{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CUFOXR3QODZLA7HR3PCSIX6ZEQ","short_pith_number":"pith:CUFOXR3Q","schema_version":"1.0","canonical_sha256":"150aebc77070f2b07cf1dbc5245fd9241896c2f2d0562f51c70a838327f04904","source":{"kind":"arxiv","id":"1008.3071","version":1},"attestation_state":"computed","paper":{"title":"Connectedness of Kisin varieties for GL_2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eugen Hellmann","submitted_at":"2010-08-18T10:27:12Z","abstract_excerpt":"We show that the Kisin varieties associated to simple $\\phi$-modules of rank $2$ are connected in the case of an arbitrary cocharacter. This proves that the connected components of the generic fiber of the flat deformation ring of an irreducible $2$-dimensional Galois representation of a local field are precisely the components where the multiplicities of the Hodge-Tate weights are fixed."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.3071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-18T10:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"8d7280e65f5fc5e8f7695da6a16eafcf54feb48cc94f19e703078472b74a0a70","abstract_canon_sha256":"58837cf23c273aa0840ecc358243d7b317f6f02c4cbd1eaf688bdc9ddeed14d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.634913Z","signature_b64":"L7RHDFu20PxuSnx4CYOiVolS+pZr9Wc94NhLC3uuvCqZicDcvftMgHtwu+UEe0J9W+jSifcIQWyvBRx+jcCcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"150aebc77070f2b07cf1dbc5245fd9241896c2f2d0562f51c70a838327f04904","last_reissued_at":"2026-05-18T04:42:03.634514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.634514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectedness of Kisin varieties for GL_2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eugen Hellmann","submitted_at":"2010-08-18T10:27:12Z","abstract_excerpt":"We show that the Kisin varieties associated to simple $\\phi$-modules of rank $2$ are connected in the case of an arbitrary cocharacter. This proves that the connected components of the generic fiber of the flat deformation ring of an irreducible $2$-dimensional Galois representation of a local field are precisely the components where the multiplicities of the Hodge-Tate weights are fixed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3071","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.3071","created_at":"2026-05-18T04:42:03.634570+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3071v1","created_at":"2026-05-18T04:42:03.634570+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3071","created_at":"2026-05-18T04:42:03.634570+00:00"},{"alias_kind":"pith_short_12","alias_value":"CUFOXR3QODZL","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CUFOXR3QODZLA7HR","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CUFOXR3Q","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ","json":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ.json","graph_json":"https://pith.science/api/pith-number/CUFOXR3QODZLA7HR3PCSIX6ZEQ/graph.json","events_json":"https://pith.science/api/pith-number/CUFOXR3QODZLA7HR3PCSIX6ZEQ/events.json","paper":"https://pith.science/paper/CUFOXR3Q"},"agent_actions":{"view_html":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ","download_json":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ.json","view_paper":"https://pith.science/paper/CUFOXR3Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3071&json=true","fetch_graph":"https://pith.science/api/pith-number/CUFOXR3QODZLA7HR3PCSIX6ZEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/CUFOXR3QODZLA7HR3PCSIX6ZEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ/action/storage_attestation","attest_author":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ/action/author_attestation","sign_citation":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ/action/citation_signature","submit_replication":"https://pith.science/pith/CUFOXR3QODZLA7HR3PCSIX6ZEQ/action/replication_record"}},"created_at":"2026-05-18T04:42:03.634570+00:00","updated_at":"2026-05-18T04:42:03.634570+00:00"}