{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WLA5BD2VDCEWUOJC4C34ZVJB4F","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":"839b2c63367744ad93596c6c60e373e8319b8ef9eb6b8e4d12a45e67358338fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-20T06:31:02Z","title_canon_sha256":"45892e020bb2c43a70abfe0181f782f9b9d8b11b956f17cce724a6595c0f8040"},"schema_version":"1.0","source":{"id":"1802.06978","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06978","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06978v2","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06978","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"WLA5BD2VDCEW","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WLA5BD2VDCEWUOJC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WLA5BD2V","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:386672d49fe596757402d89eae43c184a62511d2f64bdb3adf09ace273cdc42d","target":"graph","created_at":"2026-05-18T00:22:49Z","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":"We give an explicit description of the inner cohomology of an adelic locally symmetric space of a given level structure attached to the general linear group of prime rank $n$, with coefficients in a locally constant sheaf of complex vector spaces. We show that for all prime $n$ the inner cohomology vanishes in all degrees for nonconstant sheaves, otherwise the quotient module of the inner cohomology classes that are not cuspidal is trivial in all degrees for primes $n = 2,3$, and for all primes $n \\geq 5$ it is trivial in all but finitely many degrees where it has a `simple' description in ter","authors_text":"Krishna Kishore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-20T06:31:02Z","title":"Inner cohomology of $GL_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06978","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":"sha256:74675cd205e5eedf6ef0469942f22e0008bcdabfe6dee43bb5055b9d2e1f0f4a","target":"record","created_at":"2026-05-18T00:22:49Z","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":"839b2c63367744ad93596c6c60e373e8319b8ef9eb6b8e4d12a45e67358338fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-20T06:31:02Z","title_canon_sha256":"45892e020bb2c43a70abfe0181f782f9b9d8b11b956f17cce724a6595c0f8040"},"schema_version":"1.0","source":{"id":"1802.06978","kind":"arxiv","version":2}},"canonical_sha256":"b2c1d08f5518896a3922e0b7ccd521e14063279cfc14a655a55cd7dafdfd3443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2c1d08f5518896a3922e0b7ccd521e14063279cfc14a655a55cd7dafdfd3443","first_computed_at":"2026-05-18T00:22:49.018868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:49.018868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2jye+yxODP+4Y6WChBoxjwNE3lLGnKm1xXwVk19yd/jn+frEJEkwu4e1+3A0+kFt9AESQORZ6BMcuzcr7S7CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:49.019341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06978","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74675cd205e5eedf6ef0469942f22e0008bcdabfe6dee43bb5055b9d2e1f0f4a","sha256:386672d49fe596757402d89eae43c184a62511d2f64bdb3adf09ace273cdc42d"],"state_sha256":"80e1a67000c57fb81c9217fec87a2af798748ce20a95e47b86a3b5f9f0159fc5"}