Time, Mathematics, and the Relaxing Knot: A Geometric Foundation for Infodynamics

Time, physical law, and mathematics itself emerge from the relaxation dynamics of a constrained high-dimensional geometry. The universe is a "knot" in a high-dimensional substrate, and time is the rate at which this knot relaxes.

Part 3 of the IPI Letters trilogy:

• Part 1: Thermodynamic Foundation — microscopic thermodynamics
• Part 2: Black Hole Aperture — observer-relative time dilation

The framework predicts characteristic relaxation dynamics—slow initially, accelerating through a middle epoch, slowing toward equilibrium—that may explain dark energy as ongoing relaxation pressure rather than a cosmological constant.

Key equation (derived dark energy equation of state): $w(a) = -1 + \frac{2}{3}\left(\frac{a_0}{a}\right) e^{-a/a_0}$

where $a$ is the scale factor and $a_0 \approx 0.5$ is the relaxation onset scale. The "unreasonable effectiveness of mathematics" dissolves: mathematics describes physics because both are aspects of the same underlying knot topology.