{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3MN7D3MXVL2YD46AXUYRZ4LZI3","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":"383ecdeece594fa0f423f8c312b33610ee4c4259358a46cd8c75f948a62a889d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-16T21:05:11Z","title_canon_sha256":"f1cadd0fbec7d446e7254e17db1404894db20180bb6ace54d3222a268640d0f7"},"schema_version":"1.0","source":{"id":"1908.06174","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06174","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06174v3","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06174","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_12","alias_value":"3MN7D3MXVL2Y","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_16","alias_value":"3MN7D3MXVL2YD46A","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_8","alias_value":"3MN7D3MX","created_at":"2026-07-05T02:24:47Z"}],"graph_snapshots":[{"event_id":"sha256:c010b56adb0ceb13a12b474be5c4022c22611783a5b3952623ec44402f51db63","target":"graph","created_at":"2026-07-05T02:24:47Z","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/1908.06174/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using $p$-adic local Langlands correspondence for $\\operatorname{GL}_2(\\mathbb{Q}_2)$ and an ordinary $R = \\mathbb{T}$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi-stable deformation ring. This gives a new proof of the Breuil-M\\'{e}zard conjecture for 2-dimensional representations of the absolute Galois group of $\\mathbb{Q}_2$, which is new in the case $\\overline{r}$ a twist of an extension of the trivial character by itself. As a consequence, a local restriction in Pa\\v{s}k\\=unas' proof of Fontaine-Mazur ","authors_text":"Shen-Ning Tung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-16T21:05:11Z","title":"On the modularity of 2-adic potentially semi-stable deformation rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06174","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":"sha256:15d41401df025457d6e5c08c5ae69017223694df890d89a3e2e4e44d072ce90f","target":"record","created_at":"2026-07-05T02:24:47Z","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":"383ecdeece594fa0f423f8c312b33610ee4c4259358a46cd8c75f948a62a889d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-16T21:05:11Z","title_canon_sha256":"f1cadd0fbec7d446e7254e17db1404894db20180bb6ace54d3222a268640d0f7"},"schema_version":"1.0","source":{"id":"1908.06174","kind":"arxiv","version":3}},"canonical_sha256":"db1bf1ed97aaf581f3c0bd311cf17946f231b5eedb0addf4b0db12810f725a1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db1bf1ed97aaf581f3c0bd311cf17946f231b5eedb0addf4b0db12810f725a1d","first_computed_at":"2026-07-05T02:24:47.879146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:24:47.879146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ck29kDvDKMuBSBQzPb2tpV3S2nW4y7dhVILUTBocIxdnSZn5I5AW1QLX5pwgpIW8hL1Ell6gVAeGwfl29Jn7Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:24:47.879519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06174","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15d41401df025457d6e5c08c5ae69017223694df890d89a3e2e4e44d072ce90f","sha256:c010b56adb0ceb13a12b474be5c4022c22611783a5b3952623ec44402f51db63"],"state_sha256":"6deb4d8e9434bdacc77b51a72dd152a3691fa363301ec8393bdc41cb7e20690f"}