{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YDLHJ7OQYT6KNSCZYTBRLQ6GJV","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":"c4c085ad03c6938f3025990acc31f5131cb253f2cc324f1f4fbfc79037210564","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-02-18T17:08:50Z","title_canon_sha256":"e138af1353e798bf862e7b1c1fb3f4d19d84040ba53025192db3e3e3948562a7"},"schema_version":"1.0","source":{"id":"1002.3569","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3569","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3569v5","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3569","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"YDLHJ7OQYT6K","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YDLHJ7OQYT6KNSCZ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YDLHJ7OQ","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:632cf27943bbb6c03f334f417b8023e181b6c5226116f34e13683a9b88815931","target":"graph","created_at":"2026-05-18T04:42:14Z","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":"We prove various results on the cohomology of arithmetic lattices arising from quaternion algebras over a number field with at least one complex place, including a strong restriction on the allowable weights of cuspidal cohomological automorphic forms and a conditional power saving for their multiplicities when the associated locally symmetric space is a hyperbolic 3-manifold.","authors_text":"Simon Marshall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-02-18T17:08:50Z","title":"Bounds for multiplicities of automorphic forms of cohomological type on GL_2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3569","kind":"arxiv","version":5},"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:e8d42d1d665b92b57a8fa8244d1613509da2c1dfe8780b9b4f822b3ffcb223e4","target":"record","created_at":"2026-05-18T04:42:14Z","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":"c4c085ad03c6938f3025990acc31f5131cb253f2cc324f1f4fbfc79037210564","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-02-18T17:08:50Z","title_canon_sha256":"e138af1353e798bf862e7b1c1fb3f4d19d84040ba53025192db3e3e3948562a7"},"schema_version":"1.0","source":{"id":"1002.3569","kind":"arxiv","version":5}},"canonical_sha256":"c0d674fdd0c4fca6c859c4c315c3c64d5a6741841b41b409a49e2c9ceebbdc44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0d674fdd0c4fca6c859c4c315c3c64d5a6741841b41b409a49e2c9ceebbdc44","first_computed_at":"2026-05-18T04:42:14.605788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:14.605788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PB6RWmtfYyaJzAXQnpXMayXGn8GMG5nm6VFqdGGb7OwV98ZK3NdEStrWoJa0Cg7tJVLUIa73sXPKPMq6KyhJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:14.606162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3569","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8d42d1d665b92b57a8fa8244d1613509da2c1dfe8780b9b4f822b3ffcb223e4","sha256:632cf27943bbb6c03f334f417b8023e181b6c5226116f34e13683a9b88815931"],"state_sha256":"c5def582d954a8f58d3c3c6488d04cb6fc14fee12d81a2a7eb430c3811198810"}