{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4IGMZKPO5USL33GZE6GRUVS5CH","short_pith_number":"pith:4IGMZKPO","schema_version":"1.0","canonical_sha256":"e20ccca9eeed24bdecd9278d1a565d11f0476ab307168fa574eb3922c2eb3016","source":{"kind":"arxiv","id":"2606.15394","version":2},"attestation_state":"computed","paper":{"title":"Dominant Zeros of Nekrasov--Okounkov Polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Bernhard Heim, Markus Neuhauser, with an appendix by Ken Ono","submitted_at":"2026-06-13T16:56:59Z","abstract_excerpt":"We give an exact finite-dimensional Perron--Frobenius realization of the dominant zero of the Nekrasov--Okounkov polynomials $\\nop _n(z)$. For a normalized positive sequence $h=(h(n))_{n\\ge 1}$ with $h(1)=1$, define $\\pol _0^h(z)=1$ and, for $n\\ge 1$, \\[ \\pol _n^h(z)=\\frac{z}{h(n)}\\sum_{k=1}^n \\sigma(k)\\pol _{n-k}^h(z),\\] where $\\sigma(k)$ denotes the sum of divisors of $k$. The Nekrasov--Okounkov polynomials are obtained from the specialization $h(n)=n$ by the shift $\\nop _n(z)=\\pol _n^h(z+1)$. We derive a Hessenberg determinant representation for $\\pol _n^h(z)$. After separating the trivial "},"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":"2606.15394","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-13T16:56:59Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8587a0e37f3072a280fd7efd64702941f14b533276b3ddb90492a4528bb49615","abstract_canon_sha256":"a342270481ce5bfddcd4acc1edd0a2b85d2efc5969c4c7b1df0d8c0b30aeece1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:21.741124Z","signature_b64":"fCDH+fXvet2qRsnv+GLHjh/aWJ62FjZxtgBCL+TSDUy75SAOzQe4gFaJw0DP+bun1IRc0NK+DYF/E+/rZP6ECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e20ccca9eeed24bdecd9278d1a565d11f0476ab307168fa574eb3922c2eb3016","last_reissued_at":"2026-06-19T16:12:21.740787Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:21.740787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dominant Zeros of Nekrasov--Okounkov Polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Bernhard Heim, Markus Neuhauser, with an appendix by Ken Ono","submitted_at":"2026-06-13T16:56:59Z","abstract_excerpt":"We give an exact finite-dimensional Perron--Frobenius realization of the dominant zero of the Nekrasov--Okounkov polynomials $\\nop _n(z)$. For a normalized positive sequence $h=(h(n))_{n\\ge 1}$ with $h(1)=1$, define $\\pol _0^h(z)=1$ and, for $n\\ge 1$, \\[ \\pol _n^h(z)=\\frac{z}{h(n)}\\sum_{k=1}^n \\sigma(k)\\pol _{n-k}^h(z),\\] where $\\sigma(k)$ denotes the sum of divisors of $k$. The Nekrasov--Okounkov polynomials are obtained from the specialization $h(n)=n$ by the shift $\\nop _n(z)=\\pol _n^h(z+1)$. We derive a Hessenberg determinant representation for $\\pol _n^h(z)$. After separating the trivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.15394","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.15394/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.15394","created_at":"2026-06-19T16:12:21.740842+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.15394v2","created_at":"2026-06-19T16:12:21.740842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.15394","created_at":"2026-06-19T16:12:21.740842+00:00"},{"alias_kind":"pith_short_12","alias_value":"4IGMZKPO5USL","created_at":"2026-06-19T16:12:21.740842+00:00"},{"alias_kind":"pith_short_16","alias_value":"4IGMZKPO5USL33GZ","created_at":"2026-06-19T16:12:21.740842+00:00"},{"alias_kind":"pith_short_8","alias_value":"4IGMZKPO","created_at":"2026-06-19T16:12:21.740842+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/4IGMZKPO5USL33GZE6GRUVS5CH","json":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH.json","graph_json":"https://pith.science/api/pith-number/4IGMZKPO5USL33GZE6GRUVS5CH/graph.json","events_json":"https://pith.science/api/pith-number/4IGMZKPO5USL33GZE6GRUVS5CH/events.json","paper":"https://pith.science/paper/4IGMZKPO"},"agent_actions":{"view_html":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH","download_json":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH.json","view_paper":"https://pith.science/paper/4IGMZKPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.15394&json=true","fetch_graph":"https://pith.science/api/pith-number/4IGMZKPO5USL33GZE6GRUVS5CH/graph.json","fetch_events":"https://pith.science/api/pith-number/4IGMZKPO5USL33GZE6GRUVS5CH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH/action/storage_attestation","attest_author":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH/action/author_attestation","sign_citation":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH/action/citation_signature","submit_replication":"https://pith.science/pith/4IGMZKPO5USL33GZE6GRUVS5CH/action/replication_record"}},"created_at":"2026-06-19T16:12:21.740842+00:00","updated_at":"2026-06-19T16:12:21.740842+00:00"}