CAA-X 2.0 (V9): Structural Completeness for Socially-Embedded Agency via Dual Aspect Surprise Minimization

Abstract

This repository contains V9 of the CAA-X (Cognitive Atom Architecture eXtension) research program, subtitled "CAA-X 2.0: Structural Completeness for Socially-Embedded Agency via Dual Aspect Surprise Minimization." V9 represents a major architectural revision of the CAA-X framework — the transition from CAA-X 1.0 (intelligence-centric) to CAA-X 2.0 (four-dimensional). It argues that the pursuit of AGI has long privileged intelligence alone, while recent deployments reveal critical gaps in judgment (value-aligned decision-making), trust (reliable self-monitoring), and relationship (multi-agent social coordination). These are not engineering defects to be patched, but architectural dimensions that must be embedded as first-order primitives. Core ThesisSocially-embedded agency requires two coupled optimization processes under the Free Energy Principle:- Epistemic surprise minimization (I + J): Active inference to resolve prediction errors — exploring to acquire knowledge and evaluate values. Knowledge acquisition is the result of embracing surprise.- Social surprise minimization (T + R): Gradient flow to eliminate prediction errors about others' behavior — seeking stable, predictable social interactions. Social coordination is the result of extinguishing surprise. This duality — embracing vs. extinguishing surprise — is the soul of CAA-X 2.0. Central Contribution: The Structural Completeness TheoremWe prove that any architecture A achieving robust autonomous operation in the environment space E must satisfy C(A) = 4, embedding all four dimensions (Intelligence, Judgment, Trust, Relationship) as first-order primitives. Missing any dimension implies existence of an environment in E where A structurally fails. The proof proceeds by variational contradiction: the free energy of an architecture missing dimension D is strictly bounded below the threshold required for robust operation in the corresponding environment subclass. Key Formal Results- Theorem 1 (Taste Emergence): Judgment's quadratic cross-terms α_ij v_i v_j capture non-additive value interaction ("taste"). When ⟨v_1, v_2⟩ < 0, taste produces creative tension — a hallmark of complex judgment.- Theorem 2 (Trust Accumulation): The trust update T(t+1) = (1-η)T(t) + η·[β_1·cal(t) + β_2·bnd(t) + β_3·hist(t)] converges almost surely to T_∞ = E[u(t)] with geometric rate |T(t) - T_∞| ≤ (1-η)^t |T(0) - T_∞|.- Theorem 3 (SCM Consensus): On the Social Cognitive Manifold M_S, collective trajectories converge exponentially to consensus with rate κ ∝ min_i T_i · max_{i,j} μ_{ij}.- Theorem 4 (Structural Completeness): Necessity, insufficiency, and incompleteness — C(A) = 4 is necessary but not sufficient for robust operation; C(A) < 4 guarantees structural failure in some environment.- Theorem 5 (Constructive Completeness): CAA-X 2.0 satisfies C(CAA-X 2.0) = 4 by construction. Variational Foundation for TrustThe trust update is derived as the gradient flow of a social trust variational functional F_T, elevating T(t) from an engineering heuristic to a first-principles consequence of minimizing social free energy. The agent does not "choose" to be calibrated; calibration emerges from variational optimization. Empirical ValidationAcross three environment classes (E_J multi-armed bandit with alignment tax, E_T drift prediction requiring calibration, E_R iterated prisoner's dilemma vs. Tit-for-Tat) and five agent architectures (30 seeds × 300 episodes, Mann-Whitney U with Bonferroni correction), ablating any single dimension causes statistically significant degradation (p < 4.17×10^-3). Full CAA-X 2.0 is the only architecture not significantly worse than the best performer in any environment. Architectural Extensions- Cognitive Atoms 2.0: Four-type atoms (FUNC, VAL, REL, EMO) with reliability weights.- CML 2.0+: Four-layer symbolic system adding the Affective layer (F) for emotional state encoding and social signal transmission.- MA-GWP: Multi-Agent Global Workspace Protocol with three broadcast scopes (Intra-agent GWP_I, Inter-agent GWP_E, Social GWP_S).- Lambda Vector: Four-dimensional λ⃗ = (λ_I, λ_J, λ_T, λ_R) quantifying system state across all dimensions. Relationship to Prior VersionsV0–V2 established the single-dimension (Intelligence) framework. V3 argued "Intention is All You Need." V9 answers: Intention is necessary but not sufficient — structural completeness requires four dimensions. It is the most formally rigorous paper in the CAA-X series to date, with complete proofs, simulation validation, and explicit falsification criteria. Citation & ContextPart of the CAA-X versioned research program. See V0–V2 foundational collection (DOI: 10.5281/zenodo.21835958), V3 intention manifesto (DOI: 10.5281/zenodo.21836502), and V4 world models (DOI: 10.5281/zenodo.21836896).