What was already known
Wang previously proved D_q(n)<n and conjectured the exact value ⌊n/(q−1)⌋. A separate AI-found eleven-class F₇ example in the new paper disproves that exact formula.
AI involvement
ChatGPT 5.6 Sol supplied the truncated CRT/Brun-sieve strategy and the separate F₇ counterexample. Rongyin Wang corrected the output, completed the theorem and explained the construction; Thomas Bloom suggested probabilistic methods.
The model supplied the truncated CRT/Brun-sieve approach used in the central upper-bound lemma; Wang supplied corrections and missing arguments.
Importance
Determines the sharp leading coefficient of D_q(n) for every fixed q.
Limitations
Wang corrected generated material and supplied missing proof steps. The source documents checking that material, but not a separate completed check of the final theorem.
Technical verification
Wang explicitly checked and corrected generated material, including the model contribution, but the source does not document a completed rigorous check of the final theorem. The finite Example 3 is also checked; no machine proof is documented.
Independent checking
Independent human checking and correction of generated material
- Checker
- Rongyin Wang, paper author
- Scope
- ChatGPT-generated Example 3 and truncated CRT/Brun-sieve material used in Lemma 7
- Basis
- Reported by the linked checker
Human understanding
Wang explains the low-modulus/high-modulus split, truncated inclusion–exclusion upper bound, and nested-modulus lower construction; missing model arguments were supplied by the author.
Correction and publication history
Determines the sharp leading coefficient of D_q(n) for every fixed q.
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