Examples for the Coupling Problem: Small-n Sanity Checks

This note performs explicit small-n sanity checks for the STFO-shadow weighting introduced in The Coupling Problem Between Temporal Information Dynamics and Algebraic Complexity. We derive a closed-form expression for the weighted path measure on the Young graph and compute concrete examples for n = 3 and n = 4. The results show that the current STFO-shadow is conservative and depends only on terminal partitions, clarifying both its capabilities and its limitations.