{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NYAEF2DW2RQWIQETTRPURFNDSB","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":"01403a38b74d989befc3471f1c68ecfc0a992ee9552b25ddcd0e8e47c37237db","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T14:34:20Z","title_canon_sha256":"28a71b7a8cb6b9c37df4141ab646b540c8397dbde53c436ca07c28ecb0c765a1"},"schema_version":"1.0","source":{"id":"1706.00075","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00075","created_at":"2026-05-18T00:38:20Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00075v2","created_at":"2026-05-18T00:38:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00075","created_at":"2026-05-18T00:38:20Z"},{"alias_kind":"pith_short_12","alias_value":"NYAEF2DW2RQW","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NYAEF2DW2RQWIQET","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NYAEF2DW","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:d0a95e1dbb3cf3db9f008fc14f3c16d7d14ded050515feb262ede92886770fd3","target":"graph","created_at":"2026-05-18T00:38:20Z","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":"Subgroups $H_1$ and $H_2$ of a group $G$ are said to be locally conjugate if there is a bijection $f: H_1 \\rightarrow H_2$ such that $h$ and $f(h)$ are conjugate in $G$ for every $h \\in H_1$. This paper studies local conjugacy among subgroups of $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$, where $p$ is an odd prime, building on Sutherland's categorizations of subgroups of $\\text{GL}_2(\\mathbb{Z}/p\\mathbb{Z})$ and local conjugacy among them. There are two conditions that locally conjugate subgroups $H_1$ and $H_2$ of $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$ must satisfy: letting $\\varphi: \\text{GL}_","authors_text":"H. Kim","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T14:34:20Z","title":"Local Conjugacy in $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00075","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":"sha256:269c229285bec86187b89c75bce7b68e72d6cb6bcde8a51e5bbd40c4d9af196b","target":"record","created_at":"2026-05-18T00:38:20Z","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":"01403a38b74d989befc3471f1c68ecfc0a992ee9552b25ddcd0e8e47c37237db","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T14:34:20Z","title_canon_sha256":"28a71b7a8cb6b9c37df4141ab646b540c8397dbde53c436ca07c28ecb0c765a1"},"schema_version":"1.0","source":{"id":"1706.00075","kind":"arxiv","version":2}},"canonical_sha256":"6e0042e876d4616440939c5f4895a3905a961823514f384bccdc74aaba7acb84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e0042e876d4616440939c5f4895a3905a961823514f384bccdc74aaba7acb84","first_computed_at":"2026-05-18T00:38:20.560580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:20.560580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pbim7zZxip2z3qr1zl9vICW/VJrA8PukcEN7i26kuL1a2fIoD1Q4+IWoTprVdJWmuxwmsUm1g4APcORe1d4fCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:20.561208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00075","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:269c229285bec86187b89c75bce7b68e72d6cb6bcde8a51e5bbd40c4d9af196b","sha256:d0a95e1dbb3cf3db9f008fc14f3c16d7d14ded050515feb262ede92886770fd3"],"state_sha256":"724f8022881c2c8eba60029326c3f0fcd3ed3330f118a1c5faa6f840ea8423c8"}