What was already known
Palcoux’s question sought subgroup-interval bounds. The source cites earlier general counting results but does not establish how its proposed sharp envelope compares with all prior bounds.
AI involvement
Palcoux supplied the problem prompt. GPT-5.6 Sol produced the retained manuscript in one reported run, and later AI work formalized selected results. Palcoux reports no mathematical edits or review before this code version.
The manuscript's mathematical claims were generated in one run from Palcoux's task prompt and retained without human mathematical edits in this version.
Importance
Supplies a claimed sharp quantitative envelope for a subgroup-interval counting problem.
Limitations
Nine selected formal statements are machine checked, including bound and sharpness claims. The generated manuscript has not received a human mathematical review or an independent manuscript-to-formal-statement audit; priority and impact beyond the stated bound remain uncertain.
Technical verification
The cited source reports Lean 4.33.0 kernel checks, standard-axiom audits, Comparator and NanoDa for nine selected headline declarations, including bound and sharpness endpoints. This is machine verification of those formal statements, not independent validation of manuscript correspondence or novelty.
Independent checking
Sorry-free Lean build, standard-axiom and proof-hole audit, public statement comparison and independent kernel checks
- Checker
- Lean kernel, Comparator and NanoDa in Palcoux's pinned repository
- Scope
- Nine selected subgroup-interval bound, prime-power, elementary-abelian and optimality declarations
- Basis
- Reported by the linked checker
Human understanding
The source positively reports no human mathematical review of the one-shot draft; no human explanation of its central bound or optimality proof is documented.
Correction and publication history
Supplies a claimed sharp quantitative envelope for a subgroup-interval counting problem.
Read this published revision