A Structural Framework for Differentiation Signatures: From Molecular Forms to Predictive Materials

We present a structural framework for modeling and validating scientific forms based on the principle of differentiation signatures. This approach encodes each object—be it molecular, physical, informational, or conceptual—using a six-component descriptor: generative cause (C), quantitative metrics (M), context of activation (S), persistence conditions (U), measurement interface (I), and the resulting form signature (∆). We demonstrate the framework’s universality by applying it to classical domains (α-helix, hydrogen-bond networks, Coulomb’s law) and to predictive modeling (organic 1D conductor "Polyacetylene-X", topological insulator "Topo-Hex"). Each form is validated through a rigorous set of logical and empirical criteria, ensuring falsifiability, causal coherence, and operational access. This work establishes a novel paradigm for ontology-based modeling across disciplines, capable of both reproducing known phenomena and generating new, verifiable hypotheses.