Across psychology, artificial intelligence, biology, economics, social theory, and geophysics, scientific models have historically treated structure as an invariant background and recurrence as noise, bias, or statistical residue. This assumption creates a cross-disciplinary blind spot: systems whose internal rules change under repeated activation are systematically misclassified.
This paper identifies and formalizes this error as the Static Structure Fallacy and introduces the operator-level correction. By treating structure as a dynamic function of recurrence
S = S(R)
and defining structural sensitivity as
Ψ = ∂S/∂R
the paper establishes recurrence as the primary mechanism of structural modification rather than a disturbance to be filtered out.
The result is a domain-independent functional account of reflexive systems, unifying drift phenomena across cognitive processes, neural systems, biological regulation, AI training dynamics, institutional change, market adaptation, and tectonic stress reorganization. Ψ provides a minimal and measurable operator for reflexivity, resolving long-standing conceptual asymmetries between structure and process across scientific disciplines.
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Kognetik Series Information
KOGNETIK — Minimal Operator Definition of Reflexivity (Ψ = ∂S/∂R)
Reflexivity as structural rate-of-change:Ψ=∂S/∂R measures structural drift under recurrence.
Process, not state:Reflexivity is a transformation rule, not a content or level.
Domain-independent operator:Valid across biological, cognitive, artificial, social, industrial, and geophysical systems.
Non-ascriptive, empirically testable:Ψ compares systems by observable structure and recurrence.
Higher-order phenomena as specifications:Learning, adaptation, consciousness, governance, and identity are structured regimes of Ψ.