4. Physical Interpretation — Equal Pressure and Curved Generation

The cubic filling can be interpreted as the microscopic structure of 4D space under isotropic pressure:

• Each cubic unit experiences identical tension in all directions.

• The curvature of the 4D sphere arises from the gradual compression of cubes toward the boundary, where geometric constraints bend the discrete grid.

• The fourth dimension www represents a gradient of generative pressure, rather than a linear direction.

Hence, the hypersphere forms where the expansion of cubic volumes achieves perfect equilibrium — a balance of creation rather than mere extension

6. Conceptual Meaning

This model reveals that the Tetrachron is a geometry of generative balance, where the universe could be viewed as a tetradimensional equilibrium formed by the accumulation of discrete volumetric quanta.

• The cube represents the unit of spatial measure.

• The sphere represents the limit of isotropic curvature.

• The fourth dimension w represents the field of expansion through which cubic volumes accumulate.

Thus, the Spherical Tetracron expresses a profound geometric law:

When cubic space expands under equal pressure in all directions, it generates a hyperspherical continuum — the 4D equilibrium of creation.

7. Conclusion

The Cubic Spherical Tetrachron merges the discrete and the continuous:
a universe of unit cubes arranged in perfect isotropy, forming a hypersphere of radius 50 in the fourth dimension.

It is both mathematical and physical — a 4D space whose curvature, symmetry, and balance arise directly from the simple act of accumulating identical volumes within a finite boundary of equilibrium.

The Generative Geometry of the Spherical Tetrachron

According to the Tetrachron Principle
César A. Valencia Z., October 2025

1. Introduction — Discrete Accumulation and Spatial Pressure

The Tetrachron Principle postulates that a four-dimensional solid can be constructed by the progressive accumulation of 3D volumes along a generative coordinate w.

In its spherical version, this accumulation occurs isotropically: the 3D cubes expand and organize themselves under equal pressure in all directions, producing a four-dimensional equilibrium sphere — the Spherical Tetrachron.

Formally, we describe it as an aggregation of unit cubic cells (1×1×1) distributed within a spherical boundary of radius R=50 in both 3D and 4D coordinates.