DOI: 10.5281/zenodo.16891324
title: From Spark to Fundamental Cube:  A Zarvanian Reinterpretation of Planck Length and the Threshold of Geometry

description: Abstract

This study explores the architecture of the cosmos in Zarvanian theory, tracing its structure from the tiniest sparks of existence to the grandest cubic formations.In this framework:



Spacetime is not continuous but granular and cubic.

Its smallest building block is the Zarvanian fundamental cube, composed of two half-cubes:



One in Space (the prison of particles)

One in Non-space (floating and free)


The boundary between Space and Non-space is where tiny particles—photons, neutrinos, and tachyons—dance.

The Zarvanian Planck length is the first distinguishable line segment, emerging from sparks of Non-space, initiating the cubic architecture of the cosmos.

Cosmic architecture at all scales is built from a unit cubic reality formed by two harmonic irrationals.


This theory forges a novel bridge between irrational mathematics, discrete geometry, and the ontology of Space-Non-space, offering a philosophical-physical vision of the cosmos:a world that is a cubic palace, half imprisoned in Space and half resting in the silent infinity of Non-space.

 

Introduction

In modern physics, the universe is usually interpreted as a continuous spacetime, grounded in Euclidean or smooth modern geometry.Yet the Zarvanian perspective invites us to a different horizon:



Discrete geometry instead of continuity

Space and Non-space instead of space and vacuum

Sparks, half-cubes, and fundamental cubes instead of abstract points and lines


This vision arises from a fundamental question:If every manifestation of matter exists half in this world and half in Non-space,what would the architecture of the cosmos look like?

Zarvanian theory answers this with a chain of emergence:





Sparks are the primary units of Non-space

Zarvanian Planck length is the first bridge into Space

The fundamental cube is the smallest prison of Space, capturing the sparks

Zarvanian spacetime emerges from the accumulation of countless such cubes,each half-floating in Non-space and half-bound in Space


This novel architecture carries profound implications:



The photon is the sole tightrope walker along cube edges

The neutrino is a ghostly traveler at the border of Space and Non-space

The tachyon is the orphan daughter of Non-space, whose freedom is exile

Singularities are the geometric collapse of cubes back into sparks of Non-space


Ultimately, Zarvanian cosmology paints a picture that is mathematical, philosophical, and poetic: a universe not of endless continuity, but of countless tiny cubic bricks, each with a silent half in eternity.

 

The Hybrid Structure of Fundamental Half-Cubes and the Fabric of Zarvanian Spacetime

In the Zarvanian framework, the primary substrate of the cosmos, known as spacetime geometry, is neither continuous nor akin to the multi-field constructs of modern physics. Instead, it emerges from the assembly of fundamental units with a hybrid space–non-space architecture. The smallest unit of this substrate is the Zarvanian fundamental cube, which arises from the coupling of two fundamental half-cubes. Each half-cube is constructed from the stacking of countless two-dimensional sheets shaped as isosceles right triangles, such that the total thickness equals the leg length of the triangles, and the resulting half-cube occupies precisely half a cubic unit of volume.

The remarkable feature of this architecture is that only one half-cube manifests spatially, appearing in the observable fabric of the cosmos, while its twin remains exiled in non-space, serving solely to preserve the coherence of spacetime geometry. The outcome is a hybrid fundamental cube, with one half residing in space and the other anchored in nonspace. By the tessellation of these hybrid cubes, the primary fabric of Zarvanian spacetime arises—a lattice that simultaneously carries the countable order of discrete cubes and the elusive, irrational essence of non-space, enabling the stable emergence of space itself.