{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ILPSARCFEU5K46FLFZ3DFYXC76","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":"8a7c1c82f81c0ef79bfef8bc9da85d56a10a7e2d030e8f2d0fc50679da9cc172","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T08:46:23Z","title_canon_sha256":"43c82e6aa43d1a2141fe1a4b757da87b24f7a0aae0d16befc48f56b19df37573"},"schema_version":"1.0","source":{"id":"1609.05451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05451","created_at":"2026-05-18T01:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05451v1","created_at":"2026-05-18T01:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05451","created_at":"2026-05-18T01:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"ILPSARCFEU5K","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"ILPSARCFEU5K46FL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"ILPSARCF","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:20e0ba6f1060ed2a0b28e853af90e453536cd09a550162ebbe4d3e57663bb33a","target":"graph","created_at":"2026-05-18T01:04:26Z","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 Conjecture \\ref{conj1} for a set of representations of the group $GL_n({\\bf A})$. This Conjecture is stated in complete generality as Conjecture 1 in \\cite{G2}, and here we prove it for various cases. See Conjecture \\ref{conj2} below. First we prove it in the case when the length of the integral is four, and then we discuss the general case.","authors_text":"David Ginzburg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T08:46:23Z","title":"On the length of global integrals for $GL_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05451","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":"sha256:48bc7a2c59808f49037c0661afc092b94a32e1860110816e6c606ad408bace78","target":"record","created_at":"2026-05-18T01:04:26Z","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":"8a7c1c82f81c0ef79bfef8bc9da85d56a10a7e2d030e8f2d0fc50679da9cc172","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-18T08:46:23Z","title_canon_sha256":"43c82e6aa43d1a2141fe1a4b757da87b24f7a0aae0d16befc48f56b19df37573"},"schema_version":"1.0","source":{"id":"1609.05451","kind":"arxiv","version":1}},"canonical_sha256":"42df204445253aae78ab2e7632e2e2ffbbc095ba00f4618a553e5e5a47e8968d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42df204445253aae78ab2e7632e2e2ffbbc095ba00f4618a553e5e5a47e8968d","first_computed_at":"2026-05-18T01:04:26.360269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:26.360269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ioFABMIKeR0Ygbmzp2Auyyno46khLbqvHAOTIccUAnzd+nd7pM7/nbYZoyJhpHwM1M1TPdWoMOFsSsChk0uwCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:26.360819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48bc7a2c59808f49037c0661afc092b94a32e1860110816e6c606ad408bace78","sha256:20e0ba6f1060ed2a0b28e853af90e453536cd09a550162ebbe4d3e57663bb33a"],"state_sha256":"7b77f9bb1df98a7526254aa2f675d3b3557e070bdf4bc59ebc81919aeb3963ff"}