{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CZLKLCGJ7LDPCPGVYOV5JMXU44","short_pith_number":"pith:CZLKLCGJ","canonical_record":{"source":{"id":"1704.08546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-04-27T13:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"b0a5402d22e34c9a9885eae36287bf812a569ea4f09408cf13fbd09e7a36a144","abstract_canon_sha256":"916d1edcad5b62346ec706ced2d2263f43a10f4b1458f433132624dd45363d66"},"schema_version":"1.0"},"canonical_sha256":"1656a588c9fac6f13cd5c3abd4b2f4e71596a138751659594056dbf111d26ad0","source":{"kind":"arxiv","id":"1704.08546","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08546","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08546v1","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08546","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"CZLKLCGJ7LDP","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CZLKLCGJ7LDPCPGV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CZLKLCGJ","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CZLKLCGJ7LDPCPGVYOV5JMXU44","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-04-27T13:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"b0a5402d22e34c9a9885eae36287bf812a569ea4f09408cf13fbd09e7a36a144","abstract_canon_sha256":"916d1edcad5b62346ec706ced2d2263f43a10f4b1458f433132624dd45363d66"},"schema_version":"1.0"},"canonical_sha256":"1656a588c9fac6f13cd5c3abd4b2f4e71596a138751659594056dbf111d26ad0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:27.412456Z","signature_b64":"8ANROoAncFEEpGSTsAychXncs0C/VLDOzBuiFDxlm462ed3xYRPK1pepPDEfvPeqBRVlcFyxK/iMRcXK0+8qBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1656a588c9fac6f13cd5c3abd4b2f4e71596a138751659594056dbf111d26ad0","last_reissued_at":"2026-05-18T00:45:27.412054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:27.412054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08546","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K48Fcpa04Yt2m//oKhN8PqFX2CZnHgBqHDKkX5Zhw/wafrmWJeNqbLunakzpfFtaoEU3ldiFDcB1VIzojVntDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:06:07.998293Z"},"content_sha256":"46b8d55fbc965beb9cd4763cf28e9f13f3058f501cd7d77179d7bf99bcbc52be","schema_version":"1.0","event_id":"sha256:46b8d55fbc965beb9cd4763cf28e9f13f3058f501cd7d77179d7bf99bcbc52be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CZLKLCGJ7LDPCPGVYOV5JMXU44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L-functions and sharp resonances of infinite index congruence subgroups of $SL_2(\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Dmitry Jakobson, Frederic Naud","submitted_at":"2017-04-27T13:04:00Z","abstract_excerpt":"For convex co-compact subgroups of SL2(Z) we consider the \"congruence subgroups\" for p prime. We prove a factorization formula for the Selberg zeta function in term of L-functions related to irreducible representations of the Galois group SL2(Fp) of the covering, together with a priori bounds and analytic continuation. We use this factorization property combined with an averaging technique over representations to prove a new existence result of non-trivial resonances in an effective low frequency strip."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08546","kind":"arxiv","version":1},"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":"2026-05-18T00:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bxmju5AmXvjJRoYliYl5vu8bWQyuvz5coTUkAU1reS6wu5uddJN9BEY69fvz5X4TZUveCT8uKIZ79HmIzokcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:06:07.998648Z"},"content_sha256":"5cd4f6a349222252bbe333388f618a7ede40512421adfa860f60bdb2c4d9eac5","schema_version":"1.0","event_id":"sha256:5cd4f6a349222252bbe333388f618a7ede40512421adfa860f60bdb2c4d9eac5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44/bundle.json","state_url":"https://pith.science/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44/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":"2026-05-28T03:06:07Z","links":{"resolver":"https://pith.science/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44","bundle":"https://pith.science/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44/bundle.json","state":"https://pith.science/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZLKLCGJ7LDPCPGVYOV5JMXU44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CZLKLCGJ7LDPCPGVYOV5JMXU44","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":"916d1edcad5b62346ec706ced2d2263f43a10f4b1458f433132624dd45363d66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-04-27T13:04:00Z","title_canon_sha256":"b0a5402d22e34c9a9885eae36287bf812a569ea4f09408cf13fbd09e7a36a144"},"schema_version":"1.0","source":{"id":"1704.08546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08546","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08546v1","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08546","created_at":"2026-05-18T00:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"CZLKLCGJ7LDP","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CZLKLCGJ7LDPCPGV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CZLKLCGJ","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:5cd4f6a349222252bbe333388f618a7ede40512421adfa860f60bdb2c4d9eac5","target":"graph","created_at":"2026-05-18T00:45:27Z","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":"For convex co-compact subgroups of SL2(Z) we consider the \"congruence subgroups\" for p prime. We prove a factorization formula for the Selberg zeta function in term of L-functions related to irreducible representations of the Galois group SL2(Fp) of the covering, together with a priori bounds and analytic continuation. We use this factorization property combined with an averaging technique over representations to prove a new existence result of non-trivial resonances in an effective low frequency strip.","authors_text":"Dmitry Jakobson, Frederic Naud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-04-27T13:04:00Z","title":"L-functions and sharp resonances of infinite index congruence subgroups of $SL_2(\\mathbb{Z})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08546","kind":"arxiv","version":1},"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":"sha256:46b8d55fbc965beb9cd4763cf28e9f13f3058f501cd7d77179d7bf99bcbc52be","target":"record","created_at":"2026-05-18T00:45:27Z","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":"916d1edcad5b62346ec706ced2d2263f43a10f4b1458f433132624dd45363d66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-04-27T13:04:00Z","title_canon_sha256":"b0a5402d22e34c9a9885eae36287bf812a569ea4f09408cf13fbd09e7a36a144"},"schema_version":"1.0","source":{"id":"1704.08546","kind":"arxiv","version":1}},"canonical_sha256":"1656a588c9fac6f13cd5c3abd4b2f4e71596a138751659594056dbf111d26ad0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1656a588c9fac6f13cd5c3abd4b2f4e71596a138751659594056dbf111d26ad0","first_computed_at":"2026-05-18T00:45:27.412054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:27.412054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ANROoAncFEEpGSTsAychXncs0C/VLDOzBuiFDxlm462ed3xYRPK1pepPDEfvPeqBRVlcFyxK/iMRcXK0+8qBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:27.412456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46b8d55fbc965beb9cd4763cf28e9f13f3058f501cd7d77179d7bf99bcbc52be","sha256:5cd4f6a349222252bbe333388f618a7ede40512421adfa860f60bdb2c4d9eac5"],"state_sha256":"282dfb5330b374fba992ce4226064cd594d1ed2158dd9974296a11074ece2ce6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K1Ky+/ENHgSuS4x/C0fAwEXkHYG3qZIsQi21G2CCIaQ5pyFbfptgcRcMncVoXy/VodZZnpdBzn1XD2/W/VViDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:06:08.000621Z","bundle_sha256":"78413dce832a763db89687b020129d783ad8f0fef704a1a78d99b1e2e7a1772e"}}