{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DCCG3LEFDQPDCMCSOEE7HGDOVI","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":"8fc97916eb30655428b4251248f56c29fe728a50eb106609ecac4e5b5a518f01","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-01T15:18:30Z","title_canon_sha256":"e8f0bf054f2b90defa74f6eb9513211afbafa0458c791cb82071e607b8a98875"},"schema_version":"1.0","source":{"id":"1012.0213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0213","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0213v2","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0213","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"DCCG3LEFDQPD","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DCCG3LEFDQPDCMCS","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DCCG3LEF","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:fff35ec2747edc991104cdae6cdbe8bb8062cf7e50fd06ace5b6fd3917064d2f","target":"graph","created_at":"2026-05-18T04:20:04Z","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"},"paper":{"abstract_excerpt":"We define the $p$-adic trace of certain rank-one local systems on the multiplicative group over $p$-adic numbers, using Sekiguchi and Suwa's unification of Kummer and Artin-Schrier-Witt theories. Our main observation is that, for every non-negative integer $n$, the $p$-adic trace defines an isomorphism of abelian groups between local systems whose order divides $(p-1)p^n$ and $\\ell$-adic characters of the multiplicative group of $p$-adic integers of depth less than or equal to $n$.","authors_text":"Clifton Cunningham, Masoud Kamgarpour","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-01T15:18:30Z","title":"Geometrization of continuous characters of $\\mathbb{Z}_p^\\times$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0213","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":"sha256:9e58a042c25053452cf91d033bed18dc1b59371bb895c50693a59f6c2adb9c81","target":"record","created_at":"2026-05-18T04:20:04Z","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":"8fc97916eb30655428b4251248f56c29fe728a50eb106609ecac4e5b5a518f01","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-01T15:18:30Z","title_canon_sha256":"e8f0bf054f2b90defa74f6eb9513211afbafa0458c791cb82071e607b8a98875"},"schema_version":"1.0","source":{"id":"1012.0213","kind":"arxiv","version":2}},"canonical_sha256":"18846dac851c1e3130527109f3986eaa0d2c103829a78327ec8d8806516c92cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18846dac851c1e3130527109f3986eaa0d2c103829a78327ec8d8806516c92cc","first_computed_at":"2026-05-18T04:20:04.664000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:04.664000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NCVZ8vHuxhonTr4fSqLUT2ivQ6WYRVPjDdNe+fmVNPKaaMbIua8etLyY8pRpwHChF/Tf4tnuZl3q6lEBsxFGBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:04.664456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e58a042c25053452cf91d033bed18dc1b59371bb895c50693a59f6c2adb9c81","sha256:fff35ec2747edc991104cdae6cdbe8bb8062cf7e50fd06ace5b6fd3917064d2f"],"state_sha256":"eeb9c40ef826cec02812c06ae2239eddc7d810fe503cd8a67d970e563ebf3852"}