{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GB6BLHNPTNTAPES5RHBQ3FND3F","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":"3bb9da1cd58283d976f3fbeb46fba5f70dd1e61f2d44e5c2629fa4c3fcd1c93a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-09-18T20:17:34Z","title_canon_sha256":"1d9522778cfcf453ceab972cdabfe770f6c79abb2d2644422a3fbb9b56f334c6"},"schema_version":"1.0","source":{"id":"1909.08683","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.08683","created_at":"2026-07-05T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1909.08683v2","created_at":"2026-07-05T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.08683","created_at":"2026-07-05T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"GB6BLHNPTNTA","created_at":"2026-07-05T00:44:18Z"},{"alias_kind":"pith_short_16","alias_value":"GB6BLHNPTNTAPES5","created_at":"2026-07-05T00:44:18Z"},{"alias_kind":"pith_short_8","alias_value":"GB6BLHNP","created_at":"2026-07-05T00:44:18Z"}],"graph_snapshots":[{"event_id":"sha256:dee32078723799275fa634bdf1cdfb4b7276f9eb20d953d787064d20e69cc8d8","target":"graph","created_at":"2026-07-05T00:44:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.08683/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a non-affine latin quandle (also known as left distributive quasigroup) of order $2^k$ exists if and only if $k = 6$ or $k \\geq 8$. The construction is expressed in terms of central extensions of affine quandles.","authors_text":"Tom\\'a\\v{s} Nagy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-09-18T20:17:34Z","title":"Non-affine latin quandles of order $2^k$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.08683","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":"sha256:173cabd8ef908eb348d902beb8708ddc9272e47eedef48358953f5cb8764597f","target":"record","created_at":"2026-07-05T00:44:18Z","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":"3bb9da1cd58283d976f3fbeb46fba5f70dd1e61f2d44e5c2629fa4c3fcd1c93a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-09-18T20:17:34Z","title_canon_sha256":"1d9522778cfcf453ceab972cdabfe770f6c79abb2d2644422a3fbb9b56f334c6"},"schema_version":"1.0","source":{"id":"1909.08683","kind":"arxiv","version":2}},"canonical_sha256":"307c159daf9b6607925d89c30d95a3d97d68d59e282be03257f667e50120813f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"307c159daf9b6607925d89c30d95a3d97d68d59e282be03257f667e50120813f","first_computed_at":"2026-07-05T00:44:18.345572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:44:18.345572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yT0Nqf0s+Lgv+pENEzrTwHwJerLitSYDlUGbnkVRAmElaR7Wjc80hthT2COnMDs7Ul0695Z1dUVdF/CUJ4naBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:44:18.346020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.08683","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:173cabd8ef908eb348d902beb8708ddc9272e47eedef48358953f5cb8764597f","sha256:dee32078723799275fa634bdf1cdfb4b7276f9eb20d953d787064d20e69cc8d8"],"state_sha256":"b627f5176dba8bdc78a5e4cfbc88a4d4be7cfd902a3bba72c5b44871dd72e7f6"}