{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VO5GAHFST7H4Z7QAPERR77J7BS","short_pith_number":"pith:VO5GAHFS","schema_version":"1.0","canonical_sha256":"abba601cb29fcfccfe0079231ffd3f0cb3f60b6a3618763750774a7a6da475ba","source":{"kind":"arxiv","id":"2605.25877","version":1},"attestation_state":"computed","paper":{"title":"Banded quadratic digit functions along irreducible polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kaimin Cheng","submitted_at":"2026-05-25T14:04:47Z","abstract_excerpt":"Let $q$ be an odd prime power and let $\\F_q$ be the finite field with $q$ elements. Let $\\mathcal{P}(n)$ be the set of monic irreducible polynomials of degree $n$ over $\\mathbb{F}_q$. For $f=t^n+f_{n-1}t^{n-1}+\\cdots+f_0\\in\\mathcal{P}(n)$, fix coefficients $c_0,\\ldots,c_m\\in\\mathbb{F}_q$ with $c_m\\ne0$ and put $$ Q_A(f)=\\sum_{j=0}^m c_j\\sum_{i=j}^n f_i f_{i-j}+\\ell_n(f),$$ where $\\ell_n$ is an arbitrary linear form in the coefficients of $f$ and $f_n=1$. We prove that $Q_A$ is equidistributed on $\\mathcal{P}(n)$: for every $\\gamma\\in\\mathbb{F}_q$, $$\\#\\{f\\in\\mathcal{P}(n):Q_A(f)=\\gamma\\}=\\frac"},"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":"2605.25877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-25T14:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"086822c7d27a8c1b6006ccb47a64f7892b5a545bff690e5bec67f93df92926b8","abstract_canon_sha256":"5ddeffa9988a05c96336d9a6c4623853a91fb12652807e3c32c16ddb4d0a7fde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:16.495526Z","signature_b64":"sXGYWxiYVP2i9UWbs1+vmDfg8eCxH3nJhci47uUu/040agMtWMFBKy0Z3ZNQUvV0kq16OaXtVvsPyeRMqiT1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abba601cb29fcfccfe0079231ffd3f0cb3f60b6a3618763750774a7a6da475ba","last_reissued_at":"2026-05-26T02:05:16.494925Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:16.494925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Banded quadratic digit functions along irreducible polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kaimin Cheng","submitted_at":"2026-05-25T14:04:47Z","abstract_excerpt":"Let $q$ be an odd prime power and let $\\F_q$ be the finite field with $q$ elements. Let $\\mathcal{P}(n)$ be the set of monic irreducible polynomials of degree $n$ over $\\mathbb{F}_q$. For $f=t^n+f_{n-1}t^{n-1}+\\cdots+f_0\\in\\mathcal{P}(n)$, fix coefficients $c_0,\\ldots,c_m\\in\\mathbb{F}_q$ with $c_m\\ne0$ and put $$ Q_A(f)=\\sum_{j=0}^m c_j\\sum_{i=j}^n f_i f_{i-j}+\\ell_n(f),$$ where $\\ell_n$ is an arbitrary linear form in the coefficients of $f$ and $f_n=1$. We prove that $Q_A$ is equidistributed on $\\mathcal{P}(n)$: for every $\\gamma\\in\\mathbb{F}_q$, $$\\#\\{f\\in\\mathcal{P}(n):Q_A(f)=\\gamma\\}=\\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25877","kind":"arxiv","version":1},"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/2605.25877/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":"2605.25877","created_at":"2026-05-26T02:05:16.495021+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.25877v1","created_at":"2026-05-26T02:05:16.495021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25877","created_at":"2026-05-26T02:05:16.495021+00:00"},{"alias_kind":"pith_short_12","alias_value":"VO5GAHFST7H4","created_at":"2026-05-26T02:05:16.495021+00:00"},{"alias_kind":"pith_short_16","alias_value":"VO5GAHFST7H4Z7QA","created_at":"2026-05-26T02:05:16.495021+00:00"},{"alias_kind":"pith_short_8","alias_value":"VO5GAHFS","created_at":"2026-05-26T02:05:16.495021+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/VO5GAHFST7H4Z7QAPERR77J7BS","json":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS.json","graph_json":"https://pith.science/api/pith-number/VO5GAHFST7H4Z7QAPERR77J7BS/graph.json","events_json":"https://pith.science/api/pith-number/VO5GAHFST7H4Z7QAPERR77J7BS/events.json","paper":"https://pith.science/paper/VO5GAHFS"},"agent_actions":{"view_html":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS","download_json":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS.json","view_paper":"https://pith.science/paper/VO5GAHFS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.25877&json=true","fetch_graph":"https://pith.science/api/pith-number/VO5GAHFST7H4Z7QAPERR77J7BS/graph.json","fetch_events":"https://pith.science/api/pith-number/VO5GAHFST7H4Z7QAPERR77J7BS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS/action/storage_attestation","attest_author":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS/action/author_attestation","sign_citation":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS/action/citation_signature","submit_replication":"https://pith.science/pith/VO5GAHFST7H4Z7QAPERR77J7BS/action/replication_record"}},"created_at":"2026-05-26T02:05:16.495021+00:00","updated_at":"2026-05-26T02:05:16.495021+00:00"}