Recursive Transport Topology: Predictive and Causal Organization in Protein Fitness Landscapes

Abstract Biological sequence-function relationships are commonly modeled through local sequence similarity, engineered features, or learned embeddings. Here we evaluate whether admissible transformations can organize protein fitness landscapes into recursive transport geometry before manifold formation. In this Phase I study, we analyze GFP ortholog systems and the GB1 fitness landscape using admissibility-constrained recursive indexing. Across GFP systems, recursive basins preserved phenotype-local structure without using phenotype labels for basin formation, including ~ 38% node compression, ~ 60% edge reduction, and near-perfect path preservation in ppluGFP. Transfer-compatible GFP systems preserved meaningful recursive transfer at low capacity (~ 2–4 dimensions), whereas incompatible systems required higher capacity and exhibited perturbation-sensitive fragmentation. In GB1, dense redundant topology supported robust rerouting rather than GFP-like fragmentation, indicating that transport behavior depends strongly on topology regime. Synthetic topology interventions further showed causal control within constructed transport graphs: clustering enhancement reduced maximum edge betweenness from ~ 0.0263 to ~ 0.00005, nearly eliminating bottleneck dominance. Across analyses, redundancy, rerouting capacity, bottleneck concentration, and spectral cohesion predicted robust, transitional, and fragmentation-sensitive phase regions. These results support a predictive and intervention-capable recursive transport-topology framework for biological organization and suggest that pre-manifold constraint-consistent indexing can induce measurable, compressible, and manipulable transport structure with relevance to biological modeling and artificial representation learning.