{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QI66SGD2U2KGXMEHEVCC5ISGH4","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":"fbdc9726692241a7f801f8af683619897070f24b7eb7f4883b42a5501e8a5689","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-12T19:19:37Z","title_canon_sha256":"95b7282146f9568a51402a252120d6368360be4ede519302b616f8c78455844f"},"schema_version":"1.0","source":{"id":"1103.2472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2472","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2472v1","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2472","created_at":"2026-05-18T04:26:55Z"},{"alias_kind":"pith_short_12","alias_value":"QI66SGD2U2KG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QI66SGD2U2KGXMEH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QI66SGD2","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:c62e0331467cf2076317eb4975c2346fbb6a085c86e2d89933e49a89b703c644","target":"graph","created_at":"2026-05-18T04:26:55Z","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 an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL_2 over any number field which is not totally real. Our proof involves the theory of p-adically completed cohomology developed by Calegari and Emerton, and a bound for the growth of coinvariants in certain finitely generated non-commutative Iwasawa modules.","authors_text":"Simon Marshall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-12T19:19:37Z","title":"Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL_2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2472","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":"sha256:31dc520a767b7881bfe9381485728db3bc4da7fc0c2b47ca817b9bcf4f2b19bc","target":"record","created_at":"2026-05-18T04:26:55Z","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":"fbdc9726692241a7f801f8af683619897070f24b7eb7f4883b42a5501e8a5689","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-12T19:19:37Z","title_canon_sha256":"95b7282146f9568a51402a252120d6368360be4ede519302b616f8c78455844f"},"schema_version":"1.0","source":{"id":"1103.2472","kind":"arxiv","version":1}},"canonical_sha256":"823de9187aa6946bb08725442ea2463f28306e1dc7943acd20bf8c17a6aa585e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823de9187aa6946bb08725442ea2463f28306e1dc7943acd20bf8c17a6aa585e","first_computed_at":"2026-05-18T04:26:55.235802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:55.235802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eg0ztB5ihjaJoIEycd95cmySWR4Z7fzlhiuO9cRExf/B3DTkIc2Oy/cbyerwlHxXlXyemT7loNyMO7/m6v0tBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:55.236222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31dc520a767b7881bfe9381485728db3bc4da7fc0c2b47ca817b9bcf4f2b19bc","sha256:c62e0331467cf2076317eb4975c2346fbb6a085c86e2d89933e49a89b703c644"],"state_sha256":"f35135769d17fe75ba7f0ef517c27f4c9348bce4caf7f67737c10e252e96c35c"}