{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:G77ORAY3RDUDTQVFT7AUGTIYBC","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":"ea318d6831d156695d6d2e75dec68058a3d7760fb16f3d157f315919c9cade52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-01T06:13:02Z","title_canon_sha256":"23afa5dec197429d23e31f7dc5e39993a9f7aedf8d301ea30784697bc83d6f91"},"schema_version":"1.0","source":{"id":"1205.0097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0097","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0097v1","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0097","created_at":"2026-05-18T03:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"G77ORAY3RDUD","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G77ORAY3RDUDTQVF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G77ORAY3","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:63f534de620ba62ebac0e0b41b7620b5a012375b739e9b1a8c50ae59f8762ae4","target":"graph","created_at":"2026-05-18T03:56:35Z","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 prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the isomorphism for large weights by constructing the map from the space of cusp forms to the cohomology group.","authors_text":"Wissam Raji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-01T06:13:02Z","title":"Eichler Cohomology of Generalized Modular Forms of Real Weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0097","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":"sha256:76e35a35ad13e8dc2498c7aa946fddba3bcb70644622e017f216d59c8bb7c3fe","target":"record","created_at":"2026-05-18T03:56:35Z","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":"ea318d6831d156695d6d2e75dec68058a3d7760fb16f3d157f315919c9cade52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-01T06:13:02Z","title_canon_sha256":"23afa5dec197429d23e31f7dc5e39993a9f7aedf8d301ea30784697bc83d6f91"},"schema_version":"1.0","source":{"id":"1205.0097","kind":"arxiv","version":1}},"canonical_sha256":"37fee8831b88e839c2a59fc1434d180886f8edbdf4a4ee63aca95bf0a7bdc1f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37fee8831b88e839c2a59fc1434d180886f8edbdf4a4ee63aca95bf0a7bdc1f7","first_computed_at":"2026-05-18T03:56:35.883777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:35.883777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2/xN1Q/FRHbJyClnmwW8Vhdoqk74gBBTiNqcHEsTYMCWoEqvEA1ZtIc80dbiFHS3v3/jnypQBmIuXn4KVunDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:35.884187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76e35a35ad13e8dc2498c7aa946fddba3bcb70644622e017f216d59c8bb7c3fe","sha256:63f534de620ba62ebac0e0b41b7620b5a012375b739e9b1a8c50ae59f8762ae4"],"state_sha256":"285988b0ff67b7220137104a74f69741b5588acf5aaa89b75861371faca5bb4a"}