{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:PW272ZLR7X2MLBGYAVFPKHDHF5","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":"1c16e2b606f4d12728af721facf8c80b6d9a51ec26f60de34258c4add3d3d81c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-06-30T08:47:04Z","title_canon_sha256":"9a95c38d5f6f644f6dfed30cbcfbb2636b82f8e9646e106211f22deac5fbfe84"},"schema_version":"1.0","source":{"id":"0806.4829","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4829","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4829v3","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4829","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"pith_short_12","alias_value":"PW272ZLR7X2M","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"PW272ZLR7X2MLBGY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"PW272ZLR","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:46d09bc4704ec1382872ba204cdbbf894be186a360f097a6dc179da53497545c","target":"graph","created_at":"2026-05-18T02:27:49Z","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":"It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to any congruence subgroup of the modular groups in SL(2,R) and SL(2,C).","authors_text":"Yasufumi Hashimoto","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-06-30T08:47:04Z","title":"Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4829","kind":"arxiv","version":3},"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":"sha256:6d02049890037ce51c606f252461b9e59398f99a4fbd0001dd9e760fd47f1eb0","target":"record","created_at":"2026-05-18T02:27:49Z","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":"1c16e2b606f4d12728af721facf8c80b6d9a51ec26f60de34258c4add3d3d81c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-06-30T08:47:04Z","title_canon_sha256":"9a95c38d5f6f644f6dfed30cbcfbb2636b82f8e9646e106211f22deac5fbfe84"},"schema_version":"1.0","source":{"id":"0806.4829","kind":"arxiv","version":3}},"canonical_sha256":"7db5fd6571fdf4c584d8054af51c672f50c87b79b1924516f7d296f2f0d432b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7db5fd6571fdf4c584d8054af51c672f50c87b79b1924516f7d296f2f0d432b0","first_computed_at":"2026-05-18T02:27:49.960774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:49.960774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YdRoRlzlbNvm04tFZgMDMG+ipz3BeVqMYtz7be8WLn+q8q+o0earx8MGt9qXm6A+VrzmCliySoNzVIK5oocLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:49.961158Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4829","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d02049890037ce51c606f252461b9e59398f99a4fbd0001dd9e760fd47f1eb0","sha256:46d09bc4704ec1382872ba204cdbbf894be186a360f097a6dc179da53497545c"],"state_sha256":"d666f00ace407945a605831387295f49b6df9e0ecd31bd669cc5eb9f81c25a5d"}