{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YU5IA4TSXSJWFP6GWX4UFPIAP6","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":"7756a6a1459eda760c19547aae41835a408a469ca7d317496366aaea13bd0c76","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-03-17T18:42:15Z","title_canon_sha256":"d67555ceed75d76e6596f05ce9642c7c62edf520b246a03bd6347c75bf344631"},"schema_version":"1.0","source":{"id":"2203.09559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.09559","created_at":"2026-07-05T09:47:19Z"},{"alias_kind":"arxiv_version","alias_value":"2203.09559v2","created_at":"2026-07-05T09:47:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.09559","created_at":"2026-07-05T09:47:19Z"},{"alias_kind":"pith_short_12","alias_value":"YU5IA4TSXSJW","created_at":"2026-07-05T09:47:19Z"},{"alias_kind":"pith_short_16","alias_value":"YU5IA4TSXSJWFP6G","created_at":"2026-07-05T09:47:19Z"},{"alias_kind":"pith_short_8","alias_value":"YU5IA4TS","created_at":"2026-07-05T09:47:19Z"}],"graph_snapshots":[{"event_id":"sha256:1840f3fa86470c739ba366abf03744eb7d945e21314cb4f0b534dc74d452a81d","target":"graph","created_at":"2026-07-05T09:47:19Z","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/2203.09559/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a K3 surface over a number field. We prove that $X$ has infinitely many specializations where its Picard rank jumps, hence extending our previous work with Shankar--Shankar--Tang to the case where $X$ might have potentially bad reduction. We prove a similar result for generically ordinary non-isotrivial families of K3 surfaces over curves over $\\overline{\\mathbb{F}}_p$ which extends previous work of Maulik--Shankar--Tang. As a consequence, we give a new proof of the ordinary Hecke orbit conjecture for orthogonal and unitary Shimura varieties.","authors_text":"Salim Tayou","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-03-17T18:42:15Z","title":"Picard rank jumps for K3 surfaces with bad reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.09559","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:cbbb980ac25db022d6f279a417a876e9cd1849cb1096e8b9e7660d444a779019","target":"record","created_at":"2026-07-05T09:47:19Z","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":"7756a6a1459eda760c19547aae41835a408a469ca7d317496366aaea13bd0c76","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-03-17T18:42:15Z","title_canon_sha256":"d67555ceed75d76e6596f05ce9642c7c62edf520b246a03bd6347c75bf344631"},"schema_version":"1.0","source":{"id":"2203.09559","kind":"arxiv","version":2}},"canonical_sha256":"c53a807272bc9362bfc6b5f942bd007f8477711472c184d0e2bde4cd806d86a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c53a807272bc9362bfc6b5f942bd007f8477711472c184d0e2bde4cd806d86a1","first_computed_at":"2026-07-05T09:47:19.879943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:47:19.879943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUOoNTisvLTBOO85jps+IkwcXH45zggPcGMA7ixIPpS49p8AKdy3yoykrtFEZUl/izoU77Dr4cby7XLv/41vAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:47:19.880384Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.09559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbbb980ac25db022d6f279a417a876e9cd1849cb1096e8b9e7660d444a779019","sha256:1840f3fa86470c739ba366abf03744eb7d945e21314cb4f0b534dc74d452a81d"],"state_sha256":"3a1e0485948de3ca8692d4c6b6f77325eee7a8957c2b529cc0256fe0a978decf"}