ERGT: Attention-Free Native Geodesic Transport for Controlled Long-Horizon Relational Reasoning

We introduce Executable Relational Geometry and Transport (ergt), an attention-free architecture in which relational computation is organized by input-conditioned geometry rather than self-attention. ergtlearns a mapping from raw tokens to a persistent information field Ψ, whose pairwise observables induce multiple directed world geometries. These geometries then become the computational substrate for reasoning: GeoTransport carries typed state along admissible paths, and a geodesic boundary solver accepts the least-cost candidate consistent with propagation, memory, payload, and terminal constraints. This native answer path uses neither a Transformer nor a supplied graph, target compiler, or generic executor.Across four independent runs, ergtconverged and satisfied every registered native stability contract. Beyond its training range, mean accuracy at 32 hops was 0.955, compared with 0.500 for a strengthened direct Transformer given the same raw input and a closely matched parameter count. Frozen same-checkpoint interventions caused sharp losses when geodesic action, propagation admissibility, typed transport, geometric memory, or terminal measurement was removed.Randomizing or shuffling the geometry, or restricting inference to one world, also failed to recover the intact result. The evidence supports a bounded architectural claim: a Ψ field formed from raw tokens can become an executable geometry and provide a measurable advantage in controlled long-horizon relational reasoning.