The Ladder of Theory A: Dynamics of Theory Hierarchies—Operational Boundaries and Structural Transitions

Abstract

The evolution of scientific theories exhibits a pronounced hierarchical character,with each level providing effective predictions within specific operational boundaries, and undergoing structural transitions at these boundaries. Based on empirical patterns from the history of science and hard constraints from formal systems,this paper establishes a “structural network” model that abstracts a theory as anetwork structure with assumption nodes, logical dependency edges, and evidenceweights, and provides a systematic construction protocol for mapping theoreticaltexts to formal networks. The study shows that transitions between theoreticallevels are not smooth accumulations but are driven by four types of topologicalreconstruction mechanisms: coarse-grained embedding, hypothesis-space bifurcation, cross-domain bridging, and theory freezing. Level transitions are subject toa triple constraint of observational resolution, quantum uncertainty, and computational complexity, and empirically satisfy a structural information conservationcondition, namely that the network complexity of the new theory is not less thanthat of the old theory minus the reconstruction cost. This paper further proposesa three-dimensional assessment vector for operational completeness, transformingtheory choice from single‑metric optimisation into a cognitive‑economic decisionon the Pareto frontier, and uses spectral features to accelerate the screening. Theframework provides a computable formal description tool for phenomena such asscientific revolutions, theory deadlocks, and cross‑domain unification, and givestestable predictions through the Standard Model, the string landscape, and historical transition cases.