Observer-Dependent Navigability in Swarm Intelligence: A Path-Theoretic Decomposition of Performance into Perception and Distortion

Why do different swarm algorithms achieve different performance on the same fitness landscape? This paper proposes that navigability—the structural capacity to find improving paths—is observer-dependent: different algorithms perceive different navigability on identical landscapes, and this difference is irreducible to landscape properties alone. We formalise this through the decomposition F = P/D, where Perception (P) measures an algorithm’s differentiation capacity and Distortion (D) measures structural resistance. The ratio form is derived uniquely from three axioms (monotonicity, scale-covariance, separability). Three claims are advanced and tested across five experiments on the Deucalion supercomputer, totalling over 200,000 simulated trials. Claim 1 (Distortion is multiplicative): D compounds geometrically, not additively (R2 = 0.993 vs. 0.856; n = 250 cross-algorithm trials). Claim 2 (Perception is observer-dependent): Six navigation strategies on the same 9,913 graphs yield six different P values; a hidden variable model reconstructing P from graph features and strategy identity achieves only R2 = 0.058 (n = 9,470 strategy–graph pairs). In the CEC optimisation domain, the same hidden variable test yields R2 = 0.403 (n = 50 algorithm–function pairs), indicating a domain-dependent boundary. Claim 3 (Alignment dominates): Step-wise alignment—the fraction of moves that reduce distance to the optimum—predicts navigation efficiency at R2 = 0.82 across 57,518 trials, outperforming all tested graph-theoretic and landscape metrics (maximum alternative R2 = 0.03). Cross-domain validation spans graph navigation (10,000 graphs, 6 strategies), CEC-2017 benchmarks (10 functions, 5 algorithms), 2D continuous landscapes (79,956 trials, mediation analysis), PSO parameter sweeps (5,000 runs), and ACO pheromone dynamics (2,987 runs). Six counterfactual tests and a mediation analysis support the framework. All results are simulation-based. What fails is reported with the same rigour as what succeeds: P alone outperforms P/D at the graph level (ρ = 0.343 vs. 0.108), the FLRP multiplicative decomposition is dead (R2 = 0.0002), and the scalar F-field fails in continuous space (R2 = 0.004). Twelve falsification criteria are specified. The framework is a hypothesis under test, not a proven law.