{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4JKHT3ABPODCDHCQEBNT3XMBM7","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":"e9a09db9ae8dd2d5d44628999e92b9f317f7b10f7b496f3bd79b6dce02f1dddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-13T12:21:53Z","title_canon_sha256":"765b5a369f1f27c77fdc5b2116fef361c01d84ff2a019ad6be668c3b9a2bc102"},"schema_version":"1.0","source":{"id":"2310.09052","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.09052","created_at":"2026-07-05T10:15:14Z"},{"alias_kind":"arxiv_version","alias_value":"2310.09052v2","created_at":"2026-07-05T10:15:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.09052","created_at":"2026-07-05T10:15:14Z"},{"alias_kind":"pith_short_12","alias_value":"4JKHT3ABPODC","created_at":"2026-07-05T10:15:14Z"},{"alias_kind":"pith_short_16","alias_value":"4JKHT3ABPODCDHCQ","created_at":"2026-07-05T10:15:14Z"},{"alias_kind":"pith_short_8","alias_value":"4JKHT3AB","created_at":"2026-07-05T10:15:14Z"}],"graph_snapshots":[{"event_id":"sha256:5c5c9e83211a8e563a20623b077a5598bcfd09936d0e843030f78be53bcbad8b","target":"graph","created_at":"2026-07-05T10:15:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.09052/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the set $\\mathcal{M}_n(\\mathbb{Z}; H)$ of $n\\times n$-matrices with integer elements of size at most $H$ and obtain upper and lower bounds on the number of distinct irreducible characteristic polynomials which correspond to these matrices and thus on the number of distinct eigenvalues of these matrices. In particular, we improve some results of A.~Abrams, Z.~Landau, J.~Pommersheim and N.~Srivastava (2022).","authors_text":"Igor E. Shparlinski, L\\'aszl\\'o M\\'erai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-13T12:21:53Z","title":"Number of characteristic polynomials of matrices with bounded height"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.09052","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":"sha256:7c6ad893f825f4aa01a189341bfe5a60aad05a013338d2edb28e8a91f85f3f5b","target":"record","created_at":"2026-07-05T10:15:14Z","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":"e9a09db9ae8dd2d5d44628999e92b9f317f7b10f7b496f3bd79b6dce02f1dddc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-10-13T12:21:53Z","title_canon_sha256":"765b5a369f1f27c77fdc5b2116fef361c01d84ff2a019ad6be668c3b9a2bc102"},"schema_version":"1.0","source":{"id":"2310.09052","kind":"arxiv","version":2}},"canonical_sha256":"e25479ec017b86219c50205b3ddd8167ed6c03416aa919316319200a54555bde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e25479ec017b86219c50205b3ddd8167ed6c03416aa919316319200a54555bde","first_computed_at":"2026-07-05T10:15:14.695171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:15:14.695171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CSJIcnwhJMM//FbTZF5xOfoKltYznVJmsjOcpmC7t4llKAFFS9HubC+MWEHbAfYgiQqH1lIwj+dBD85ZqwTNAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:15:14.695694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.09052","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c6ad893f825f4aa01a189341bfe5a60aad05a013338d2edb28e8a91f85f3f5b","sha256:5c5c9e83211a8e563a20623b077a5598bcfd09936d0e843030f78be53bcbad8b"],"state_sha256":"2ed86373db66d1a6b9df41e2bc88e7d7d95a978192f3293e7713440560565b9d"}