Pensieve header: The full list of V equations is seeking a topological narrative.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2012-05\\beta5.0"];
<< betaCalculus.m
Clear[ℏ]; Unprotect[C];
$PerturbativeDegree=6;
βSimplify[expr_]:= Replace[
Series[Normal[expr], {ℏ, 0, $PerturbativeDegree}],sd_SeriesData :> MapAt[Expand, sd, 3]
];
βCollect[B[ω_, μ_]] := B[
βSimplify[ω],
βSimplify[μ]
];
{V, C, sol} = Get["SolutionToDegree6-120501.m"];

{
"R4" -> R[2,3]**R[1,3]**V==V**(R[1,3] // dΔ[1,1,2]),
"TwistEq" -> V**Θ[1,2]==R[1,2]**(V // dP[2,1]),
"Unitarity" -> V**(V // dA[1] // dA[2]) == B[1,0],
"VerticalFlipEquation" -> V**(V // dS[1] // dS[2]) == R[1,2],
"CapEquation" -> (V**(C // dP[12])  // dcap[1] // dcap[2]) == (C*(C // dP[2]) // dcap[1] // dcap[2]),
"SidesNonDegeneracy" -> (V // dη[1])==B[1,0] && (V // dη[2])==B[1,0],
"CapsAndCups" -> C ==(C//dS[1])
}