{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NYAEF2DW2RQWIQETTRPURFNDSB","short_pith_number":"pith:NYAEF2DW","canonical_record":{"source":{"id":"1706.00075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T14:34:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"28a71b7a8cb6b9c37df4141ab646b540c8397dbde53c436ca07c28ecb0c765a1","abstract_canon_sha256":"01403a38b74d989befc3471f1c68ecfc0a992ee9552b25ddcd0e8e47c37237db"},"schema_version":"1.0"},"canonical_sha256":"6e0042e876d4616440939c5f4895a3905a961823514f384bccdc74aaba7acb84","source":{"kind":"arxiv","id":"1706.00075","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NYAEF2DW2RQWIQETTRPURFNDSB","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T14:34:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"28a71b7a8cb6b9c37df4141ab646b540c8397dbde53c436ca07c28ecb0c765a1","abstract_canon_sha256":"01403a38b74d989befc3471f1c68ecfc0a992ee9552b25ddcd0e8e47c37237db"},"schema_version":"1.0"},"canonical_sha256":"6e0042e876d4616440939c5f4895a3905a961823514f384bccdc74aaba7acb84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:20.561208Z","signature_b64":"Pbim7zZxip2z3qr1zl9vICW/VJrA8PukcEN7i26kuL1a2fIoD1Q4+IWoTprVdJWmuxwmsUm1g4APcORe1d4fCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e0042e876d4616440939c5f4895a3905a961823514f384bccdc74aaba7acb84","last_reissued_at":"2026-05-18T00:38:20.560580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:20.560580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00075","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghZpJoD8lxUqU44afFpbyKP8i2ewdGy8g9VNxuD7Rb+Vlfnx/WzwMSw9tV3fZKCpL9eqzJZTc98xx+AyVyJvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:39:38.988043Z"},"content_sha256":"269c229285bec86187b89c75bce7b68e72d6cb6bcde8a51e5bbd40c4d9af196b","schema_version":"1.0","event_id":"sha256:269c229285bec86187b89c75bce7b68e72d6cb6bcde8a51e5bbd40c4d9af196b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NYAEF2DW2RQWIQETTRPURFNDSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Conjugacy in $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.GR","authors_text":"H. Kim","submitted_at":"2017-05-30T14:34:20Z","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}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00075","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZFcQD3dAzhu0sg+9vzvGPKsDfxrfOVBoVlUhf6YSeNoujnanIH2gCrAm/u49EvGi0bLgG9wsUU4ceu7LGX1aAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:39:38.988409Z"},"content_sha256":"d0a95e1dbb3cf3db9f008fc14f3c16d7d14ded050515feb262ede92886770fd3","schema_version":"1.0","event_id":"sha256:d0a95e1dbb3cf3db9f008fc14f3c16d7d14ded050515feb262ede92886770fd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYAEF2DW2RQWIQETTRPURFNDSB/bundle.json","state_url":"https://pith.science/pith/NYAEF2DW2RQWIQETTRPURFNDSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYAEF2DW2RQWIQETTRPURFNDSB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T10:39:38Z","links":{"resolver":"https://pith.science/pith/NYAEF2DW2RQWIQETTRPURFNDSB","bundle":"https://pith.science/pith/NYAEF2DW2RQWIQETTRPURFNDSB/bundle.json","state":"https://pith.science/pith/NYAEF2DW2RQWIQETTRPURFNDSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYAEF2DW2RQWIQETTRPURFNDSB/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9dfHcEiFu0Cv2GH3iejiPqjRD8YAazwtyhMn1i+NGz++w2HWzifWshhegPniMen773qkOsGB01N4iT8Kbg2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:39:38.990531Z","bundle_sha256":"69b67d7507e51756df67a2385fb032f0d29f37338e5e0c059b133b3aab7e526f"}}