Unique Extension conjecture for 4 × n Chomp

A position in $4 \times n$ Chomp is a quadruple $(a,b,c,d)$ of non-negative integers with $a\geq b\geq c\geq d\geq 0$; a P-position is a position from which the previous player has a winning strategy. For any triple $(a,b,c)$ with $a\geq b\geq c\geq 0$, Unique Extension conjecture. there exists at most one non-negative integer $d$ such that $(a,b,c,d)$ is a P-position of $4\times n$ Chomp. The conjecture was tested on all 4,316,097 computed P-positions with $n\leq 500$, but the stated claim is disproved because multiple $(a,b,c,d)$ may share the same $(b,c,d)$ triple; the distinction between prefix and suffix projections should be checked against the intended formulation.