{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NK4VTT56Y2QWIWPBOEOGCIZB63","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":"b7b4937c6572e29bf79aa47b452c57da2bbc9e0ca5bfb1e538b49fe538ee6f3c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-10-19T19:03:18Z","title_canon_sha256":"f36ea20fccf1802135337f6133001e7a20afb66fe175c738a852d3a70f520f45"},"schema_version":"1.0","source":{"id":"2510.16961","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.16961","created_at":"2026-05-20T02:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"2510.16961v4","created_at":"2026-05-20T02:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.16961","created_at":"2026-05-20T02:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"NK4VTT56Y2QW","created_at":"2026-05-20T02:05:37Z"},{"alias_kind":"pith_short_16","alias_value":"NK4VTT56Y2QWIWPB","created_at":"2026-05-20T02:05:37Z"},{"alias_kind":"pith_short_8","alias_value":"NK4VTT56","created_at":"2026-05-20T02:05:37Z"}],"graph_snapshots":[{"event_id":"sha256:89d274098a8b7d0cb4545f4d3c352dc0985708cfbdead6df5f38e21ce5f47a18","target":"graph","created_at":"2026-05-20T02:05:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2510.16961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $p$ be a prime, and let $\\mathrm{X}$ be a smooth $p$-adic formal scheme over $\\mathrm{Spf} \\mathcal{O}_K$ where $K/\\mathbf{Q}_p$ is a finite extension. We show that reflexive sheaves on the stack $\\mathrm{X}^{\\mathrm{Syn}}$ are equivalent to $\\mathbf{Z}_p$-lattices in crystalline local systems on the rigid generic fiber $\\mathrm{X}_\\eta$, and then use this to study the essential image of the \\'{e}tale realization functor on the isogeny category of perfect complexes on $\\mathrm{X}^{\\mathrm{Syn}}$. We also show that when $\\mathrm{X}/\\mathrm{Spf} \\mathcal{O}_K$ is smooth and proper that $\\mat","authors_text":"Dylan Pentland","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-10-19T19:03:18Z","title":"Syntomification and crystalline local systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.16961","kind":"arxiv","version":4},"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:d7a9ebce3d65739a66f4dbe3d3488b72952c7683de88a8584783f56415269a82","target":"record","created_at":"2026-05-20T02:05:37Z","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":"b7b4937c6572e29bf79aa47b452c57da2bbc9e0ca5bfb1e538b49fe538ee6f3c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-10-19T19:03:18Z","title_canon_sha256":"f36ea20fccf1802135337f6133001e7a20afb66fe175c738a852d3a70f520f45"},"schema_version":"1.0","source":{"id":"2510.16961","kind":"arxiv","version":4}},"canonical_sha256":"6ab959cfbec6a16459e1711c612321f6cd43b0d49063945979d2e4fe5c293e5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ab959cfbec6a16459e1711c612321f6cd43b0d49063945979d2e4fe5c293e5f","first_computed_at":"2026-05-20T02:05:37.220080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T02:05:37.220080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wACI/rPUDTZXFzsVt05eCot2GApailrkktzRjcwnFpG+Sowte5wFTAujuvv1Q7QpcEWxZgcZhsrrwgxv4ZACA==","signature_status":"signed_v1","signed_at":"2026-05-20T02:05:37.220966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.16961","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7a9ebce3d65739a66f4dbe3d3488b72952c7683de88a8584783f56415269a82","sha256:89d274098a8b7d0cb4545f4d3c352dc0985708cfbdead6df5f38e21ce5f47a18"],"state_sha256":"b6638039d58f2d527ff80d200a26cad5d9419cd96d5ebee3d41d105e7a00c04a"}