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We consider the equidistribution in $\\mathbb T=\\mathbb K_\\infty/\\mathbb F_q[t]$ of the values of polynomials $f(u)\\in \\mathbb K_\\infty [u]$ as $u$ varies over $\\mathbb F_q[t]$. Let $\\mathcal K$ be a finite set of positive integers, and suppose that $\\alpha_r\\in \\mathbb K_\\infty$ for $r\\in \\mathcal K\\cup \\{0\\}$. We show that the polynomial $\\sum_{r\\in \\mathcal K\\cup\\{0\\}}\\alpha_ru^r$ is equidistributed in $\\mathbb T$ wh"},"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":"2512.16118","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T03:11:48Z","cross_cats_sorted":[],"title_canon_sha256":"d5e3ecc164c1504e80b634481b0405f0cf24653139198af7f4e78604b8ca0e89","abstract_canon_sha256":"4d9333c301e98eea86b80aa887a55e3fdb67b3448f9986a8d918cb99f3180f39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:38.594084Z","signature_b64":"rZKkXMsqiErkHWlsv8ZWoEG5YBpL15HcEUFuquNB6Nc6QbzKVRcSCg3A4kjuxe8y/ZoMnZYEHYdORFLb2FfgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"446a91e99351b0dcd5fb29bd71d2bf62bc2d2f3239988c052a0b0ad4c4ab115e","last_reissued_at":"2026-05-22T02:04:38.593099Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:38.593099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equidistribution of polynomial sequences in function fields: resolution of a conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\'er\\'emy Champagne, Th\\'ai Ho\\`ang L\\^e, Trevor D. Wooley, Yu-Ru Liu, Zhenchao Ge","submitted_at":"2025-12-18T03:11:48Z","abstract_excerpt":"Let $\\mathbb F_q$ be the finite field of $q$ elements having characteristic $p$, and denote by $\\mathbb K_\\infty=\\mathbb F_q((1/t))$ the field of formal Laurent series in $1/t$. We consider the equidistribution in $\\mathbb T=\\mathbb K_\\infty/\\mathbb F_q[t]$ of the values of polynomials $f(u)\\in \\mathbb K_\\infty [u]$ as $u$ varies over $\\mathbb F_q[t]$. Let $\\mathcal K$ be a finite set of positive integers, and suppose that $\\alpha_r\\in \\mathbb K_\\infty$ for $r\\in \\mathcal K\\cup \\{0\\}$. We show that the polynomial $\\sum_{r\\in \\mathcal K\\cup\\{0\\}}\\alpha_ru^r$ is equidistributed in $\\mathbb T$ wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.16118","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.16118/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":"2512.16118","created_at":"2026-05-22T02:04:38.593243+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.16118v3","created_at":"2026-05-22T02:04:38.593243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.16118","created_at":"2026-05-22T02:04:38.593243+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRVJD2MTKGYN","created_at":"2026-05-22T02:04:38.593243+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRVJD2MTKGYNZVP3","created_at":"2026-05-22T02:04:38.593243+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRVJD2MT","created_at":"2026-05-22T02:04:38.593243+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/IRVJD2MTKGYNZVP3FG6XDUV7MK","json":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK.json","graph_json":"https://pith.science/api/pith-number/IRVJD2MTKGYNZVP3FG6XDUV7MK/graph.json","events_json":"https://pith.science/api/pith-number/IRVJD2MTKGYNZVP3FG6XDUV7MK/events.json","paper":"https://pith.science/paper/IRVJD2MT"},"agent_actions":{"view_html":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK","download_json":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK.json","view_paper":"https://pith.science/paper/IRVJD2MT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.16118&json=true","fetch_graph":"https://pith.science/api/pith-number/IRVJD2MTKGYNZVP3FG6XDUV7MK/graph.json","fetch_events":"https://pith.science/api/pith-number/IRVJD2MTKGYNZVP3FG6XDUV7MK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/action/storage_attestation","attest_author":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/action/author_attestation","sign_citation":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/action/citation_signature","submit_replication":"https://pith.science/pith/IRVJD2MTKGYNZVP3FG6XDUV7MK/action/replication_record"}},"created_at":"2026-05-22T02:04:38.593243+00:00","updated_at":"2026-05-22T02:04:38.593243+00:00"}