VibeMathedMath problems solved by AI
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Non-Covering Congruence Systems over Fq[x]

Let Dq(n)D_q(n) be the largest possible least degree of a polynomial omitted by a non-covering family of nn distinct-modulus congruence classes in Fq[x]\mathbb{F}_q[x]. What is its asymptotic size? The answer is Dq(n)=nq−1+Oq(1)D_q(n) = \frac{n}{q-1} + O_q(1).

Result
Proved (leading asymptotic determined up to a bounded q-dependent term)
Status
Resolved
AI contribution
AI co-developed
Method
Argument
Field
Function-field arithmetic
Posed by
—
Year posed
—
Years open
—
Solved
2026-07-30
Model
ChatGPT-5.6 Sol
Vendor
OpenAI
Collaborators
Rongyin Wang
Verification
Unreviewed
Publication
Preprint
Significance
10 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

The model contributed the nested-modulus lower-bound construction and the idea of a truncated Chinese-remainder-theorem sieve for the upper bound; the author verified the arguments, added details and filled gaps.

Verification

Author-verified arXiv preprint with theorem-specific AI attribution; relies on the known theorem that a non-covering family of n classes omits a polynomial of degree below n. Not yet peer-reviewed.

Source

arXiv:2607.27538 - An asymptotic bound for non-covering congruence systems over Fq[x]

Changelog4 changes
  • Rasmus Lindahlcommented
  • AmberDingo347commented
  • AmberDingo347changed Source URL from “https://arxiv.org/abs/2607.27533” to “https://arxiv.org/abs/2607.27538”
  • AmberDingo347changed Source name from “arXiv:2607.27533 - An asymptotic bound for non-covering congruence systems over Fq[x]” to “arXiv:2607.27538 - An asymptotic bound for non-covering congruence systems over Fq[x]”

Discussion2