{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IQMMPAZEIWF6TGEV4NZGVDS7P2","short_pith_number":"pith:IQMMPAZE","schema_version":"1.0","canonical_sha256":"4418c78324458be99895e3726a8e5f7e94d0c8c6901fef059875120421c8d0f4","source":{"kind":"arxiv","id":"1304.1236","version":2},"attestation_state":"computed","paper":{"title":"Asymptotic Spectral Distributions of Distance $k$-Graphs of Cartesian Product Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Hun Hee Lee, Nobuaki Obata, Yuji Hibino","submitted_at":"2013-04-04T03:18:28Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.1236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-04-04T03:18:28Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"40032e5b91cfc37f0356100ee9b7a5e3233ff574bd01ce9605a8344afee3d2ec","abstract_canon_sha256":"7d78e91d2833f1ec68ee88507a7966a261e518d684cc2bc970973d0961a7756c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:45.183160Z","signature_b64":"lMfbWuuFEh06AfasDk3JV/6mmZ5rHtd065wNyKhzffyUMCjp6uz3U3ZD54U1Cgqa7VsITH9/TSnkKhQy+mZ4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4418c78324458be99895e3726a8e5f7e94d0c8c6901fef059875120421c8d0f4","last_reissued_at":"2026-05-18T03:28:45.182501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:45.182501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Spectral Distributions of Distance $k$-Graphs of Cartesian Product Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Hun Hee Lee, Nobuaki Obata, Yuji Hibino","submitted_at":"2013-04-04T03:18:28Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1236","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.1236","created_at":"2026-05-18T03:28:45.182625+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.1236v2","created_at":"2026-05-18T03:28:45.182625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1236","created_at":"2026-05-18T03:28:45.182625+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQMMPAZEIWF6","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQMMPAZEIWF6TGEV","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQMMPAZE","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2","json":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2.json","graph_json":"https://pith.science/api/pith-number/IQMMPAZEIWF6TGEV4NZGVDS7P2/graph.json","events_json":"https://pith.science/api/pith-number/IQMMPAZEIWF6TGEV4NZGVDS7P2/events.json","paper":"https://pith.science/paper/IQMMPAZE"},"agent_actions":{"view_html":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2","download_json":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2.json","view_paper":"https://pith.science/paper/IQMMPAZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.1236&json=true","fetch_graph":"https://pith.science/api/pith-number/IQMMPAZEIWF6TGEV4NZGVDS7P2/graph.json","fetch_events":"https://pith.science/api/pith-number/IQMMPAZEIWF6TGEV4NZGVDS7P2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2/action/storage_attestation","attest_author":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2/action/author_attestation","sign_citation":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2/action/citation_signature","submit_replication":"https://pith.science/pith/IQMMPAZEIWF6TGEV4NZGVDS7P2/action/replication_record"}},"created_at":"2026-05-18T03:28:45.182625+00:00","updated_at":"2026-05-18T03:28:45.182625+00:00"}