{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D3DKNMVKBUVFVOUBXCO6CJNG46","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":"6c058bdc81cbd78195b6ab6a4274b1f620938f550d791abe7800a9101f025cd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-28T17:34:00Z","title_canon_sha256":"2c88cb2aae99ba6db6e191b53bfdfbad9a0c16c22e42eb8b88ff7cb0dfbf63e9"},"schema_version":"1.0","source":{"id":"1508.07287","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07287","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07287v2","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07287","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"pith_short_12","alias_value":"D3DKNMVKBUVF","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D3DKNMVKBUVFVOUB","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D3DKNMVK","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:df2dc662eba0a5dc6e69d23bf24d3a7acc98df606c1e6180a1ab4de2f3f1ab4b","target":"graph","created_at":"2026-05-18T00:46:26Z","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":"The zeta function of an integral lattice $\\Lambda$ is the generating function $\\zeta_{\\Lambda}(s) = \\sum\\limits_{n=0}^{\\infty} a_n n^{-s}$, whose coefficients count the number of left ideals of $\\Lambda$ of index $n$. We derive a formula for the zeta function of $\\Lambda_1 \\otimes \\Lambda_2$, where $\\Lambda_1$ and $\\Lambda_2$ are $\\mathbb{Z}$-orders contained in finite-dimensional semisimple $\\mathbb{Q}$-algebras that satisfy a \"locally coprime\" condition. We apply the formula obtained above to $\\mathbb{Z}S \\otimes \\mathbb{Z}T$ and obtain the zeta function of the adjacency algebra of the direc","authors_text":"Allen Herman, Mitsugu Hirasaka, Semin Oh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-28T17:34:00Z","title":"Zeta functions for tensor products of locally coprime integral adjacency algebras of association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07287","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:e4d7b27808404d06e1195f7fe366c00dd331b9b1c2e0e36d7c8802d054bb481d","target":"record","created_at":"2026-05-18T00:46:26Z","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":"6c058bdc81cbd78195b6ab6a4274b1f620938f550d791abe7800a9101f025cd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-28T17:34:00Z","title_canon_sha256":"2c88cb2aae99ba6db6e191b53bfdfbad9a0c16c22e42eb8b88ff7cb0dfbf63e9"},"schema_version":"1.0","source":{"id":"1508.07287","kind":"arxiv","version":2}},"canonical_sha256":"1ec6a6b2aa0d2a5aba81b89de125a6e7ba818b16edf6ae169c5ed97005dfb3b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ec6a6b2aa0d2a5aba81b89de125a6e7ba818b16edf6ae169c5ed97005dfb3b2","first_computed_at":"2026-05-18T00:46:26.536354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:26.536354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rGUb13889accunGIvozrb5D0npBqrlf2fJvlmof2Gz44NtF5NJjY/Q/rBICcYLgkZ+JnSShDYVjOqdQYTczIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:26.536851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07287","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4d7b27808404d06e1195f7fe366c00dd331b9b1c2e0e36d7c8802d054bb481d","sha256:df2dc662eba0a5dc6e69d23bf24d3a7acc98df606c1e6180a1ab4de2f3f1ab4b"],"state_sha256":"2904ea468b4cd0a9b61287b2c3da997c2f80b747bf28d9ff20ecad84d81dcc8d"}