Every 3-colouring of the edges of $K_{17}$ has a monochromatic triangle (Erdős 624 packet obstruction)

Let $g:\{0,\dots,16\}^2\to\{0,1,2\}$ be symmetric ($g(x,y)=g(y,x)$); think of $g(x,y)$ for $x\ne y$ as the colour of edge $xy$ of $K_{17}$. Then there are distinct $x,y,z$ with $g(x,y)=g(x,z)=g(y,z)$. (The classical bound $R(3,3,3)\le17$; the diagonal values $g(x,x)$ play no role.)

This is the Ramsey step of Sol's 'A Triple-Colour Ramsey Obstruction'.

Context: Erdős Problem 624 asks whether $H(n)-\log_2 n\to\infty$, where $H(n)$ is the least $m$ such that some $f:\mathcal P(X)\to X$ with $|X|=n$ satisfies $f[\mathcal P(Y)]=X$ for all $|Y|\ge m$. This is an auxiliary finite statement from Sol's Round 13 notes on the two-track (PAIR) case. It does not settle Erdős Problem 624, PAIR or Step 17; the initial near-critical population those notes start from is not established.