χ: A New Irrational Constant Emerging from a Universal Stability Equation

This paper introduces χ (the Chronos constant), a newly identified dimensionless constant selected by a universal bounded-stability principle in a symmetric two-variable dynamical system. While the constant originally emerged in a time-field modeling context, the present work treats χ as a standalone mathematical object defined through invariant stability selection and fixed-point structure.

The paper develops χ from a formal stability framework and shows how it arises through nonlinear iteration and attractor selection rather than parameter fitting or arbitrary insertion.

The work includes:

• A coordinate-independent, operational definition of χ based on bounded-stability selection

• A nonlinear iteration map formulation that selects χ as a unique attracting fixed point

• Contraction-mapping and uniqueness statements ensuring well-posed selection

• A dimensionless invariant stability functional defining χ via an extremum principle

• High-precision numerical value and continued fraction expansion of χ

• Convergent rational approximations and reproducible generation rules

• Structural comparison with classical constants such as π, e, φ, and the Feigenbaum constants

• Explicit falsifiers and auditability criteria for testing universality claims

• A toy model iteration demonstrating concrete attractor selection behavior

• Visualization examples showing structured patterns generated under χ-based scaling and rotation

Like π and the Feigenbaum constants, χ is associated with a stability-selection mechanism rather than arbitrary definition, placing it in the class of constants generated by dynamical and fixed-point processes.