{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OIQGNO6HDDWI3JQU64QWXQ6DSF","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":"77ad6ce0dad994a6155797177cb8c238cfc04c5ba43e2210b0e9fe8b182187e2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-04-01T00:19:54Z","title_canon_sha256":"5ef04e37624544183edbe9b0a0aa7e905b9e377d3e1e6614fd8b96e9c3a8db9f"},"schema_version":"1.0","source":{"id":"2504.00305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.00305","created_at":"2026-07-05T10:54:45Z"},{"alias_kind":"arxiv_version","alias_value":"2504.00305v2","created_at":"2026-07-05T10:54:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.00305","created_at":"2026-07-05T10:54:45Z"},{"alias_kind":"pith_short_12","alias_value":"OIQGNO6HDDWI","created_at":"2026-07-05T10:54:45Z"},{"alias_kind":"pith_short_16","alias_value":"OIQGNO6HDDWI3JQU","created_at":"2026-07-05T10:54:45Z"},{"alias_kind":"pith_short_8","alias_value":"OIQGNO6H","created_at":"2026-07-05T10:54:45Z"}],"graph_snapshots":[{"event_id":"sha256:35ab7c3cde110d9944d201e5961582b3e069ec002b498d168a7e7f7dcc13deea","target":"graph","created_at":"2026-07-05T10:54:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.00305/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $(G, X)$ be a Shimura datum. In previous work with Christian Klevdal, we showed that the canonical $G(\\mathbb{Q}_{\\ell})$-valued local systems on Shimura varieties for $G$ form compatible systems after projection to the adjoint group of $G$. In this note, we strengthen this result to prove compatibility for the $G(\\mathbb{Q}_{\\ell})$-local systems themselves. We also include the crystalline compatibility, extending the adjoint case established in our joint work Jake Huryn, Kiran Kedlaya, and Christian Klevdal.","authors_text":"Stefan Patrikis","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-04-01T00:19:54Z","title":"Compatibility of canonical $\\ell$-adic local systems on Shimura varieties, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.00305","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":"sha256:619215dadd08fc508bde9a506926e33151446496fede88c3c01960f898f38c15","target":"record","created_at":"2026-07-05T10:54:45Z","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":"77ad6ce0dad994a6155797177cb8c238cfc04c5ba43e2210b0e9fe8b182187e2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-04-01T00:19:54Z","title_canon_sha256":"5ef04e37624544183edbe9b0a0aa7e905b9e377d3e1e6614fd8b96e9c3a8db9f"},"schema_version":"1.0","source":{"id":"2504.00305","kind":"arxiv","version":2}},"canonical_sha256":"722066bbc718ec8da614f7216bc3c39150f27dbc97d321ccd4df371284ae51a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"722066bbc718ec8da614f7216bc3c39150f27dbc97d321ccd4df371284ae51a3","first_computed_at":"2026-07-05T10:54:45.612200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:54:45.612200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V+lqQA1uDZV6/5TjJRB+tLygDMJm0nQFby+42wuxDfSz0eXmL0FyN93XBi2yfCaLOlzuZ31E5b2afG8HFNLCBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:54:45.612717Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.00305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:619215dadd08fc508bde9a506926e33151446496fede88c3c01960f898f38c15","sha256:35ab7c3cde110d9944d201e5961582b3e069ec002b498d168a7e7f7dcc13deea"],"state_sha256":"bfe274144d043bb408da3aa7adf3041e97b4b7b7a2eb71286a7bcb4f7f1135b4"}