{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IKQFAM4JKWQY3F5LZ6YMATYHZT","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":"41fb81b70e74c9716af7ab8ebdba4459599af81c7c138c581d8a66885768b6bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-09T10:08:13Z","title_canon_sha256":"e1da99e27b78050111cfb974b46686ebf81b690806f18178919c712013616f4e"},"schema_version":"1.0","source":{"id":"1803.03446","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03446","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03446v2","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03446","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"IKQFAM4JKWQY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IKQFAM4JKWQY3F5L","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IKQFAM4J","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:486c4bdc4a92056a914bdcc2a7d460a020c364ab8bb13ac296f2573aea7eba4f","target":"graph","created_at":"2026-05-18T00:21:33Z","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"},"paper":{"abstract_excerpt":"Given a convex co-compact hyperbolic surface $X=\\Gamma\\backslash \\mathbb{H}^2$, we investigate the resonance spectrum $\\mathcal{R}_j$ of the laplacian $\\Delta_j$ on large finite abelian covers $X=\\Gamma_j\\backslash \\mathbb{H}^2$, where $\\Gamma_j$ is a finite index normal subgroup of $\\Gamma$. Let $\\delta$ be the Hausdorff dimension of the limit set of $\\Gamma$. We show that there exists an $\\varepsilon>0$, such that for all $j$, resonances $\\mathcal{R}_j$ in $\\{ \\delta-\\varepsilon< \\mathrm{Re}(s) \\leq \\delta \\}$ are all real and satisfy a Weyl law given by the degree of the cover i.e. $\\vert \\","authors_text":"Frederic Naud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-09T10:08:13Z","title":"Spectral gaps and abelian covers of convex co-compact surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03446","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":"sha256:73423edff618db29d0bfbb8884ae5bcc0a3cbb90929380aa9fc0e7b1c0f87eb5","target":"record","created_at":"2026-05-18T00:21:33Z","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":"41fb81b70e74c9716af7ab8ebdba4459599af81c7c138c581d8a66885768b6bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-09T10:08:13Z","title_canon_sha256":"e1da99e27b78050111cfb974b46686ebf81b690806f18178919c712013616f4e"},"schema_version":"1.0","source":{"id":"1803.03446","kind":"arxiv","version":2}},"canonical_sha256":"42a050338955a18d97abcfb0c04f07ccc2d2c5da3c8c44abcd34e4cf27e018eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42a050338955a18d97abcfb0c04f07ccc2d2c5da3c8c44abcd34e4cf27e018eb","first_computed_at":"2026-05-18T00:21:33.932450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:33.932450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dq/b8ENFLV5B189N3izgcniO2g6f4uTFItK0Zx/yr//1ist3GA6we0C++CZioWLIVtte73GRA+m/2ALGnRroBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:33.933179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03446","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73423edff618db29d0bfbb8884ae5bcc0a3cbb90929380aa9fc0e7b1c0f87eb5","sha256:486c4bdc4a92056a914bdcc2a7d460a020c364ab8bb13ac296f2573aea7eba4f"],"state_sha256":"b241778c166e5ad2ce350b46bd17f28e3588cbba43592d6d95789e18f12a16e9"}