{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BY6Y7UQH2QRUICJUOYITKZJMPZ","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":"76483b7a28ea8e69f50e4b11ffd324a81811a497c38242ebf4674cdebfc13dee","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-13T15:16:10Z","title_canon_sha256":"54371a3dafb48dfafda215c8ab6ad6d2de8e93ca5a9d378f2b6d46cbcd88c6bf"},"schema_version":"1.0","source":{"id":"1701.03699","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03699","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03699v3","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03699","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"BY6Y7UQH2QRU","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BY6Y7UQH2QRUICJU","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BY6Y7UQH","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:5d677680b577a3e20b41eee538b1defc60fda2f96cc9e096a3fc7a8440702d3e","target":"graph","created_at":"2026-05-18T00:16:19Z","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":"Given any polynomial $p$ in $C[X]$, we show that the set of irreducible matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we count the number of irreducible matrices in this set and analyze the arising sequences and their asymptotics. Such matrices turn out to be related to generalized compositions and generalized partitions.","authors_text":"Erik Th\\\"ornblad, Jakob Zimmermann","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-13T15:16:10Z","title":"Counting Quasi-Idempotent Irreducible Integral Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03699","kind":"arxiv","version":3},"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:bac5f9f1abdae1e4c399afcdcb376d281ccb3ee14a8bfeadd3376384f7c0db75","target":"record","created_at":"2026-05-18T00:16:19Z","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":"76483b7a28ea8e69f50e4b11ffd324a81811a497c38242ebf4674cdebfc13dee","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-13T15:16:10Z","title_canon_sha256":"54371a3dafb48dfafda215c8ab6ad6d2de8e93ca5a9d378f2b6d46cbcd88c6bf"},"schema_version":"1.0","source":{"id":"1701.03699","kind":"arxiv","version":3}},"canonical_sha256":"0e3d8fd207d423440934761135652c7e4f602e446edd5fa7e3087ee9130c5c3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e3d8fd207d423440934761135652c7e4f602e446edd5fa7e3087ee9130c5c3a","first_computed_at":"2026-05-18T00:16:19.572733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:19.572733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9UkswiFwj/hw3bGzUZGLiJ1g5OZ4jjQ4CIi2Ier+xD/7tyEsUluv+3Dy4DTTgUIF/Nrt7xB56W+zO5ux0wIDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:19.573171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03699","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bac5f9f1abdae1e4c399afcdcb376d281ccb3ee14a8bfeadd3376384f7c0db75","sha256:5d677680b577a3e20b41eee538b1defc60fda2f96cc9e096a3fc7a8440702d3e"],"state_sha256":"353882dfe1db6482a055c369620f703ee354c5b246cad6e0758b1995d7cbf5ce"}