Theory of the Universe of Immaterial and Dimensionless Geometry – TUIDG

Absolutely distinct from the two conventional, antagonistic branches of physics—General Relativity and Quantum Theory—which accept a substantial, corpuscular reality with finite volume and a potentially multiple nature originating from nothing, TUGIA, through the full use of reason and its four axiomatic principles (termed the Restrictive Axiomatic Principles of Reality and Illogical Functionalities), asserts that the universe is eternal, absolutely impalpable, and dimensionally infinite, existing solely as a single absolute void, herein referred to as the Omega Dimension. TUGIA maintains that the universe is inherently immaterial, as the Axiomatic Principle of Void-Matter Indistinction establishes that it is impossible to differentiate between "being" and "non-being." Furthermore, it guarantees that no indivisible element can exist, as the Axiomatic Principle of Necessarily Indefinite Fragmentation establishes that for any supposedly minimal element, there exists an internal intermediate element contained within it.

It asserts that interaction at a distance between substantial, corpuscular elements is impossible, as the Axiomatic Principle of Logical-Constructive Interactive Incapacity establishes that interaction between two separated elements, A and B, is impossible without a third element, C, being directly connected to them. Moreover, it guarantees that finite universes cannot exist, as the Axiomatic Principle of Necessarily Indefinite Containment establishes that for any supposed "maximum volume," there exists a "greater volume" that contains it in an infinite process of containment. Faced with the complete nonexistence of substantial corpuscular elements, it ensures that the purported substance of which everything is composed is merely "Apparent Matter," formed by an interaction process between specific geometric elements devoid of substantiality, constituted solely by an Immaterial Geometry in the form of infinite-dimensional toroids, called Alpha Components or Compalphas.

It claims that what we perceive as motion and time are merely appearances or illusions. Thus, this "Apparent Motion" is caused by the relationship between different static geometric configurations that form bodies in various spatial positions, rendering "Apparent Time" as merely a consequence of these relationships at every point in space. It guarantees that the Immaterial Geometry of these Compalphas possesses a specific functionality called "Rotating Interaction" and that, due to its inherent order and existence within infinite sets of six structural dimensions (called Coexistent Structural Hexalevels), they are capable of generating interaction patterns at infinite levels of complexity, forming infinite "Apparent Realities."

It ensures that the interaction between the infinite elements of the universe is promoted by Apparent Motion; for since these elements are formed by immaterial geometric components with static, logical, and mathematical functionality, there is no element that can move or be moved. Therefore, within this same Apparent Reality, which we certify as dynamic, what exists is an Apparent Motion and, consequently, an Apparent Time, since time, according to these propositions, is a product of the relationship between the intensities of this movement. TUGIA affirms that it is the Compalphas, existing in infinite numbers and structural dimensions, that organize themselves from any of these dimensions—using any one of them as an arbitrary base—in order to construct other infinite geometric structures called "Geometric Continua."

A Compalpha, as an individual functional geometric element, takes the form of a composite toroid formed by six concentric toroidal layers of varying diameters, whose intrinsic dimensions are numerically infinite. These interact geometrically to form "Merons" and, simultaneously, the infinitely interconnected structure of this Geometric Continuum, whose appearance is verbally indescribable given the quantity of elements constituting it, yet perfectly possible to be grasped by human rationality. It states that it is within these Geometric Continua that one of the two fundamental modes of geometric interaction arises: "Rotating Interaction." This is primarily responsible for the logical formation of this structure and, subsequently, in more complex levels of interaction, for three of the four fundamental forces described by traditional physics: the strong nuclear, weak nuclear, and gravitational forces.

It ensures that the Geometric Continua, in turn, rotated across infinite axes—like a geometric solid superimposed in infinite positions—constitute other types of structures called "Geometric Hypercontinua," where the second fundamental type of geometric interaction arises: "Cyclic Interaction," responsible for what is termed the fourth fundamental force of physics: the "electromagnetic force." It asserts that it is in this Geometric Hypercontinuum that Apparent Motion emerges as a result of the infinite relationships between the infinite static geometric snapshots of its infinitely superimposed and related individual elements; and due to these infinite relationships between such states, the "Apparent Reality" of which we are a part emerges.

It guarantees that it is within the Geometric Hypercontinua that the modes of interaction derived from Rotating Interaction—termed here "Attractor and Repulsor Interactions"—also prevail. These are, to a greater or lesser degree, the physical equivalents of the magnetic, electric, gravitational, color, and weak fields, thus representing the physical equivalents of all natural forces. It asserts that in these structures, with the sole exception of what is called the "Geometric Ultracontinuum," absolutely everything is possible; that is, infinite Apparent Realities exist as an infinity of infinities, as a plurality of different realities within the same Apparent Reality. Finally, it asserts that these same structures constitute the Geometric Ultracontinuum, the final structure where, without exception, absolutely everything is possible: infinite universes with infinite laws of their own, where the flow of Apparent Time and gravitational attraction may very well be reversed, among other infinite possibilities.