq T$ is less than $O(T^{1+\\delta-\\epsilon(\\sigma)})$ with $\\epsilon>0$ as long as $\\sigma>\\delta/2$. This improves the fractal Weyl upper bounds of Zworski and supports numerical results obtained for various models of quantum chaotic scattering."},"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":"1203.4378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-03-20T10:38:16Z","cross_cats_sorted":[],"title_canon_sha256":"ef055d3c34c4a3a516634809bbed62962085d803dc436bdb72285c68ec5156d2","abstract_canon_sha256":"b11a2f12c1c5a7614d20613f1f4fa5b5d66f7a1f1333a774d87b80a0f21deb6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:39.214249Z","signature_b64":"bTJLbOubGcGLlWXikx14H0hs9xPb/mEDAgNGqJdjSlfp/7HWjDTcNRloggWXDvPaDddBs9vcTFGZQwEkfoJ4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f598f2de75a99b7142dd6f6a9e48987510ee45699fa64a7ffc0914d86d3a3062","last_reissued_at":"2026-05-18T03:59:39.213561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:39.213561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Density and localization of resonances for convex co-compact hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fr\\'ed\\'eric Naud (LANLG)","submitted_at":"2012-03-20T10:38:16Z","abstract_excerpt":"Let $X$ be a convex co-compact hyperbolic surface and let $\\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips ${\\sigma\\leq \\re(s) \\leq \\delta}$ with $|\\im(s)| \\leq T$ is less than $O(T^{1+\\delta-\\epsilon(\\sigma)})$ with $\\epsilon>0$ as long as $\\sigma>\\delta/2$. This improves the fractal Weyl upper bounds of Zworski and supports numerical results obtained for various models of quantum chaotic scattering."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4378","kind":"arxiv","version":1},"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":"1203.4378","created_at":"2026-05-18T03:59:39.213686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.4378v1","created_at":"2026-05-18T03:59:39.213686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4378","created_at":"2026-05-18T03:59:39.213686+00:00"},{"alias_kind":"pith_short_12","alias_value":"6WMPFXTVVGNX","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6WMPFXTVVGNXCQW5","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6WMPFXTV","created_at":"2026-05-18T12:26:56.085431+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/6WMPFXTVVGNXCQW5N5VJ4SEYOU","json":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU.json","graph_json":"https://pith.science/api/pith-number/6WMPFXTVVGNXCQW5N5VJ4SEYOU/graph.json","events_json":"https://pith.science/api/pith-number/6WMPFXTVVGNXCQW5N5VJ4SEYOU/events.json","paper":"https://pith.science/paper/6WMPFXTV"},"agent_actions":{"view_html":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU","download_json":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU.json","view_paper":"https://pith.science/paper/6WMPFXTV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.4378&json=true","fetch_graph":"https://pith.science/api/pith-number/6WMPFXTVVGNXCQW5N5VJ4SEYOU/graph.json","fetch_events":"https://pith.science/api/pith-number/6WMPFXTVVGNXCQW5N5VJ4SEYOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU/action/storage_attestation","attest_author":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU/action/author_attestation","sign_citation":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU/action/citation_signature","submit_replication":"https://pith.science/pith/6WMPFXTVVGNXCQW5N5VJ4SEYOU/action/replication_record"}},"created_at":"2026-05-18T03:59:39.213686+00:00","updated_at":"2026-05-18T03:59:39.213686+00:00"}