From Multiscale Structural Discovery to the Continuous Evolution of Theory: Topological Enhancement of the Ancestor–Mother–Child Machine Architecture

This paper proposes using multiscale topological analysis for theory building within the ancestor–mother–child machine architecture, making the organizational features of research objects a basis for proposing explanations, testing predictions and generating subsequent tasks. Filtrations and persistent homology track the emergence and disappearance of connected components, loops and other structures across scales, translating these changes into comparable research variables. The mother machine combines domain knowledge with structural variables to propose explanations with specified conditions of applicability. Child machines test their contribution relative to existing understanding and submit proposed changes. Approved findings enter domain theory while changing the comparison variables, research objects and testing conditions of later tasks. The ancestor machine maintains rules for method use and transfer based on results across rounds. A simple four-point construction explains topological representation, and the case of memory retention under artificial hibernation illustrates how structural analysis can inform theoretical revision and the next research round. We also propose a comparative design that distinguishes gains from representation from gains through accumulation across tasks. The scheme provides a structural-analysis approach to the continuous evolution of theory; its practical effects require empirical evaluation.