What kinda geometry is the sculpture? Is it a mesh or a n.u.r.b.s. surface? Is it already the result of parametric modelling in GH or where does it come from? Have you created it?
You need to be far more specific, since the solution might greatly depend on the kind of geometry that you’re working with!
Also your sketch looks rather like a flattened, distorted torus or ring. Are you sure that you’re working with a three-dimensional tube?
Let’s say you’re sculpture is a surface or solid. You could simply find the middle curve, resulting in some sort of deformed ring, divide it into segments of equal length (i.e. 1m), and get perpendicular curve frames at each of the division points. These planes/frames could then be used to split the surface/solid into individual parts.
Since, you are writing about vertices, I guess that you’re working with a mesh?
If so, I’d recommend you to construct your mesh in such a way that its topology (its subdivisions) corresponds to your desired divisions, since splitting/boolean-ing meshes can get messy fast, and you probably want to maintain a clean geometry throughout the process!?
Tagging the vertices with IDs is pretty straightforward once you have figured the other stuff out.
Furthermore, it would be much simpler to help you, if you would upload a file!