?? extent to which it's cheating / helpful / provable to define "good embedding of 1d object into 2d ..." (for example ... ??? ...) in terms of reps of invertible 2-by-2 triangular matrixes ?? .... .... ??? ... ???? ...

??? _does_ p^1 have nice "partial function classifier" property ??? ... ?? toric case ... ??? constraint involving openly / densely defined .... ??? ....

?? comm monoid hom into .... p+ ... ??? .... n+ ..... ???? ..... ??? .... point .... good path .... ???? ..... ?????

?? homomorphisms from commutative monoid into z ... ??? .... ?? lattice where fan lives .... ???? .... "toric rational functions" .... ????? .... duality (?? to say the least .... ??? ....) confusion here .... ???? .....

?? good paths ... ??? ....

?? commutative monoid homs from z into real^1 and / or complex^1 .... ??? .... some special one ?? ... (?? "evaluation of good path at real and / or complex value k" ??? ... any particular good value of k to use ???? ....k = i ???? .... ?? or other root of unity ??? ... ???? ..... ?? k = -1 ??? .... ??? ....) ... to use to interpret lattice point in fan as ... ?? point of real spectrum ?? ... ?? well, or to relate interpretation as real (or complex ... ?? ...) point to interpretation as good path ... ??? ....