Routing, Not Computing: Semantic Processing via Potential Descent on Random Nonlinear Terrains

We present a routing model for semantic processing in which base structure (randomnonlinear terrains) and dynamics (potential-descent routing) are explicitly separated. Fourproperties are established experimentally across dimensions 8 to 128: (R1) Givens rota-tions preserve cosine similarity exactly, (R2) nonlinear activations create terrain diversity,(R3) classification information resides solely in routing weights, and (R4) parameter efficiencyscales as O(d2). Input-dependent route selection obtains 97.6% agreement with an Oracleselector, with no trainable parameters in the routing mechanism. We observe a power-lawpotential exponent that is category-dependent, ranging from 0.01 to 0.99 across 18 semanticcategories, with the inverse-square law (γ = 2) rejected in all tested conditions. A compari-son across three independent encoders identifies five categories exhibiting encoder-invariantstructure. Recipe-based communication, extending the framework of the first report, re-constructs semantic content from 82 bytes of routing metadata with 100% accuracy. Theseresults suggest that the regeneration behavior observed in the prior reports can be furthercharacterized by a potential-descent mechanism with measurable, category-dependent expo-nents.