Constitutional Intelligence as Formal Science The Karimov–Alekberli Framework as Mathematical Foundation for Governed Institutional Cognition

Abstract

We present a synthesis of the Karimov–Alekberli (KA) Framework into a unified theory ofConstitutional Intelligence: the capacity of an adaptive system to make consequentialdecisions that are simultaneously governed, explainable, accountable, reconstructable,verifiable, and capable of learning without retroactive falsification of the historical record.We formulate six formal results — one per required property — organized into three prooftiers: Tier A (two unconditional geometric results), Tier B (three conditional results validunder explicit identifiability and compactness assumptions), Tier C (one KA extensionunder a physical implementation assumption). Results draw on viability theory,informationgeometry, and thermodynamics. The theorems are organized in three tiers reflecting theircurrent proof status: Tier A (fully proved geometric results), Tier B (conditional theoremsunder explicit identifiability and compactness assumptions), and Tier C (KA extensionsrequiring additional physical or topological conditions). A unifying condition, theConstitutional Integrity Criterion (CIC), is formulated as a representation theoremcharacterizing systems that satisfy all six properties simultaneously. We derive, under theCIC, that the governance loop Govern → Reason → Act → Remember → Learn → Governdefines a well-defined autonomous map on the constitutional moduli space that preservesthe admissible region; fixed-point existence follows as a corollary under compactness. Weposition the framework within the existing literature on viability theory, formal verification,safe reinforcement learning, AI governance, and constitutional economics. We proposeConstitutional Intelligence Science as the emerging discipline that unifies these results.