{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OTH2G76QW4UGWCFQHDY6R3GWCQ","short_pith_number":"pith:OTH2G76Q","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"},"canonical_sha256":"74cfa37fd0b7286b08b038f1e8ecd614230d87929b73cc8daf9777737769a1af","source":{"kind":"arxiv","id":"2106.02555","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OTH2G76QW4UGWCFQHDY6R3GWCQ","target":"record","payload":{"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"},"canonical_sha256":"74cfa37fd0b7286b08b038f1e8ecd614230d87929b73cc8daf9777737769a1af","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"},"source_kind":"arxiv","source_id":"2106.02555","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0bsG2zJjhwzIteNNGJnJbFgFgSibbHRw5UJ4TVyjmSVrSuWQeRSm0QKVb2mC0pp0DMtt/wNBvk7eLjfEeTyNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:31:38.796196Z"},"content_sha256":"665c58baefc9982f7d4bb90ebd096135c04e5edad7f363966d79c26cd4578157","schema_version":"1.0","event_id":"sha256:665c58baefc9982f7d4bb90ebd096135c04e5edad7f363966d79c26cd4578157"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OTH2G76QW4UGWCFQHDY6R3GWCQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xPu2Pjkj3C90CWduNuR4u8LH3ZQyIyTQSBOxAPSmv2cPSiED1ZlwfvTxCfQMRhgAs5dp4kFtRGukUl3qpAP+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:31:38.796852Z"},"content_sha256":"9d1c3ddd082e25bacf49f8e42ecb35cab62a8822d98036b080af94686da76286","schema_version":"1.0","event_id":"sha256:9d1c3ddd082e25bacf49f8e42ecb35cab62a8822d98036b080af94686da76286"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/bundle.json","state_url":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T16:31:38Z","links":{"resolver":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ","bundle":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/bundle.json","state":"https://pith.science/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OTH2G76QW4UGWCFQHDY6R3GWCQ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZhz7w0J8mIXmEfctUnpT82F7SENR8somE4F0Z8xEtWx2syI1ScvlXuGnRvM2NeHnsYtM8kZnPJw3Y76K4JhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:31:38.801518Z","bundle_sha256":"245a104df021746a80cb24c4a6a2c0d116c6e7a692ca2fb3ed0c495f11bf4052"}}