{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:J6LWTOB64UBNNGVV6YEWUUIKS7","short_pith_number":"pith:J6LWTOB6","schema_version":"1.0","canonical_sha256":"4f9769b83ee502d69ab5f6096a510a97c30b346bdedbae572b22bf3c6021ed1c","source":{"kind":"arxiv","id":"1301.6332","version":3},"attestation_state":"computed","paper":{"title":"Integer-valued polynomials over matrices and divided differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Giulio Peruginelli","submitted_at":"2013-01-27T08:24:28Z","abstract_excerpt":"Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a positive integer. We give a characterization of the polynomials in $K[X]$ which are integer-valued over the set of matrices $M_n(D)$ in terms of their divided differences. A necessary and sufficient condition on $f\\in K[X]$ to be integer-valued over $M_n(D)$ is that, for each $k$ less than $n$, the $k$-th divided difference of $f$ is integral-valued on every subset of the roots of any monic polynomial over $D$ of degree $n$. If in addition the intersection of the maximal ideals of finite index is $(0)$ then it is sufficie"},"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":"1301.6332","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-27T08:24:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"38cebc7a593743d10f91401e9888c651556eea4f7b992bfb7a2ee0d2a1ed6bbd","abstract_canon_sha256":"f775bb23b25872924c0ada8c04b12b96ed810bf269d852c61234ef0ab73dd07f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:24.569133Z","signature_b64":"yiJt/JpGXzAG1NGwtPAZMnMYMHN35YB7WE23S0q3kBBsYEYKCUiAaKXcxet5NrKGLJQz/eu8GV+7O46ktmzRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f9769b83ee502d69ab5f6096a510a97c30b346bdedbae572b22bf3c6021ed1c","last_reissued_at":"2026-05-18T00:04:24.568560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:24.568560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integer-valued polynomials over matrices and divided differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Giulio Peruginelli","submitted_at":"2013-01-27T08:24:28Z","abstract_excerpt":"Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a positive integer. We give a characterization of the polynomials in $K[X]$ which are integer-valued over the set of matrices $M_n(D)$ in terms of their divided differences. A necessary and sufficient condition on $f\\in K[X]$ to be integer-valued over $M_n(D)$ is that, for each $k$ less than $n$, the $k$-th divided difference of $f$ is integral-valued on every subset of the roots of any monic polynomial over $D$ of degree $n$. If in addition the intersection of the maximal ideals of finite index is $(0)$ then it is sufficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6332","kind":"arxiv","version":3},"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":"1301.6332","created_at":"2026-05-18T00:04:24.568652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6332v3","created_at":"2026-05-18T00:04:24.568652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6332","created_at":"2026-05-18T00:04:24.568652+00:00"},{"alias_kind":"pith_short_12","alias_value":"J6LWTOB64UBN","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"J6LWTOB64UBNNGVV","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"J6LWTOB6","created_at":"2026-05-18T12:27:49.015174+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/J6LWTOB64UBNNGVV6YEWUUIKS7","json":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7.json","graph_json":"https://pith.science/api/pith-number/J6LWTOB64UBNNGVV6YEWUUIKS7/graph.json","events_json":"https://pith.science/api/pith-number/J6LWTOB64UBNNGVV6YEWUUIKS7/events.json","paper":"https://pith.science/paper/J6LWTOB6"},"agent_actions":{"view_html":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7","download_json":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7.json","view_paper":"https://pith.science/paper/J6LWTOB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6332&json=true","fetch_graph":"https://pith.science/api/pith-number/J6LWTOB64UBNNGVV6YEWUUIKS7/graph.json","fetch_events":"https://pith.science/api/pith-number/J6LWTOB64UBNNGVV6YEWUUIKS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7/action/storage_attestation","attest_author":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7/action/author_attestation","sign_citation":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7/action/citation_signature","submit_replication":"https://pith.science/pith/J6LWTOB64UBNNGVV6YEWUUIKS7/action/replication_record"}},"created_at":"2026-05-18T00:04:24.568652+00:00","updated_at":"2026-05-18T00:04:24.568652+00:00"}