{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WB6IG2GN5733PTL6BK5AC76QPU","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":"966dde55f8018de2cae091227b622babe59bd2d934366aa1a31710042a0bf82d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-06-19T20:22:56Z","title_canon_sha256":"28ff6b46b66404fa1bf08d90c2940688bf6911ef154629b93b5ee0d49f0f9bed"},"schema_version":"1.0","source":{"id":"1006.3886","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3886","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3886v2","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3886","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"WB6IG2GN5733","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WB6IG2GN5733PTL6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WB6IG2GN","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:1d5d7b261feaddb2b501b75789c8ade0f916c7ee18a5d110c33536c0dd6b1df3","target":"graph","created_at":"2026-05-17T23:53:19Z","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 (right) automorphic if all its (right) inner mappings are automorphisms. Using the classification of primitive groups of small degrees, we show that there is no nonassociative simple commutative automorphic loop of order less than $2^{12}$, and no nonassociative simple automorphic loop of order less that 2500. We obtain examples of nonassociative simple right automorphic loops.","authors_text":"Gabor Nagy, Kenneth W. Johnson, Michael Kinyon, Petr Vojtechovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-06-19T20:22:56Z","title":"Searching for small simple automorphic loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3886","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:c593a0c17a2e1b29a322e07de2b0662f6e02f8a3f66008f421ed782270ee8440","target":"record","created_at":"2026-05-17T23:53:19Z","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":"966dde55f8018de2cae091227b622babe59bd2d934366aa1a31710042a0bf82d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-06-19T20:22:56Z","title_canon_sha256":"28ff6b46b66404fa1bf08d90c2940688bf6911ef154629b93b5ee0d49f0f9bed"},"schema_version":"1.0","source":{"id":"1006.3886","kind":"arxiv","version":2}},"canonical_sha256":"b07c8368cdeff7b7cd7e0aba017fd07d109ee68e696359a3c24c375319f8a4cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b07c8368cdeff7b7cd7e0aba017fd07d109ee68e696359a3c24c375319f8a4cd","first_computed_at":"2026-05-17T23:53:19.709094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:19.709094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MpFbjgvgWM8Tbk//KreRJnn6kGZ9o7a2/QvldAsSVAP0HmuznncUbJEJkslw0x6Ar590nB8jlFZrPO8YKAzpBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:19.709710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3886","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c593a0c17a2e1b29a322e07de2b0662f6e02f8a3f66008f421ed782270ee8440","sha256:1d5d7b261feaddb2b501b75789c8ade0f916c7ee18a5d110c33536c0dd6b1df3"],"state_sha256":"4fefdf1b88e3a5eb7fcc9a94f300416fa9639582cd1416fb5f6c5803535ffdf1"}