Since we have a gauge transformation $v \rightarrow v \pm W$ for each plaquette it is legal to transform any plaquette according to that rule. In fact, we could send $v \rightarrow v$ (mod $W$) without any physical effect. Furthermore when $W=1$ we should be able to absorb the entirety of $v$ into $m$.
While I was comparing the reference and production Spin_Spin implementation there was a disagreement, precisely because in the Worldline formulation we update $v$ even when $W=1$, and the production implementation was operating on Links while the reference was operating on bare $m$s. It ought to be possible to set $v \rightarrow 0$ at the expense of sending $m \rightarrow m - \delta v$ (in the $W=1$ case).
[x] Gauge-transform away the integer part of $v/W$
[x] Utility to re-express $(m, v)$ as $(m-\delta v, 0)$ when $W=1$.
[x] I guess when $W\neq1$ we can go all the way $(m-\delta(v \/\/ W), v$ mod $W)$, where $//$ is integer division of some kind?
Since we have a gauge transformation $v \rightarrow v \pm W$ for each plaquette it is legal to transform any plaquette according to that rule. In fact, we could send $v \rightarrow v$ (mod $W$) without any physical effect. Furthermore when $W=1$ we should be able to absorb the entirety of $v$ into $m$.
While I was comparing the reference and production Spin_Spin implementation there was a disagreement, precisely because in the Worldline formulation we update $v$ even when $W=1$, and the production implementation was operating on Links while the reference was operating on bare $m$s. It ought to be possible to set $v \rightarrow 0$ at the expense of sending $m \rightarrow m - \delta v$ (in the $W=1$ case).