The NTU framework reaches an important milestone with the publication of the first closed derivation of the fractal coarse-graining mechanism : https://notimeuniverse.com/the-ntu-framework/. This result represents one of the central structural components of the No-Time Universe framework, as it provides a possible mathematical bridge between:

• the discrete relational NTU substrate,
• and the emergence of continuous relativistic spacetime.

Within NTU, coarse-graining is not treated as a simple approximation method.

It is interpreted as the physical emergence mechanism through which:

• causality,
• temporal ordering,
• quantum probabilities,
• relativistic geometry,
• and effective physical laws

appear at observable scales.

The newly derived formalism describes how recursive fractal pre-link structures may progressively generate stable macroscopic continuity through large-scale statistical organization and symmetry breaking.

This derivation constitutes a key step toward addressing one of the fundamental open problems of theoretical physics:

how continuous spacetime and relativistic physics can emerge from an underlying discrete substrate.

The NTU framework proposes that:

• quantum discreteness,
• non-local relational organization,
• and relativistic continuity

are not incompatible descriptions of reality, but different emergent regimes connected through fractal coarse-graining dynamics.

This publication also strengthens the role of the pantograph principle and recursive scaling laws introduced inside the NTU framework.

Future work will focus on:

• numerical simulations,
• stability analysis,
• cosmological implications,
• and possible observational signatures near the discrete/continuous transition frontier.