{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OW2H2G7Q7MNQHYRS2DUQ45ZEED","short_pith_number":"pith:OW2H2G7Q","canonical_record":{"source":{"id":"1210.5979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-22T17:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"a1ed7df49ee0a06bc58a68608d9506fc3233505d8a0cacd991e4ea0fe1328a9f","abstract_canon_sha256":"11adc76f76eaaba6396b542aff3416ce97d636491a7b1cdbbdcd9dbeb96d4168"},"schema_version":"1.0"},"canonical_sha256":"75b47d1bf0fb1b03e232d0e90e772420f3791470cc3f188ba7c863e234f6c2ac","source":{"kind":"arxiv","id":"1210.5979","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5979","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5979v2","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5979","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"OW2H2G7Q7MNQ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OW2H2G7Q7MNQHYRS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OW2H2G7Q","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OW2H2G7Q7MNQHYRS2DUQ45ZEED","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-22T17:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"a1ed7df49ee0a06bc58a68608d9506fc3233505d8a0cacd991e4ea0fe1328a9f","abstract_canon_sha256":"11adc76f76eaaba6396b542aff3416ce97d636491a7b1cdbbdcd9dbeb96d4168"},"schema_version":"1.0"},"canonical_sha256":"75b47d1bf0fb1b03e232d0e90e772420f3791470cc3f188ba7c863e234f6c2ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:14.467266Z","signature_b64":"EEUYSl6liNIHvJwpthdgTHvw3qJzmf5F9sY7Iooc2XmrJ2Gu7HLK1aHZDU4krTobBfsagv1YyKcIV37uzLsACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75b47d1bf0fb1b03e232d0e90e772420f3791470cc3f188ba7c863e234f6c2ac","last_reissued_at":"2026-05-18T03:25:14.466794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:14.466794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5979","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":"2026-05-18T03:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ru2pI6uui3cd3gIlX4mT6nwn8Buue5qzFZUmGHJxi9f0fEym/MO7mKuoy2jqWmHmJDBGCpSxAp45Cb1PSfodDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:45:23.301894Z"},"content_sha256":"faf26705475a9ed67a824ad9713c5035dfa1dbe79f48b4d11c9f56c9c9e4279e","schema_version":"1.0","event_id":"sha256:faf26705475a9ed67a824ad9713c5035dfa1dbe79f48b4d11c9f56c9c9e4279e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OW2H2G7Q7MNQHYRS2DUQ45ZEED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Congruence properties of induced representations and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexei Venkov, Arash Momeni, Dieter Mayer","submitted_at":"2012-10-22T17:37:34Z","abstract_excerpt":"In this paper we study congruence properties of the representations $U_\\alpha:=U^{PSL(2,\\mathbb{Z})}_{\\chi_\\alpha}$ of the projective modular group ${\\rm PSL}(2,\\mathbb{Z})$ induced from a family $\\chi_\\alpha$ of characters for the Hecke congruence subgroup $\\Gamma_0(4)$ basically introduced by A. Selberg. Interest in the representations $U_\\alpha$ stems from their appearance in the transfer operator approach to Selberg's zeta function for this Fuchsian group and character $\\chi_\\alpha$. Hence the location of the nontrivial zeros of this function and therefore also the spectral properties of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5979","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":"2026-05-18T03:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q69iSF7H88Bi4MVZ1UiCQgFkcBwpkjFR9KSrJFQ2CersWC/OJW0ZPwMF5Lxt2INA18uBYXeynRvI0xa+T3wUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:45:23.302236Z"},"content_sha256":"50f832a5da46312761cba46c27768a39c457e5218cc8c22ce878617b7113fa98","schema_version":"1.0","event_id":"sha256:50f832a5da46312761cba46c27768a39c457e5218cc8c22ce878617b7113fa98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED/bundle.json","state_url":"https://pith.science/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED/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":"2026-06-25T23:45:23Z","links":{"resolver":"https://pith.science/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED","bundle":"https://pith.science/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED/bundle.json","state":"https://pith.science/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OW2H2G7Q7MNQHYRS2DUQ45ZEED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OW2H2G7Q7MNQHYRS2DUQ45ZEED","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":"11adc76f76eaaba6396b542aff3416ce97d636491a7b1cdbbdcd9dbeb96d4168","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-22T17:37:34Z","title_canon_sha256":"a1ed7df49ee0a06bc58a68608d9506fc3233505d8a0cacd991e4ea0fe1328a9f"},"schema_version":"1.0","source":{"id":"1210.5979","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5979","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5979v2","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5979","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"OW2H2G7Q7MNQ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OW2H2G7Q7MNQHYRS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OW2H2G7Q","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:50f832a5da46312761cba46c27768a39c457e5218cc8c22ce878617b7113fa98","target":"graph","created_at":"2026-05-18T03:25:14Z","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":"In this paper we study congruence properties of the representations $U_\\alpha:=U^{PSL(2,\\mathbb{Z})}_{\\chi_\\alpha}$ of the projective modular group ${\\rm PSL}(2,\\mathbb{Z})$ induced from a family $\\chi_\\alpha$ of characters for the Hecke congruence subgroup $\\Gamma_0(4)$ basically introduced by A. Selberg. Interest in the representations $U_\\alpha$ stems from their appearance in the transfer operator approach to Selberg's zeta function for this Fuchsian group and character $\\chi_\\alpha$. Hence the location of the nontrivial zeros of this function and therefore also the spectral properties of t","authors_text":"Alexei Venkov, Arash Momeni, Dieter Mayer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-22T17:37:34Z","title":"Congruence properties of induced representations and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5979","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:faf26705475a9ed67a824ad9713c5035dfa1dbe79f48b4d11c9f56c9c9e4279e","target":"record","created_at":"2026-05-18T03:25:14Z","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":"11adc76f76eaaba6396b542aff3416ce97d636491a7b1cdbbdcd9dbeb96d4168","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-22T17:37:34Z","title_canon_sha256":"a1ed7df49ee0a06bc58a68608d9506fc3233505d8a0cacd991e4ea0fe1328a9f"},"schema_version":"1.0","source":{"id":"1210.5979","kind":"arxiv","version":2}},"canonical_sha256":"75b47d1bf0fb1b03e232d0e90e772420f3791470cc3f188ba7c863e234f6c2ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75b47d1bf0fb1b03e232d0e90e772420f3791470cc3f188ba7c863e234f6c2ac","first_computed_at":"2026-05-18T03:25:14.466794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:14.466794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EEUYSl6liNIHvJwpthdgTHvw3qJzmf5F9sY7Iooc2XmrJ2Gu7HLK1aHZDU4krTobBfsagv1YyKcIV37uzLsACw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:14.467266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5979","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faf26705475a9ed67a824ad9713c5035dfa1dbe79f48b4d11c9f56c9c9e4279e","sha256:50f832a5da46312761cba46c27768a39c457e5218cc8c22ce878617b7113fa98"],"state_sha256":"cf54378e99e92675c96b638d2d8075426c10468d5fb455623dee05533bb4d98b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjwNedyFLSrU2w6p0Er+p2wj6hGpHHKRRYv+91scesV1/ZbvW0BpIQSun/wrm/FE32C5g4YYJCDZ5QmY5d44Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:45:23.304277Z","bundle_sha256":"449402df400f4432b690626f765aa9e719c40d32c3c593b36ae19f49359216ac"}}