Physarum-EAS Structural Isomorphism: A Survey on Target-Free Emergent Optimization and Epistemic Axiomatic Systems

This survey investigates the deep structural isomorphism between the slime mold Physarum polycephalum target-free network optimization mechanism and the Epistemic Axiomatic System (EAS) Collective Mode potential-driven modal selection. We identify a shared three-stage dynamics paradigm: local rules + global constraints + selection-elimination. The Physarum TKN adaptation equations coupled with Poiseuille flow have been rigorously proven to converge to shortest paths on arbitrary graph topologies, providing a mathematical reference for the universality of phi-potential-driven modal selection in EAS. The report includes: (1) biophysical mechanisms and experimental evidence chains, (2) TKN mathematical model with convergence proofs, (3) a 5-dimension 10-concept-pair structural isomorphism mapping table, (4) formal mathematical correspondence distinguishing established results from conjectures, (5) comparative analysis with reaction-diffusion systems and ant colony optimization, (6) 4 testable predictions, and (7) 5 concrete engineering design insights.