{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:26KG5MLSZYJ5GE3JRIMM7XI6RT","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":"a74ecb14a99592bd6a16183afb7a747b88d5e949d6852db8c2eba685134e2be1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-10-30T20:51:01Z","title_canon_sha256":"d3ab14de735f6ef548a4bd4a2c9e499fec2c119cb2b969e2a577cb221389cc85"},"schema_version":"1.0","source":{"id":"2410.23453","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23453","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23453v2","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23453","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"26KG5MLSZYJ5","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"26KG5MLSZYJ5GE3J","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"26KG5MLS","created_at":"2026-05-28T01:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:c2f2240c955f0107b74fc80fc47ae3f350ce821ed59c19fd21b2c6d5845f107c","target":"graph","created_at":"2026-05-28T01:04:25Z","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/2410.23453/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an instance of $q$-crystalline cohomology (in its prismatic form), we thus obtain improved bounds on the ramification of $\\mathrm{H}^{i}_{et}(X_{\\mathbb{C}_K}, \\mathbb{Z}/p\\mathbb{Z})$ for a smooth proper $p$-adic formal scheme $X$ over $\\mathcal{O}_K$, for arbitrarily large degree $i$.","authors_text":"Pavel \\v{C}oupek","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-10-30T20:51:01Z","title":"Ramification bounds via Wach modules and q-crystalline cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23453","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":"sha256:9e4816444c0e0d3b4c8153ff688adbfd79939326725cf4e0fe6568a719f9b673","target":"record","created_at":"2026-05-28T01:04:25Z","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":"a74ecb14a99592bd6a16183afb7a747b88d5e949d6852db8c2eba685134e2be1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-10-30T20:51:01Z","title_canon_sha256":"d3ab14de735f6ef548a4bd4a2c9e499fec2c119cb2b969e2a577cb221389cc85"},"schema_version":"1.0","source":{"id":"2410.23453","kind":"arxiv","version":2}},"canonical_sha256":"d7946eb172ce13d313698a18cfdd1e8ce4127dc75fa50adb7bb51090116cda9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7946eb172ce13d313698a18cfdd1e8ce4127dc75fa50adb7bb51090116cda9c","first_computed_at":"2026-05-28T01:04:25.626547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:25.626547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eUnS5jOyMj7fFsqVn9gP4xNq0Y2qngw3VCHkgOt+IpFzIussHDKk+/frZguevyFxYhhmP9FcOyJU87a/a2EWAg==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:25.627123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.23453","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e4816444c0e0d3b4c8153ff688adbfd79939326725cf4e0fe6568a719f9b673","sha256:c2f2240c955f0107b74fc80fc47ae3f350ce821ed59c19fd21b2c6d5845f107c"],"state_sha256":"791b31e77ce9078e7ca3dc8f8a6e30fc5d086d033cfe2591b8b3e52dc89837b6"}