Deception as Bias-Injection Dynamics near Viability Boundaries: A Lyapunov and Alignness Characterization

Deception as Bias-Injection Dynamics near Viability Boundaries: A Lyapunov and Alignness Characterization This paper develops a non-normative, dynamical formulation of deception within a viability-based systems framework. Rather than treating deception as a moral or psychological category, the paper defines it structurally as bias injection on perception operators near a viability boundary. Let the system state remain viable while it stays inside a set Ω, and define risk through the boundary distance r(t)=dist(X(t),∂Ω).r(t) = \text{dist}(X(t), \partial \Omega).r(t)=dist(X(t),∂Ω). Agents act not on the true boundary distance but on a collective perceived distance rˉ(t)=r(t)+Δ(t),\bar r(t) = r(t) + \Delta(t),rˉ(t)=r(t)+Δ(t), where Δ(t)\Delta(t)Δ(t) aggregates resolution–speed phase error and injected bias. Deception as Bias-Injection Dyn… Using a barrier Lyapunov function V(r)=−ln⁡rV(r) = -\ln rV(r)=−lnr, the paper derives drift criteria that determine whether the system exhibits structural stability or collapse tendency near the boundary. The central theoretical contribution is the introduction of the alignness index, which measures the systematic sign-coherence of perception bias near the boundary. The main results show: Negative barrier drift implies viability preservation, preventing finite-time boundary blow-up. Positive barrier drift implies collapse tendency, independent of moral interpretation. The sign of drift is governed not by the magnitude of distortion alone, but by its alignness relative to intrinsic restoring dynamics. The alignness threshold remains invariant under meta-dynamical rule changes that preserve uniform regularity, but becomes structurally fragile under strategic weakening of restoring dynamics. Overestimation of safety (positive alignness) is structurally destabilizing; underestimation is structurally conservative—an asymmetry arising from the barrier structure itself. A key design principle of the paper is diagnostic neutrality. The framework does not distinguish between unintentional error and intentional deception at the level of dynamical analysis. Both enter identically as perturbations on perception channels. Collapse tendency depends solely on aggregate alignness, not on intent. The results extend naturally to: Self-deception (single-agent case), Collective deception (multi-agent aggregation), Institutional deception (concentrated influence weights), Meta-dynamics where the update rule itself evolves. Within the broader Yang Jihoon Dynamics (YJD) program, this paper provides a rigorous Lyapunov characterization of perception–state separation near viability boundaries, complementing prior work on distortion energy, governance convergence, and structural survival. The decisive insight is structural: Instability near a viability boundary is governed not by the existence of distortion, but by the systematic alignment of perception bias in the direction of overestimated safety. This result reframes deception as a boundary-dynamical phenomenon, with implications for governance, institutional reform, collective cognition, and systemic collapse analysis.