The Bras-Amorós conjecture (Bras-Amorós 2008) asserts that the numbers 
of numerical semigroups of genus 
satisfy
 |
for 
.
The weaker monotonicity assertion 
is also called the weak form of the conjecture
(Kaplan 2017).
Liu (2026) reported a computer-assisted proof of the weak form for every 
.
A partial injection handles all but a specified family of source numerical
semigroups. Unused targets are bounded using exact transfer computations for
and generating function estimates for 
. The finite
computations bound relaxed counts rather than enumerating all numerical
semigroups through genus 836. GPT-6 Astra and Anthropic Fable 5.1 assisted proof
development, computation, and checking. As of Oct. 8, 2026, checks of the stored
arithmetic outputs had been repeated, but independent verification of the full proof
and regeneration of its coefficient arrays had not been reported (VibeMathed 2026).
The stronger Fibonacci number inequality and
monotonicity at fixed multiplicity remain open.
