THE SURFACE-CORE FUNCTIONAL DIVERGENCE THEORY (SCFDT)

This paper proposes the Surface-Core Functional Divergence Theory (SCFDT), a medium- and domain-general conceptual framework for investigating cases in which an activity retains the outward identity, presentation, formal structure, or claimed legitimacy of a reference system while its internal processing diverges materially from the constitutive requirements and function associated with that system.The theory distinguishes surface resemblance from internal process fidelity, ordinary error from constitutive violation, functional displacement from functional inversion, and actual process change from its representation to observers. Its principal mechanism, the Identity-Preserving Core-Process Divergence Mechanism (IPC-DM), is intended to describe how an activity can retain an established identity while its actual internal process no longer adequately performs the function that gives the identity its relevant meaning.Pseudoscience and pseudomathematics are designated as two separate primary analytical cases. The framework is also designed for conditional application to other rule-governed activities, including logical reasoning, statistical analysis, information processing, computational systems, language-mediated activities, technical systems, and organizational processes. Such applications require domain-specific reference standards rather than an assumption that all domains share identical validity criteria.The framework uses fifteen core analytical layers, nine cross-layer modules, a temporal dimension, a medium dimension, and a domain-specific reference-standard architecture. It introduces a formal vocabulary of variables and candidate indicators for surface compliance, core-process fidelity, constitutive violation, functional displacement, functional inversion, identity persistence, transparency, correction responsiveness, temporal persistence, consequences, and uncertainty.The mathematical expressions are proposed formalizations, not established universal laws. The paper supplies operational definitions, candidate classification rules, boundary conditions, illustrative cases, falsifiable hypotheses, alternative explanations, a structured audit protocol, and an empirical validation roadmap. It reports no new empirical dataset and does not claim that the framework has already been demonstrated to be universally valid.The intended contribution is an integrated research architecture for testing whether surface-core divergence provides a useful common analytical structure across otherwise different forms of pseudo-systemic activity.Keywords: Surface core divergence; functional displacement; functional inversion; pseudo-systemic activity; pseudoscience; pseudomathematics; system identity; internal processing; reference standards; medium independence; temporal dynamics; operationalization; falsifiability; empirical validation.