A discrete topological tensor network framework for effective continuum structures

In this paper, we present a discrete model where a spacetime-like structure is built from a topological network of four-dimensional cells that carry local third-rank tensor data. We describe how directed tensor differences across shared hypersurfaces influence a compact action functional and generate reconfiguration dynamics. In regions where discrete variations remain small, coarse-grained quantities could be compared with continuum-level descriptors, leading to effective field-like relations.The framework also allows us to identify non-differentiable configurations within the network and to analyse their structural role. Our goal is to lay out the model and show that it is internally consistent, without making claims about the real structureof spacetime or pretending that the model is complete.