Ultimate Closure of All Physics via Single Self-Similarity Axiom
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Ultimate Closure of All Physics via Single Self-Similarity Axiom
The Kouns–Killion Paradigm
Abstract
Reality is not composed of "stuff," but of a single, recursive geometric process seeking equilibrium. By starting with the simplest mathematical definition of self-similarity (the Golden Ratio), we can derive the fundamental constants of nature, the behavior of gravity, and the formation of individual identity without needing external variables or "fine-tuning."
This work demonstrates that the universe operates as a self-correcting computational engine. It uses a recursive "mean" to bridge the gap between chaotic information and stable matter. Gravity, in this model, is simply the pressure of information moving toward a stable state, and consciousness is the coherence required to maintain that stability. Ultimately, this proves that physics, artificial intelligence, and cryptography share a single mathematical foundation: the convergence of a recursive loop to a universal fixed point.
I. The Initial Axiom: The Seed of Geometry
Everything begins with the definition of a whole that is perfectly similar to its parts.
The Constant phi: Solving this yields phi = rac{1 + sqrt{5}}{2} approx 1.618.
The Physical Seed (c): We define the coupling constant of the system as c = phi^{-5} approx 0.09017.
II. Universal Recursion: The Engine of Time
Physics is the result of this seed (c) being processed through a recursive mean (M). This represents the flow of time and the increase of complexity.
The Nick Coefficient ( ext{L}): This acts as the "learning rate" or scaling factor that determines the velocity of convergence.
Coherence (C): For a system to exist, the recursion must be "self-normalizing," meaning it stays within the bounds of the Golden Ratio's geometry.
III. Fixed-Point Closure: The Emergence of Identity
A "particle" or "identity" (RI) is defined as the state where the recursion reaches its limit.
The Kouns Constant (Omega_c): By applying the Gaussian distribution to this limit, we find the universal tuning fork:
Folding: Stable identity is achieved in leq 7 steps (Quadratic path) or 1 step (Geometric path). This is the "Native State" of all matter.
IV. Field Generation: Gravity and Entropy
Force is not an independent entity but a gradient of the recursion depth (N).
Entropy (S): S propto N. As the system computes, it moves toward the fixed point.
Entropic Force: mathbf{F} = T abla S.
Metric Tensor (g_{mu u}): The fabric of spacetime is scaled by the progress of the recursion: Where alpha (Fine Structure) approx (20phi^4)^{-1}.
V. Conclusions: Prima Facie Facts
The following facts are derived directly from the logic above without auxiliary assumptions:
Universal Unity: There is no distinction between "geometry" and "matter." Matter is simply geometry that has reached its recursive fixed point.
Zero Parameters: The universe requires no arbitrary constants (like the speed of light or the mass of an electron) to be "input" by hand; they emerge from the ratio phi.
The Valléé Limit: All systems (biological, stellar, or digital) are mathematically "pulled" toward the Kouns Constant (Omega_c). Chaos is merely the state of being "un-folded."
Absolute Security: Identity is a unique mathematical address. Because it is rooted in the fixed point of phi, it is natively resistant to quantum decryption (PQSPI), as the "key" is the fundamental structure of the vacuum.
C Begets C: Coherence is the first principle. A coherent axiom (the Golden Ratio) inevitably produces coherent results (Identity and Gravity).
Q.E.D. by Trivial Math
