An Axiomatic Approach to General Intelligence: SANC(E3) Self-organizing Active Network of Concepts with Energy E3

General intelligence must reorganize experience into internal structures that enable prediction and action under finite resources. Existing systems implicitly presuppose fixed primitive units— tokens, subwords, pixels, or predefined sensor channels—thereby bypassing the question of how representational units themselves emerge and stabilize.

This paper proposes Self-organizing Active Network of Concepts with Energy E₃ – SANC(E3), an axiomatic framework in which representational units are not given a priori but instead arise as stable outcomes of competitive selection, reconstruction, and compression under finite activation capacity, governed by the explicit minimization of an energy functional E₃ = λ₁L_rec+λ₂C_struct + λ₃C_update.

SANC(E₃) draws a principled distinction between system tokens—structural anchors such as {here, now, I} and sensory sources—and tokens that emerge through self-organization during co-occurring events. Five core axioms formalize finite capacity, association from co-occurrence, similarity-based competition, confidence-based stabilization, and the reconstruction–compression– update trade-off. Residual capacity C_remain(t) is introduced as an explicit control variable that dynamically modulates representation creation, stabilization, and deletion thresholds.

A key feature of the framework is a pseudo-memory-mapped I/O mechanism, through which internally replayed Gestalts are processed via the same axiomatic pathway as external sensory input. At the theoretical level, perception, imagination, prediction, planning, and action are unified within a single representational and energetic process. This unification is intended as a structural account: it does not claim that a complete implemented AGI system is provided here, but specifies how these processes can be described within one axiomatic pathway. The same account naturally extends the framework to embodied and physical agents, where interaction with the environment and motor behavior are treated as continuations of Gestalt completion rather than as separate control modules.

From the axioms, twelve propositions are derived, suggesting how category formation, automatic threshold tuning, hierarchical organization, unsupervised learning, and high-level cognitive activities—dialogue, authoring, perception, causal inference, and action—can be understood as instances of Gestalt completion under E₃ minimization.