{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IXX36KL2AGN6QZ5RCC53ISPUWV","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":"266c95c9d0f4d32e620d7244534a0b18e4f0c64ee4202db8aaaaebcac677cfe3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-07T13:07:36Z","title_canon_sha256":"5745fa3f311dae2464deefa3719d6401060897dc1433d633cf87596a010c9aa1"},"schema_version":"1.0","source":{"id":"2303.03863","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.03863","created_at":"2026-07-05T09:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"2303.03863v2","created_at":"2026-07-05T09:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.03863","created_at":"2026-07-05T09:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"IXX36KL2AGN6","created_at":"2026-07-05T09:16:06Z"},{"alias_kind":"pith_short_16","alias_value":"IXX36KL2AGN6QZ5R","created_at":"2026-07-05T09:16:06Z"},{"alias_kind":"pith_short_8","alias_value":"IXX36KL2","created_at":"2026-07-05T09:16:06Z"}],"graph_snapshots":[{"event_id":"sha256:797d3ccb4bd67337deb0ba46ae0c9f2fd576d019275db970a4ceaea56e73529f","target":"graph","created_at":"2026-07-05T09:16:06Z","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/2303.03863/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a Shimura variety $(G, X)$ in the superrigid regime and neat level subgroup $K_0$, we show that the canonical family of $\\ell$-adic representations associated to a number field point $y \\in \\mathrm{Sh}_{K_0}(G, X)(F)$,\n  \\[\n  \\left\\{ \\rho_{y, \\ell} \\colon \\mathrm{Gal}(\\overline{\\mathbb{Q}}/F) \\to G^{\\mathrm{ad}}(\\mathbb{Q}_{\\ell}) \\right\\}_{\\ell},\n  \\]\n  form a compatible system of $G^{\\mathrm{ad}}(\\mathbb{Q}_{\\ell})$-representations: there is an integer $N(y)$ such that for all $\\ell$, $\\rho_{y, \\ell}$ is unramified away from $N(y) \\ell$, and for all $\\ell \\neq \\ell'$ and $v \\nmid N(y)\\el","authors_text":"Christian Klevdal, Stefan Patrikis","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-07T13:07:36Z","title":"Compatibility of canonical $\\ell$-adic local systems on Shimura varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03863","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":"sha256:961c8741553ebc0aa64fda459a348e81766196bad1800b3b1a6f098f831f174e","target":"record","created_at":"2026-07-05T09:16:06Z","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":"266c95c9d0f4d32e620d7244534a0b18e4f0c64ee4202db8aaaaebcac677cfe3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-07T13:07:36Z","title_canon_sha256":"5745fa3f311dae2464deefa3719d6401060897dc1433d633cf87596a010c9aa1"},"schema_version":"1.0","source":{"id":"2303.03863","kind":"arxiv","version":2}},"canonical_sha256":"45efbf297a019be867b110bbb449f4b553e736cd1df3befee320aba100bc1b88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45efbf297a019be867b110bbb449f4b553e736cd1df3befee320aba100bc1b88","first_computed_at":"2026-07-05T09:16:06.299192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:16:06.299192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8LSUxk+mmXwfcPK3yn8e2MC1Zw9XnXnLQGLDM0wdbfzJB70N2YPogAVjj6D7Hr3WqPPt+JhaYHB0ra7U2jmbAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:16:06.299624Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.03863","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:961c8741553ebc0aa64fda459a348e81766196bad1800b3b1a6f098f831f174e","sha256:797d3ccb4bd67337deb0ba46ae0c9f2fd576d019275db970a4ceaea56e73529f"],"state_sha256":"3019f6bf4cd191c88f2815e06f1b18b913ee44810b0731d3d299abfe17c0992b"}