The minimum overlap problem asks how evenly the differences between two equal parts of a set of consecutive integers
can be distributed (Erdős 1955, White 2023). Partition 
into sets 
and 
with cardinalities 
. For an integer 
, define
 |
(1)
|
The minimum possible largest overlap is
 |
(2)
|
where the minimum ranges over these set partitions. For example, 
admits 
and 
, for which every nonzero overlap has size 1, so 
.
The limiting minimum overlap constant is
 |
(3)
|
Its exact value is unknown. Haugland (2016) and White (2023) established the respective upper and lower bounds giving
 |
(4)
|
The problem is numbered 36 in the Erdős problems collection (Bloom 2026).
Price (2026) reported the improved lower bound
 |
(5)
|
The argument uses an optimization certificate with rigorous interval arithmetic. Price reports assistance from GPT Pro. As of Oct. 5, 2026, VibeMathed had independently reproduced the finite certificate checks, but independent specialist review of the complete reduction to the limiting problem had not been reported (VibeMathed 2026). The computed certificate and the general reduction have different verification scopes.
