The Binary Anchor: Cognition, Symbolic Loops, and Systems Failure

The Binary Anchor Model (BAM) is a conceptual framework that describes cognition and behavioral decision-making as a two-layer structure comprising a biological anchor (System A) and a social anchor (System B). This paper formalizes the master equation A_t = WTA(V_t) ∈ {0,1} (V_t = r_t m_t + (1-r_t)m_{sys,t}) as the apex organizing principle and systematizes all equations within a Level 0–3 modular argument-space structure. The divergence Δ_t between the two systems accumulates as Hesitation Energy H_t via the responsibility allocation parameter r_t, manifesting as a Burst (computational breakdown) upon threshold exceedance. As a probabilistic extension of the WTA output, Soft-WTA P(Y_t = 1) = σ(V_{WTA} - T_E) is introduced, with convergence to deterministic WTA in the high-confidence limit. Furthermore, η_A0 is identified as a neurobiological entity representing individual-difference amygdala plasticity (Raine et al., 2009; Hölzel et al., 2011), and the recovery path from chronic de-solidification is quantified as T_{recovery} ∝ φ_t ÷ (η_A0 · A_{t,safe}). The framework articulates its distinctions from Kahneman's dual-process theory and the Free Energy Principle, while presenting pathways for individual-level extension through a multi-domain profiling model and operationalization via existing social indicators.