{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J4DR3NAT6IVFVSMNLGARTYLFTT","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":"64af3f66164bb391c6bc700982845edc9857905725e78a251aae94eb18b1abff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T08:55:49Z","title_canon_sha256":"8d07cb77ca9c6f6e114ac0e015fe4b9a3d9bde7b729ec10c6e9c6730189f245a"},"schema_version":"1.0","source":{"id":"1809.06598","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06598","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06598v3","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06598","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"pith_short_12","alias_value":"J4DR3NAT6IVF","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"pith_short_16","alias_value":"J4DR3NAT6IVFVSMN","created_at":"2026-07-05T00:42:51Z"},{"alias_kind":"pith_short_8","alias_value":"J4DR3NAT","created_at":"2026-07-05T00:42:51Z"}],"graph_snapshots":[{"event_id":"sha256:d4828151b90e54651b5615f4061667d7d6d9fd31cd16d045efc5fa9d45791f1f","target":"graph","created_at":"2026-07-05T00:42:51Z","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/1809.06598/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Zariski closure of points in local deformation rings corresponding to potential semi-stable representations with certain prescribed $p$-adic Hodge theoretic properties. We show in favourable cases that the closure is equal to a union of irreducible components of the deformation space. We also study an analogous question for global Hecke algebras.","authors_text":"Matthew Emerton, Vytautas Paskunas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T08:55:49Z","title":"On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06598","kind":"arxiv","version":3},"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:e0da795a5761941b3d390d9621ada6f9c2c098edb5d7f524712f0e74e0c60cdb","target":"record","created_at":"2026-07-05T00:42:51Z","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":"64af3f66164bb391c6bc700982845edc9857905725e78a251aae94eb18b1abff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T08:55:49Z","title_canon_sha256":"8d07cb77ca9c6f6e114ac0e015fe4b9a3d9bde7b729ec10c6e9c6730189f245a"},"schema_version":"1.0","source":{"id":"1809.06598","kind":"arxiv","version":3}},"canonical_sha256":"4f071db413f22a5ac98d598119e1659ccd930b7ee9f63cef0fd485270ba68c5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f071db413f22a5ac98d598119e1659ccd930b7ee9f63cef0fd485270ba68c5d","first_computed_at":"2026-07-05T00:42:51.658475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:42:51.658475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p7Mp6UnRq4TlFnNoddocKc+qdLePoxZ8NwsTfoeQdB7aak6pFogxe9lnNjOUabF0kxQ/GXm3bLq98LxIhFB2Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:42:51.658867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06598","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0da795a5761941b3d390d9621ada6f9c2c098edb5d7f524712f0e74e0c60cdb","sha256:d4828151b90e54651b5615f4061667d7d6d9fd31cd16d045efc5fa9d45791f1f"],"state_sha256":"12dcb132a852e24b1c803104aeb19b4866caea3fd071e7140d2e35654a9111d6"}