Phase 13 · path dependence of identity response

Same Destination, Different Path

AT-0103 → AT-0110. If every road to the same place causes the same damage, choosing a better road cannot help. This lab proves that statement inside its model class, then isolates the smallest change to the rules that makes the route matter again.

The obstacle

dI = C dR ⟹ ΔI = C (R_f − R_i)

Constant linear coupling: the endpoint identity change is fixed by the endpoints alone.

If identity response obeys a constant linear coupling dI = C dR with fixed C, then ΔI = C (R_f − R_i) for every path with those endpoints. Path optimisation cannot reduce endpoint identity damage in this model class.

Model & search limits

SeedCoupling field C(R)Lattice cells per unit = 12Identity tolerance = 0.020Detour region = ±0.60Random paths (AT-0103) = 240

Running the path-dependence sweep…