{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IQMMPAZEIWF6TGEV4NZGVDS7P2","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":"7d78e91d2833f1ec68ee88507a7966a261e518d684cc2bc970973d0961a7756c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-04T03:18:28Z","title_canon_sha256":"40032e5b91cfc37f0356100ee9b7a5e3233ff574bd01ce9605a8344afee3d2ec"},"schema_version":"1.0","source":{"id":"1304.1236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1236","created_at":"2026-05-18T03:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1236v2","created_at":"2026-05-18T03:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1236","created_at":"2026-05-18T03:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"IQMMPAZEIWF6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IQMMPAZEIWF6TGEV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IQMMPAZE","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:dc8c9262fcb4148b87f99f039b83ad8d415bab8b533604942d77422ddfa6f2ca","target":"graph","created_at":"2026-05-18T03:28:45Z","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":"Let $G$ be a finite connected graph on two or more vertices and $G^{[N,k]}$ the distance $k$-graph of the $N$-fold Cartesian power of $G$. For a fixed $k\\ge1$, we obtain explicitly the large $N$ limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of $G^{[N,k]}$. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","authors_text":"Hun Hee Lee, Nobuaki Obata, Yuji Hibino","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-04T03:18:28Z","title":"Asymptotic Spectral Distributions of Distance $k$-Graphs of Cartesian Product Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1236","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:ef5965b12eee1345cce60f2c1a9dc5b869a88b43f39d4537b99d493bf60c7420","target":"record","created_at":"2026-05-18T03:28:45Z","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":"7d78e91d2833f1ec68ee88507a7966a261e518d684cc2bc970973d0961a7756c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-04T03:18:28Z","title_canon_sha256":"40032e5b91cfc37f0356100ee9b7a5e3233ff574bd01ce9605a8344afee3d2ec"},"schema_version":"1.0","source":{"id":"1304.1236","kind":"arxiv","version":2}},"canonical_sha256":"4418c78324458be99895e3726a8e5f7e94d0c8c6901fef059875120421c8d0f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4418c78324458be99895e3726a8e5f7e94d0c8c6901fef059875120421c8d0f4","first_computed_at":"2026-05-18T03:28:45.182501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:45.182501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lMfbWuuFEh06AfasDk3JV/6mmZ5rHtd065wNyKhzffyUMCjp6uz3U3ZD54U1Cgqa7VsITH9/TSnkKhQy+mZ4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:45.183160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef5965b12eee1345cce60f2c1a9dc5b869a88b43f39d4537b99d493bf60c7420","sha256:dc8c9262fcb4148b87f99f039b83ad8d415bab8b533604942d77422ddfa6f2ca"],"state_sha256":"aac6d7e84934c97505da168d1684016ad31eb42ba90c8740dccfb0cf0722941b"}