{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:OTH2G76QW4UGWCFQHDY6R3GWCQ","short_pith_number":"pith:OTH2G76Q","schema_version":"1.0","canonical_sha256":"74cfa37fd0b7286b08b038f1e8ecd614230d87929b73cc8daf9777737769a1af","source":{"kind":"arxiv","id":"2106.02555","version":2},"attestation_state":"computed","paper":{"title":"Extension of Alon's and Friedman's conjectures to Schottky surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.SP","authors_text":"Fr\\'ed\\'eric Naud, Michael Magee","submitted_at":"2021-06-04T15:39:28Z","abstract_excerpt":"Let $X=\\Lambda\\backslash\\mathbb{H}$ be a Schottky surface, that is, a conformally compact hyperbolic surface of infinite area. Let $\\delta$ denote the Hausdorff dimension of the limit set of $\\Lambda$.\n  We prove that for any compact subset $\\mathcal{K} \\subset\\{\\,s\\,:\\,\\Re(s)>\\frac{\\delta}{2}\\,\\}$, if one picks a random degree $n$ cover $X_{n}$ of $X$ uniformly at random, then with probability tending to one as $n\\to\\infty$, there are no resonances of $X_{n}$ in $\\mathcal{K}$ other than those already belonging to $X$ (and with the same multiplicity). This result is conjectured to be the optim"},"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":"2106.02555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2021-06-04T15:39:28Z","cross_cats_sorted":["math.AP","math.PR"],"title_canon_sha256":"44b291b9898bb1ebc5f188517c7031238b2eff9c913836b09644007afd941e51","abstract_canon_sha256":"a510ae8cacc1e745418b98cb1f06ed81b2d3c94536fa4edbcb548e22cec7e399"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:48:23.692988Z","signature_b64":"uN269g/VDw5pkLaPGHLQAOMoB7iUdlxvd1uxfNREocGbk32ERA+bMdRcagRL6XoZzHrNzkIQkznzUgGqFamJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74cfa37fd0b7286b08b038f1e8ecd614230d87929b73cc8daf9777737769a1af","last_reissued_at":"2026-07-05T02:48:23.692576Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:48:23.692576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension of Alon's and Friedman's conjectures to Schottky surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.SP","authors_text":"Fr\\'ed\\'eric Naud, Michael Magee","submitted_at":"2021-06-04T15:39:28Z","abstract_excerpt":"Let $X=\\Lambda\\backslash\\mathbb{H}$ be a Schottky surface, that is, a conformally compact hyperbolic surface of infinite area. Let $\\delta$ denote the Hausdorff dimension of the limit set of $\\Lambda$.\n  We prove that for any compact subset $\\mathcal{K} \\subset\\{\\,s\\,:\\,\\Re(s)>\\frac{\\delta}{2}\\,\\}$, if one picks a random degree $n$ cover $X_{n}$ of $X$ uniformly at random, then with probability tending to one as $n\\to\\infty$, there are no resonances of $X_{n}$ in $\\mathcal{K}$ other than those already belonging to $X$ (and with the same multiplicity). This result is conjectured to be the optim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.02555","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.02555/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":"2106.02555","created_at":"2026-07-05T02:48:23.692637+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.02555v2","created_at":"2026-07-05T02:48:23.692637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.02555","created_at":"2026-07-05T02:48:23.692637+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTH2G76QW4UG","created_at":"2026-07-05T02:48:23.692637+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTH2G76QW4UGWCFQ","created_at":"2026-07-05T02:48:23.692637+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTH2G76Q","created_at":"2026-07-05T02:48:23.692637+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.17466","citing_title":"On the spectral stability of finite coverings","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ","json":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ.json","graph_json":"https://pith.science/api/pith-number/OTH2G76QW4UGWCFQHDY6R3GWCQ/graph.json","events_json":"https://pith.science/api/pith-number/OTH2G76QW4UGWCFQHDY6R3GWCQ/events.json","paper":"https://pith.science/paper/OTH2G76Q"},"agent_actions":{"view_html":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ","download_json":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ.json","view_paper":"https://pith.science/paper/OTH2G76Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.02555&json=true","fetch_graph":"https://pith.science/api/pith-number/OTH2G76QW4UGWCFQHDY6R3GWCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OTH2G76QW4UGWCFQHDY6R3GWCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/action/storage_attestation","attest_author":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/action/author_attestation","sign_citation":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/action/citation_signature","submit_replication":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/action/replication_record"}},"created_at":"2026-07-05T02:48:23.692637+00:00","updated_at":"2026-07-05T02:48:23.692637+00:00"}