Jacobian Invariance and Temporal Redistribution in the Lorenz System Under Fibonacci-Window λ Feedback

We present a validation study demonstrating that a variance-derived λ feedback, computed over a Fibonacci-windowed temporal history, modifies the internal temporal structure of a chaotic system without altering its global dynamical regime. Using the classical Lorenz system integrated via RK4, we compare baseline dynamics to a λ-modulated variant in which λ(t) is computed as a bounded inverse function of recent state variance over a trailing Fibonacci window and applied as a centered isotropic correction.. We show that while the mean Jacobian determinant per integration step remains invariant—preserving the system’s dissipative character—the distribution of instantaneous Jacobian deviations broadens significantly under λ feedback. Phase-space geometry remains chaotic and bounded, while dissipation is redistributed in time. These results support interpreting λ as a structural coherence modulator rather than a force or control term, and motivate a temporal-band interpretation of coherence in chaotic dynamics.The λ formulation used here is an intentionally minimal operational proxy chosen for diagnostic purposes and should not be interpreted as a general or complete expression of λ across physical regimes.