{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:454PKDSSGLTYPZY6ACRHUIXYNP","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":"f06e7dd2bcefe42814000fd408e7995e54eaca6dec56ce7f61605312c59194f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-13T13:30:11Z","title_canon_sha256":"76cc0796c24f778cbef74056bab9e6ea21b0f089f67d55ddf3441b49c81c4963"},"schema_version":"1.0","source":{"id":"1211.2988","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2988","created_at":"2026-05-18T03:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2988v2","created_at":"2026-05-18T03:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2988","created_at":"2026-05-18T03:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"454PKDSSGLTY","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"454PKDSSGLTYPZY6","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"454PKDSS","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:1e2f9db0b5eecd4757a12c63acda9df4b4464a34812942f3aabbc24b38ceaf5f","target":"graph","created_at":"2026-05-18T03:37:07Z","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":"Let $\\Gamma$ be a finitely generated Fuchsian group of the first kind which has at least one parabolic class. Eichler introduced a cohomology theory for Fuchsian groups, called as \"Eichler cohomology theory\", and established the $\\CC$-linear isomorphism from the direct sum of two spaces of cusp forms on $\\Gamma$ with the same integral weight to the Eichler cohomology group of $\\Gamma$. After the results of Eichler, the Eichler cohomology theory was generalized in various ways. For example, these results were generalized by Knopp to the cases with arbitrary real weights. In this paper, we exten","authors_text":"Dohoon Choi, Subong Lim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-13T13:30:11Z","title":"The Eichler cohomology theorem for Jacobi forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2988","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":"sha256:2c97059f4feff8f0a3377a7c87f6b4c9fae93c57f7e065f69a3418e5e0b921f9","target":"record","created_at":"2026-05-18T03:37:07Z","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":"f06e7dd2bcefe42814000fd408e7995e54eaca6dec56ce7f61605312c59194f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-13T13:30:11Z","title_canon_sha256":"76cc0796c24f778cbef74056bab9e6ea21b0f089f67d55ddf3441b49c81c4963"},"schema_version":"1.0","source":{"id":"1211.2988","kind":"arxiv","version":2}},"canonical_sha256":"e778f50e5232e787e71e00a27a22f86bf0013abeeb55bb78bd9ba361e3b6c567","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e778f50e5232e787e71e00a27a22f86bf0013abeeb55bb78bd9ba361e3b6c567","first_computed_at":"2026-05-18T03:37:07.835673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:07.835673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKB2ZYQmaePhFLtDyq6YIE4sM+vw2h3VYzP2SFZKHNqVP1y7NAyQaBiuvkpxu5PseXV7HsbNl6zU7B8JD+UkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:07.836285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2988","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c97059f4feff8f0a3377a7c87f6b4c9fae93c57f7e065f69a3418e5e0b921f9","sha256:1e2f9db0b5eecd4757a12c63acda9df4b4464a34812942f3aabbc24b38ceaf5f"],"state_sha256":"258a8997af8393bcdbf0b532f44820f9345d607de648764957a668da964f3af9"}