The Carlo Architecture : A Unified, Deterministically Closed Operator Model of Psychological and Symbolic Systems v2 (With Visualiser)

Abstract

This specification delivers the definitive, mathematically closed engineering blueprint for the Carlo Unified Operator Model (V2). By mapping six historically divergent psychological, developmental, and linguistic frameworks—Freud, Jung, Lacan, Piaget, Chomsky, and Skinner—into a rigid, 10-variable global state vector (The Carlo Spine), this framework entirely replaces metaphorical ambiguity with non-probabilistic, deterministic execution. Version 3 Update: Includes the complete original documentation sprint in PDF alongside the interactive WebGL 3D visualizer, which dynamically renders the 10-variable Carlo Spine, closed operator dynamics, and real-time state transitions directly in the browser. \begin{gathered}\textbf{The Carlo Architecture (V2) Master Composite Specification} \\[15pt]\textbf{Master State Transition Equation:} \\[5pt]\text{State}(t+1) = \mathbf{U}(\text{State}(t), \text{Input}(t)) \\[15pt]\textbf{Modular Operator Execution Composition } (\mathbf{U}): \\[5pt]\mathbf{U} = \mathcal{U}_{\text{Chomsky}} \rightarrow \mathcal{U}_{\text{Jung}} \rightarrow \mathcal{U}_{\text{Freud}} \rightarrow \mathcal{U}_{\text{Lacan}} \rightarrow \mathcal{U}_{\text{Piaget}} \rightarrow \mathcal{U}_{\text{Skinner}} \\[15pt]\textbf{The 10-Primitive Carlo Spine Vector } (\text{State}(t)): \\[5pt]\text{State}(t) = \{D, C, A, F, T, R, Sy, Sm, I, \text{Dev}\} \\[15pt]\textbf{Individual Modular Operator Formulations:} \\[5pt]\begin{aligned}\mathcal{U}_{\text{Chomsky}}: & \quad Sm(t) = \text{Parser}(\text{Input}(t), Sy(t), \text{Dev}(t)) \\\mathcal{U}_{\text{Jung}}: & \quad A(t) = \sum_{i} \left( \text{Archetype}_i \times Symbol_i(t) \times \text{Weight}_i \right), \quad \Delta I_{\text{Jung}}(t) = W_J \times A(t) \\\mathcal{U}_{\text{Freud}}: & \quad P_{\text{net}}(t) = D(t) - C(t), \quad \Delta F_{\text{Freud}}(t) = \kappa \times P_{\text{net}}(t) \\\mathcal{U}_{\text{Lacan}}: & \quad Sm(t+1) = \text{Recurse}(Sm(t), I(t), \text{Real}(t)), \quad \Delta I_{\text{Lacan}}(t) = W_L \times Sm(t) \\\mathcal{U}_{\text{Piaget}}: & \quad \text{Capacity}(t) = \text{CalculateCap}(R(t), Sm(t), \text{Complexity}(t)) \\& \quad \text{Dev}(t+1) = \text{Dev}(t) + \text{StepFunction}(\text{Capacity}(t) - \text{ThresholdDev}) \\\mathcal{U}_{\text{Skinner}}: & \quad R(t+1) = \text{FeedbackLoop}(\text{Behavior}(t), \text{Outcome}(t)) \\& \quad D(t+1) = D(t) + \alpha_D \times R(t), \quad C(t+1) = C(t) + \alpha_C \times R(t)\end{aligned} \\[15pt]\textbf{System Integrity and Terminal Accumulation Equations:} \\[5pt]\begin{aligned}F(t) & = \text{ComputeConflict}(D(t), A(t), C(t), Sm(t)) + \Delta F_{\text{Freud}}(t) \\I(t+1) & = I(t) + \Delta I_{\text{Jung}}(t) + \Delta I_{\text{Lacan}}(t) + \Delta I_{\text{Freud}}(t) + \Delta I_{\text{Piaget}}(t) + \Delta I_{\text{Skinner}}(t) \\\text{Clamp}(\text{Value}) & = \min(1.0, \max(0.0, \text{Value}))\end{aligned}\end{gathered} This specification completes the operator lineage initiated by the Reset Operator—closing the loop and defining the deterministic foundation of the Carlo system. Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com