{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BVL6PFRH4YHSRSGGLWDSWA2ACN","short_pith_number":"pith:BVL6PFRH","canonical_record":{"source":{"id":"1010.1010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-05T20:14:34Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"62934e0c9f0222d15062dbd3df0aa69c76df63ddf700ae2e1f869aca05a15711","abstract_canon_sha256":"fda7765c747baca48aefc69d2f99544c7d4a3b8a796e450db739e2c274b08741"},"schema_version":"1.0"},"canonical_sha256":"0d57e79627e60f28c8c65d872b03401351b2450212633c57bf409bc8b93e6821","source":{"kind":"arxiv","id":"1010.1010","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1010","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1010v2","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1010","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"BVL6PFRH4YHS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BVL6PFRH4YHSRSGG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BVL6PFRH","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BVL6PFRH4YHSRSGGLWDSWA2ACN","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-05T20:14:34Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"62934e0c9f0222d15062dbd3df0aa69c76df63ddf700ae2e1f869aca05a15711","abstract_canon_sha256":"fda7765c747baca48aefc69d2f99544c7d4a3b8a796e450db739e2c274b08741"},"schema_version":"1.0"},"canonical_sha256":"0d57e79627e60f28c8c65d872b03401351b2450212633c57bf409bc8b93e6821","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:47.590270Z","signature_b64":"IZnVNrNRhorqBY93/s5Hc/fkCQi4bvQAEkSgOSEGi0uC+sIhGzlBgUsMmGUc7mFbBGgkcba0WthKbTiyxKGBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d57e79627e60f28c8c65d872b03401351b2450212633c57bf409bc8b93e6821","last_reissued_at":"2026-05-18T04:35:47.589772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:47.589772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1010","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":"2026-05-18T04:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVNHyaFu9JhxFiXFugrPJaRZGfZmWbXCNuYnqWqF85UdwT0Etw5ARUhF9Hd8e67lEZnnt/hYUPtkf5CTuT4bAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:24:08.489835Z"},"content_sha256":"5aefbd182351cc884adec59d2bba75be28b91c36ab1338aa0810d3b4977c3690","schema_version":"1.0","event_id":"sha256:5aefbd182351cc884adec59d2bba75be28b91c36ab1338aa0810d3b4977c3690"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BVL6PFRH4YHSRSGGLWDSWA2ACN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A uniform spectral gap for congruence covers of a hyperbolic manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NT","authors_text":"Dubi Kelmer, Lior Silberman","submitted_at":"2010-10-05T20:14:34Z","abstract_excerpt":"Let $G$ be $\\SO(n,1)$ or $\\SU(n,1)$ and let $\\Gamma\\subset G$ denote an arithmetic lattice. The hyperbolic manifold $\\Gamma\\backslash \\calH$ comes with a natural family of covers, coming from the congruence subgroups of $\\Gamma$. In many applications, it is useful to have a bound for the spectral gap that is uniform for this family. When $\\Gamma$ is itself a congruence lattice, there are very good bounds coming from known results towards the Ramanujan conjectures. In this paper, we establish an effective bound that is uniform for congruence subgroups of a non-congruence lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1010","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":""},"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":"2026-05-18T04:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hNLn567lvnqAIjeJLAXBLGgKwobpF0qxl1PXV/yvkSxZ/VRPkbykoAB+5RUkXRAfqaIp6Vr1bkxiO72OK/QrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:24:08.490233Z"},"content_sha256":"ad66bd2965b1f2fd3a43242c9d7ea76cf8c65ba68dc8e745dccf8ab88d6a018e","schema_version":"1.0","event_id":"sha256:ad66bd2965b1f2fd3a43242c9d7ea76cf8c65ba68dc8e745dccf8ab88d6a018e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN/bundle.json","state_url":"https://pith.science/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN/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":"2026-06-09T11:24:08Z","links":{"resolver":"https://pith.science/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN","bundle":"https://pith.science/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN/bundle.json","state":"https://pith.science/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVL6PFRH4YHSRSGGLWDSWA2ACN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BVL6PFRH4YHSRSGGLWDSWA2ACN","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":"fda7765c747baca48aefc69d2f99544c7d4a3b8a796e450db739e2c274b08741","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-05T20:14:34Z","title_canon_sha256":"62934e0c9f0222d15062dbd3df0aa69c76df63ddf700ae2e1f869aca05a15711"},"schema_version":"1.0","source":{"id":"1010.1010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1010","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1010v2","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1010","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"BVL6PFRH4YHS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BVL6PFRH4YHSRSGG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BVL6PFRH","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ad66bd2965b1f2fd3a43242c9d7ea76cf8c65ba68dc8e745dccf8ab88d6a018e","target":"graph","created_at":"2026-05-18T04:35:47Z","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":"Let $G$ be $\\SO(n,1)$ or $\\SU(n,1)$ and let $\\Gamma\\subset G$ denote an arithmetic lattice. The hyperbolic manifold $\\Gamma\\backslash \\calH$ comes with a natural family of covers, coming from the congruence subgroups of $\\Gamma$. In many applications, it is useful to have a bound for the spectral gap that is uniform for this family. When $\\Gamma$ is itself a congruence lattice, there are very good bounds coming from known results towards the Ramanujan conjectures. In this paper, we establish an effective bound that is uniform for congruence subgroups of a non-congruence lattice.","authors_text":"Dubi Kelmer, Lior Silberman","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-05T20:14:34Z","title":"A uniform spectral gap for congruence covers of a hyperbolic manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1010","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":"sha256:5aefbd182351cc884adec59d2bba75be28b91c36ab1338aa0810d3b4977c3690","target":"record","created_at":"2026-05-18T04:35:47Z","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":"fda7765c747baca48aefc69d2f99544c7d4a3b8a796e450db739e2c274b08741","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-05T20:14:34Z","title_canon_sha256":"62934e0c9f0222d15062dbd3df0aa69c76df63ddf700ae2e1f869aca05a15711"},"schema_version":"1.0","source":{"id":"1010.1010","kind":"arxiv","version":2}},"canonical_sha256":"0d57e79627e60f28c8c65d872b03401351b2450212633c57bf409bc8b93e6821","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d57e79627e60f28c8c65d872b03401351b2450212633c57bf409bc8b93e6821","first_computed_at":"2026-05-18T04:35:47.589772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:47.589772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IZnVNrNRhorqBY93/s5Hc/fkCQi4bvQAEkSgOSEGi0uC+sIhGzlBgUsMmGUc7mFbBGgkcba0WthKbTiyxKGBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:47.590270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aefbd182351cc884adec59d2bba75be28b91c36ab1338aa0810d3b4977c3690","sha256:ad66bd2965b1f2fd3a43242c9d7ea76cf8c65ba68dc8e745dccf8ab88d6a018e"],"state_sha256":"211cb0ffc43c852f187c0b5a52b5585cbbac4d27e3cc27b85d5cae0b9a26a21c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ULxLJk9MM9DYMQw/J/dO5LdncfVdoPwA/Pu6YI/75r1/20UlGWd6/ibeHsAQVm/1GaLc4L/zDbQh/CMVJvmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:24:08.492647Z","bundle_sha256":"d4718366d0ed769aa2d3614a2dc496f8fab2923cc4efdd3245ef592ee1156d1b"}}