{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CNBJWHB6KGL3EY6YN5F2OM4OG4","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":"965f0d301d8a0f2cae978fdfc83c3c1767fec7714037a812ed6b67eff1ccb6b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-11-03T19:31:08Z","title_canon_sha256":"2220659722264a4ac60e339b0dc1ab5c7a21fe14eb037267b70603f150ab1906"},"schema_version":"1.0","source":{"id":"1011.0982","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0982","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0982v2","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0982","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"pith_short_12","alias_value":"CNBJWHB6KGL3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CNBJWHB6KGL3EY6Y","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CNBJWHB6","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ba34935372299cf37796e0ef3fc78ad7a4a1ad06fdf7e85dbc0adbb2b93b771f","target":"graph","created_at":"2026-05-18T03:44:34Z","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":"A loop is automorphic if its inner mappings are automorphisms. Using so-called associated operations, we show that every commutative automorphic loop of odd prime power order is centrally nilpotent. Starting with anisotropic planes in the vector space of $2\\times 2$ matrices over the field of prime order $p$, we construct a family of automorphic loops of order $p^3$ with trivial center.","authors_text":"Michael Kinyon, Petr Vojtechovsky, Premysl Jedlicka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-11-03T19:31:08Z","title":"Nilpotency in automorphic loops of prime power order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0982","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":"sha256:28e6022dc68435e17a9643cfe50cb2f46a26dbc85e229c1e5d1801e4795153ed","target":"record","created_at":"2026-05-18T03:44:34Z","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":"965f0d301d8a0f2cae978fdfc83c3c1767fec7714037a812ed6b67eff1ccb6b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-11-03T19:31:08Z","title_canon_sha256":"2220659722264a4ac60e339b0dc1ab5c7a21fe14eb037267b70603f150ab1906"},"schema_version":"1.0","source":{"id":"1011.0982","kind":"arxiv","version":2}},"canonical_sha256":"13429b1c3e5197b263d86f4ba7338e37363ea91000b544bbdbb49dcc5ecb9002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13429b1c3e5197b263d86f4ba7338e37363ea91000b544bbdbb49dcc5ecb9002","first_computed_at":"2026-05-18T03:44:34.097519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:34.097519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GmTpddUibkX55P1KBOPyCdIeg88ShjBvIiQ30nPdwQ7qxOJ/qJiRJVNyaDQUCTYQnH1AksnbQ3YtQTGJCaDJAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:34.098216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0982","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28e6022dc68435e17a9643cfe50cb2f46a26dbc85e229c1e5d1801e4795153ed","sha256:ba34935372299cf37796e0ef3fc78ad7a4a1ad06fdf7e85dbc0adbb2b93b771f"],"state_sha256":"1b0214af635d5e408ab74bfb597218940e8be344efa931d11c7a6ec9b5eae509"}