{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:27ZSTWBX3CRAZ3LAUOJXPJATZX","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":"cfc42c17cda15a54390ca0cec5fcce6c4d3b3f3478863bc163ccde52d7ce3e00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-30T09:35:25Z","title_canon_sha256":"4666df0eaca9a2a1e48922f14e445b019a225b834889f56bd4e950548a7db5d9"},"schema_version":"1.0","source":{"id":"1310.8078","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8078","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8078v2","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8078","created_at":"2026-05-18T03:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"27ZSTWBX3CRA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"27ZSTWBX3CRAZ3LA","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"27ZSTWBX","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:0f54f1168aee699bdb3575e023cf9fe6f32491200461de311a04f9c64248e333","target":"graph","created_at":"2026-05-18T03:04:36Z","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":"In this paper, we show that the eigenvalues of certain classes of Cayley graphs are integers. The (n,k,r)-arrangement graph A(n,k,r) is a graph with all the k-permutations of an n-element set as vertices where two k-permutations are adjacent if they differ in exactly r positions. We establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain Cayley graphs. As a result, the conjecture on integrality of eigenvalues of A(n,k,1) follows.","authors_text":"Bai Fan Chen, Ebrahim Ghorbani, Kok Bin Wong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-30T09:35:25Z","title":"On the eigenvalues of certain Cayley graphs and arrangement graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8078","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:da75b9b1115c2a8ab9b29dcde39ef738673584fb9c65939fe21d34892c6874bd","target":"record","created_at":"2026-05-18T03:04:36Z","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":"cfc42c17cda15a54390ca0cec5fcce6c4d3b3f3478863bc163ccde52d7ce3e00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-30T09:35:25Z","title_canon_sha256":"4666df0eaca9a2a1e48922f14e445b019a225b834889f56bd4e950548a7db5d9"},"schema_version":"1.0","source":{"id":"1310.8078","kind":"arxiv","version":2}},"canonical_sha256":"d7f329d837d8a20ced60a39377a413cdfb3163d0c569c299c1af5e3647ac2004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7f329d837d8a20ced60a39377a413cdfb3163d0c569c299c1af5e3647ac2004","first_computed_at":"2026-05-18T03:04:36.778515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:36.778515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucSXIZYMuAYRbsmRrf/jWeOmRu9MFzckvmqEXGIKwXGB8LPA10LCSLA529oBaHpZ3lXpfDf4+yIcUnibigsPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:36.779240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8078","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da75b9b1115c2a8ab9b29dcde39ef738673584fb9c65939fe21d34892c6874bd","sha256:0f54f1168aee699bdb3575e023cf9fe6f32491200461de311a04f9c64248e333"],"state_sha256":"d59f97dc2f9dd8e45646178cc7b02aac588d115857d72fc9e6938d72b9f044df"}