Recursive Curvature & the τ-Field Principle

An interactive exploration into how dimensionless physical constants, including the fine-structure constant α, emerge naturally from the dynamics of a recursively defined informational substrate.

Explore the Principle

Core Concepts of UNNS Dynamics

The UNNS framework posits that reality's fundamental laws are not imposed but are emergent properties of a recursive system settling into stable states. Interact with the core ideas below.

Constants as Recursive Equilibria

Dimensionless constants arise as fixed-point ratios where the system's curvature reaches a stable, unchanging state through recursion.
The τ-Field Principle

A quantized phase variable, τ, governs the system's evolution. Its discrete states dictate the stable configurations the substrate can inhabit.
Quantized Entropy & Noise

Introducing noise reveals a phase transition. The system shifts from a perfectly ordered state (zero entropy) to a chaotic one as noise increases.
Deterministic Collapse

Under sufficient noise, the system undergoes a deterministic collapse, where informational variance amplifies, linking theory to observation.

Recursion Depth (n)

The Emergence of Alpha (α)

The primary achievement of the τ-Field Principle is deriving the fine-structure constant from first principles. When the quantization index q=1 and the scale Q₀=137, the system naturally settles into a state corresponding to α.

1/137.036

This links the abstract UNNS recursion directly to a fundamental constant of our universe, with a deviation of less than 2x10^-9 from the measured CODATA value.

Interactive τ-Field Chamber

Experience the core dynamics firsthand. Adjust the quantization index `q` and noise `σ` to see how the curvature field (κ) responds in real-time. Observe the stability of quantized states and the disruptive effect of noise.

Chamber Controls

Quantization Index (q) 1

Noise Amplitude (σ) 0.00