{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:LMXIFG3UZ4SJKE5HCSKLRN3UUW","short_pith_number":"pith:LMXIFG3U","schema_version":"1.0","canonical_sha256":"5b2e829b74cf249513a71494b8b774a5adbc6fc6b25a9f34c680926ec311ef5b","source":{"kind":"arxiv","id":"2205.10344","version":2},"attestation_state":"computed","paper":{"title":"Hecke orbits on Shimura varieties of Hodge type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Marco D'Addezio, Pol van Hoften","submitted_at":"2022-05-20T17:56:27Z","abstract_excerpt":"We prove the Hecke orbit conjecture of Chai--Oort for Shimura varieties of Hodge type at odd primes of good reduction. We use a novel result for the local monodromy groups of $F$-isocrystals \"coming from geometry\", which refines Crew's parabolicity conjecture. In the course of the proof, we also introduce a noncommutative generalisation of Serre--Tate coordinates for formal neighbourhoods of central leaves, built upon the previous work of Caraiani--Scholze and Kim. Using these coordinates, we reinterpret Chai--Oort's notion of strongly Tate-linear subspaces and we establish upper bounds for th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2205.10344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-05-20T17:56:27Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d7696630a631f539ce19ed1235de4ae303fdc3c83cf03f81832d095a45237f92","abstract_canon_sha256":"91b55ec58017802f99af6334c423b376d711f4ca2b1e95fb8ea85c3b1c4bf8f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:31:21.249615Z","signature_b64":"P1mudvu4Kx2kbhpVGlEz73W5z1sgTH0tCTJ+pgOnURlp7EQLCNCnuN5iZBSMVLgSJ02UNzWu66popm8EYwLBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b2e829b74cf249513a71494b8b774a5adbc6fc6b25a9f34c680926ec311ef5b","last_reissued_at":"2026-07-05T10:31:21.249092Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:31:21.249092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hecke orbits on Shimura varieties of Hodge type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Marco D'Addezio, Pol van Hoften","submitted_at":"2022-05-20T17:56:27Z","abstract_excerpt":"We prove the Hecke orbit conjecture of Chai--Oort for Shimura varieties of Hodge type at odd primes of good reduction. We use a novel result for the local monodromy groups of $F$-isocrystals \"coming from geometry\", which refines Crew's parabolicity conjecture. In the course of the proof, we also introduce a noncommutative generalisation of Serre--Tate coordinates for formal neighbourhoods of central leaves, built upon the previous work of Caraiani--Scholze and Kim. Using these coordinates, we reinterpret Chai--Oort's notion of strongly Tate-linear subspaces and we establish upper bounds for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.10344","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.10344/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2205.10344","created_at":"2026-07-05T10:31:21.249156+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.10344v2","created_at":"2026-07-05T10:31:21.249156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.10344","created_at":"2026-07-05T10:31:21.249156+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMXIFG3UZ4SJ","created_at":"2026-07-05T10:31:21.249156+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMXIFG3UZ4SJKE5H","created_at":"2026-07-05T10:31:21.249156+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMXIFG3U","created_at":"2026-07-05T10:31:21.249156+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07427","citing_title":"$p$-adic Maass--Shimura operators on $\\mu$-ordinary Igusa varieties","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2606.10573","citing_title":"The convergent stack","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW","json":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW.json","graph_json":"https://pith.science/api/pith-number/LMXIFG3UZ4SJKE5HCSKLRN3UUW/graph.json","events_json":"https://pith.science/api/pith-number/LMXIFG3UZ4SJKE5HCSKLRN3UUW/events.json","paper":"https://pith.science/paper/LMXIFG3U"},"agent_actions":{"view_html":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW","download_json":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW.json","view_paper":"https://pith.science/paper/LMXIFG3U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.10344&json=true","fetch_graph":"https://pith.science/api/pith-number/LMXIFG3UZ4SJKE5HCSKLRN3UUW/graph.json","fetch_events":"https://pith.science/api/pith-number/LMXIFG3UZ4SJKE5HCSKLRN3UUW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW/action/storage_attestation","attest_author":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW/action/author_attestation","sign_citation":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW/action/citation_signature","submit_replication":"https://pith.science/pith/LMXIFG3UZ4SJKE5HCSKLRN3UUW/action/replication_record"}},"created_at":"2026-07-05T10:31:21.249156+00:00","updated_at":"2026-07-05T10:31:21.249156+00:00"}