[[κ]]: The Symbolic Stabilizer Constant — An Irrational Resonator for Modular Cognition and Field Dynamics

This paper introduces a newly discovered irrational constant, written as ⟦κ⟧ (kappa double-bracket), which emerges from a nonlinear feedback equation involving the Golden Ratio. We show that ⟦κ⟧ plays a stabilizing role across symbolic, cognitive, and physical systems by regulating feedback, suppressing volatility, and enhancing coherence. The paper explores five experimental tests that demonstrate how ⟦κ⟧ stabilizes memory decay, modulates symbolic loops, regulates chaotic signals, improves symbolic decision-making, and generates non-repeating geometric structures. Each test reveals a unique stabilizing behavior that makes ⟦κ⟧ suitable for applications in symbolic AI, cognitive modeling, and dynamic field systems. We then apply ⟦κ⟧ in two advanced domains: symbolic modular gravity (SMG), where it helps modulate curvature and geometric resonance; and symbolic quantum computation (SQC), where it offers a novel approach to controlling quantum states and entanglement decay. Altogether, this paper establishes ⟦κ⟧ as a symbolic constant with wide applicability in nonlinear systems, modular feedback loops, and symbolic reasoning architectures. All equations, simulations, and symbolic interpretations are provided for replication and extension.