{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZCAZIVSFPGTS6USSGE7UZVW4IP","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":"b22a388bb772714658b95de80539506d83ec15b1ce46a422896ae9f6527bdccc","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-27T17:03:40Z","title_canon_sha256":"4e57143014faf76d40aca381b5d408622bad0a1542dcf82e28e9634fe35145eb"},"schema_version":"1.0","source":{"id":"1508.07257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07257","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07257v1","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07257","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZCAZIVSFPGTS","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZCAZIVSFPGTS6USS","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZCAZIVSF","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:5cd7f4173b3227815025a60a6c2c5ca843095568d2230ec879422208040b4a47","target":"graph","created_at":"2026-05-18T01:34:36Z","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":"\\noindent The augmented cube graph $AQ_n$ is the Cayley graph of $\\mathbb{Z}_2^n$ with respect to the set of $2n-1$ generators $\\{e_1,e_2, \\ldots,e_n, 00\\ldots0011, 00\\ldots0111, 11\\ldots1111 \\}$. It is known that the order of the automorphism group of the graph $AQ_n$ is $2^{n+3}$, for all $n \\ge 4$. In the present paper, we obtain the structure of the automorphism group of $AQ_n$ to be \\[ \\Aut(AQ_n) \\cong \\mathbb{Z}_2^n \\rtimes D_8~~(n \\ge 4),\\] where $D_8$ is the dihedral group of order 8. It is shown that the Cayley graph $AQ_3$ is non-normal and that $AQ_n$ is normal for all $n \\ge 4$. We","authors_text":"Ashwin Ganesan","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-27T17:03:40Z","title":"Structure of the automorphism group of the augmented cube graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07257","kind":"arxiv","version":1},"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:f8bd5d3b78fbc0fbea33cac3540fbabc2db6a601804f1ac45241625e177efbd0","target":"record","created_at":"2026-05-18T01:34:36Z","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":"b22a388bb772714658b95de80539506d83ec15b1ce46a422896ae9f6527bdccc","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-27T17:03:40Z","title_canon_sha256":"4e57143014faf76d40aca381b5d408622bad0a1542dcf82e28e9634fe35145eb"},"schema_version":"1.0","source":{"id":"1508.07257","kind":"arxiv","version":1}},"canonical_sha256":"c88194564579a72f5252313f4cd6dc43deabad00bb8cfc2bb53f0508f7adabb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c88194564579a72f5252313f4cd6dc43deabad00bb8cfc2bb53f0508f7adabb9","first_computed_at":"2026-05-18T01:34:36.503720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:36.503720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y+in3QXPwvUfcI3zRHBrYYmSKH0Lp5Vhl4zUyq4+TRK0Tt/SiyRvoor6cKITjqRSr6D4TjD+/NlkUysIwKzjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:36.504387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8bd5d3b78fbc0fbea33cac3540fbabc2db6a601804f1ac45241625e177efbd0","sha256:5cd7f4173b3227815025a60a6c2c5ca843095568d2230ec879422208040b4a47"],"state_sha256":"7451fe48a62b1d0950c539e25114644bc9e7cab00d19409abb68cac9832376e1"}