{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OTH2G76QW4UGWCFQHDY6R3GWCQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a510ae8cacc1e745418b98cb1f06ed81b2d3c94536fa4edbcb548e22cec7e399","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2021-06-04T15:39:28Z","title_canon_sha256":"44b291b9898bb1ebc5f188517c7031238b2eff9c913836b09644007afd941e51"},"schema_version":"1.0","source":{"id":"2106.02555","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.02555","created_at":"2026-07-05T02:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"2106.02555v2","created_at":"2026-07-05T02:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.02555","created_at":"2026-07-05T02:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"OTH2G76QW4UG","created_at":"2026-07-05T02:48:23Z"},{"alias_kind":"pith_short_16","alias_value":"OTH2G76QW4UGWCFQ","created_at":"2026-07-05T02:48:23Z"},{"alias_kind":"pith_short_8","alias_value":"OTH2G76Q","created_at":"2026-07-05T02:48:23Z"}],"graph_snapshots":[{"event_id":"sha256:9d1c3ddd082e25bacf49f8e42ecb35cab62a8822d98036b080af94686da76286","target":"graph","created_at":"2026-07-05T02:48:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.02555/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Fr\\'ed\\'eric Naud, Michael Magee","cross_cats":["math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2021-06-04T15:39:28Z","title":"Extension of Alon's and Friedman's conjectures to Schottky surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.02555","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:665c58baefc9982f7d4bb90ebd096135c04e5edad7f363966d79c26cd4578157","target":"record","created_at":"2026-07-05T02:48:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a510ae8cacc1e745418b98cb1f06ed81b2d3c94536fa4edbcb548e22cec7e399","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2021-06-04T15:39:28Z","title_canon_sha256":"44b291b9898bb1ebc5f188517c7031238b2eff9c913836b09644007afd941e51"},"schema_version":"1.0","source":{"id":"2106.02555","kind":"arxiv","version":2}},"canonical_sha256":"74cfa37fd0b7286b08b038f1e8ecd614230d87929b73cc8daf9777737769a1af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74cfa37fd0b7286b08b038f1e8ecd614230d87929b73cc8daf9777737769a1af","first_computed_at":"2026-07-05T02:48:23.692576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:48:23.692576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uN269g/VDw5pkLaPGHLQAOMoB7iUdlxvd1uxfNREocGbk32ERA+bMdRcagRL6XoZzHrNzkIQkznzUgGqFamJCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:48:23.692988Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.02555","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:665c58baefc9982f7d4bb90ebd096135c04e5edad7f363966d79c26cd4578157","sha256:9d1c3ddd082e25bacf49f8e42ecb35cab62a8822d98036b080af94686da76286"],"state_sha256":"2e8ac29cf8e65281497bc94639a70560b5762d72aafac4dff09b3c9ad6c6ec72"}