Pensieve header: Solving R4, Unitarity, Cap, and Vertical Flip. Data file: <a href=R4UniCapVFlipSolution-to-12.m>R4UniCapVFlipSolution-to-12.m</a>.

SetDirectory["~drorbn/AcademicPensieve/Projects/WKO4"];
<< FreeLie.m;
<< AwCalculus.m;
Rs[a_,b_]:= Es[⟨a->LS[0], b->LS[LW@a]⟩, CWS[0]];
α=LS[{x,y}, αs]; β=LS[{x,y}, βs];γ=CWS[{x,y}, γs];
V=Es[⟨x->α, y->β⟩, γ];
κ=CWS[{x}, κs]; Cap=Es[⟨x->LS[0]⟩,κ];
R4Eqn=V**(Rs[x,z] // dΔ[x,x,y]) ≡ Rs[y,z]**Rs[x,z]**V ;UnitarityEqn=(V**(V//dA[x]//dA[y]) ≡ Es[⟨x->LS[0], y->LS[0]⟩,CWS[0]]);
CapEqn=((V**(Cap//dΔ[x,x,y])//dc[x]//dc[y]) ≡ (Cap(Cap//dσ[x,y])//dc[x]//dc[y]));
FlipEqn = V**(V//dS) ≡ Rs[x,y];
βs[x]= 1/2; βs[y]=0;
SeriesSolve[{α, β,γ, κ}, ((ℏ^(-1))R4Eqn) && UnitarityEqn && CapEqn && FlipEqn];
{V, κ}

V@{6}

κ@{12}

{TimeUsed[], MaxMemoryUsed[]}

Put[Sum[{(Subscript[V[[1]], x])[k], (Subscript[V[[1]], y])[k], V[[2]][k]}, {k,12}], "R4UniCapVFlipSolution-to-12.m"];
PutAppend[Sum[κ[k], {k,12}], "R4UniCapVFlipSolution-to-12.m"]