{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CM4GPOCVZBNFO5VTOVCMDOMSHV","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":"36277dc02d89aca52a01dbf18cb2ea9c270e93a3b9ebd17a4441f2e8a1748953","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-19T22:08:39Z","title_canon_sha256":"587af87567f7c74f914b49f39cc252ed52253a254e4129e1c5417629c644c407"},"schema_version":"1.0","source":{"id":"1509.05941","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05941","created_at":"2026-05-18T00:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05941v2","created_at":"2026-05-18T00:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05941","created_at":"2026-05-18T00:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"CM4GPOCVZBNF","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CM4GPOCVZBNFO5VT","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CM4GPOCV","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:2f22b4087b68c1b785a9d5e8b328822cfd525e3ab59e2413467a0fad84d1da62","target":"graph","created_at":"2026-05-18T00:51:37Z","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":"Deligne conjectured that a single l-adic lisse sheaf on a normal variety over a finite field can be embedded into a compatible system of l'-adic lisse sheaves with various l'. Drinfeld used Lafforgue's result as an input and proved this conjecture when the variety is smooth. We consider an analogous existence problem for a regular flat scheme over Z and prove some cases using Lafforgue's result and the work of Barnet-Lamb, Gee, Geraghty, and Taylor.","authors_text":"Koji Shimizu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-19T22:08:39Z","title":"Existence of compatible systems of lisse sheaves on arithmetic schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05941","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:aa6082c3018cee470b9cff0c980d7540dfc66fb4851aca678a249703de9ce59c","target":"record","created_at":"2026-05-18T00:51:37Z","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":"36277dc02d89aca52a01dbf18cb2ea9c270e93a3b9ebd17a4441f2e8a1748953","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-19T22:08:39Z","title_canon_sha256":"587af87567f7c74f914b49f39cc252ed52253a254e4129e1c5417629c644c407"},"schema_version":"1.0","source":{"id":"1509.05941","kind":"arxiv","version":2}},"canonical_sha256":"133867b855c85a5776b37544c1b9923d71b496c67f848dee9bbb5b14f54bc37b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"133867b855c85a5776b37544c1b9923d71b496c67f848dee9bbb5b14f54bc37b","first_computed_at":"2026-05-18T00:51:37.838870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:37.838870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5CP6Eej617ueoo/c3oWaCEd44BTz0ACu+n3UTKTyvM04zVBRykKjHiHKsViIvkJ2C/1TT/9FMI7776JDjVaXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:37.839260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05941","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa6082c3018cee470b9cff0c980d7540dfc66fb4851aca678a249703de9ce59c","sha256:2f22b4087b68c1b785a9d5e8b328822cfd525e3ab59e2413467a0fad84d1da62"],"state_sha256":"4ea98fb3bf86bfbf4f29e6fb433397c56fcdd0c6a3e7feaf76ea9e301936a301"}