One of the important recent advances of the No-Time Universe (NTU) framework concerns the interpretation of the stochastic coefficient appearing in the coarse-graining equation.

The NTU no longer interprets stochasticity as a fundamental Brownian noise added to reality. Instead, the apparent stochasticity of the observable universe emerges from the existence of non-closed pre-links. At the substrate level, two geometrical structures coexist:

Closed surfaces:

Σ_closed

representing rigidified configurations generated by closed pre-links. The pre-links closure is obtained by a measure which has generated the energy transfer (NTU dynamic) and also generated the causality.

Open surfaces:

Σ_open

representing unresolved configurations corresponding to non-closed pre-links. The open pre-links (or non-closed surfaces) correspond to superposed configurations, analogous to Schrödinger-like states, which remain inaccessible until a measurement process occurs.

The total accessible surface is therefore:

Σ_total = Σ_closed + Σ_open

The fundamental NTU stochastic coefficient is defined as:

χ = Σ_open / Σ_total

This coefficient measures the fraction of the substrate that remains unresolved.

Its interpretation is immediate:

• χ ≈ 1 : most configurations remain open; the system is highly quantum and strongly fractal.
• χ ≈ 0 : most configurations are closed; the system becomes rigidified and classical.
• Intermediate values correspond to coexistence between open and closed configurations.

This clarification introduces an important distinction between two observers.

NTU Observer

An observer located at the substrate level has direct access to both:

Σ_open

and

Σ_closed.

For such an observer there is no randomness. The apparent uncertainty is simply the existence of multiple unresolved configurations. You will find all the NTU equations here : https://notimeuniverse.com/the-ntu-framework/