{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:TCWJGTOYWSE5GZXXD2I4TPPUVN","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":"1a93d93d0f139d5ba3e481a7b1e171a6de6079c89073378d8fda150a0ad5a134","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-12T20:03:30Z","title_canon_sha256":"847cb91cb73d38ebe433143a0ec77aa165d0c891cd4061e654bed949b324f2f2"},"schema_version":"1.0","source":{"id":"0811.1930","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1930","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1930v2","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1930","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"TCWJGTOYWSE5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"TCWJGTOYWSE5GZXX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"TCWJGTOY","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a55e957c74ae0b10fc6d31d254bd2c8d98185508cdbc6ea9ce525cf5514ffaa6","target":"graph","created_at":"2026-05-18T01:02:14Z","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":"We investigate the least common multiple of all subdeterminants, lcmd(A x B), of a Kronecker product of matrices, of which one is an integral matrix A with two columns and the other is the incidence matrix of a complete graph with n vertices. We prove that this quantity is the least common multiple of lcmd(A) to the power n-1 and certain binomial functions of the entries of A.","authors_text":"Christopher R. H. Hanusa, Thomas Zaslavsky","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-12T20:03:30Z","title":"Determinants in the Kronecker product of matrices: The incidence matrix of a complete graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1930","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:ef9c2fb23683bc489a4d6c58f897bf8b5b1dd81302a46c5035dbe7c445f50239","target":"record","created_at":"2026-05-18T01:02:14Z","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":"1a93d93d0f139d5ba3e481a7b1e171a6de6079c89073378d8fda150a0ad5a134","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-11-12T20:03:30Z","title_canon_sha256":"847cb91cb73d38ebe433143a0ec77aa165d0c891cd4061e654bed949b324f2f2"},"schema_version":"1.0","source":{"id":"0811.1930","kind":"arxiv","version":2}},"canonical_sha256":"98ac934dd8b489d366f71e91c9bdf4ab5542e2396d1a1e6506f25f6d1936ec1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98ac934dd8b489d366f71e91c9bdf4ab5542e2396d1a1e6506f25f6d1936ec1b","first_computed_at":"2026-05-18T01:02:14.592528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:14.592528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yPXS51F4owBp5siLolZfFAJWoDNqk3eLWoH7aCy1yP0p6BhocGtMrTdqrvym2pECdxzIwUy4zsKSewQkMAPEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:14.593087Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef9c2fb23683bc489a4d6c58f897bf8b5b1dd81302a46c5035dbe7c445f50239","sha256:a55e957c74ae0b10fc6d31d254bd2c8d98185508cdbc6ea9ce525cf5514ffaa6"],"state_sha256":"246c52f0b967259f0c099e3c4f670420ca4f64740dc8c7f355fec94d7e163f45"}