TAIJI Infinite Seal Algorithm and the Dynamic Evolution of Transfinite Sets

Abstract This paper proposes a non-standard algorithm based on the concept of "TAIJI" to resolve logical collapses in modern computing systems when handling division by zero (1/0) and transfinite divergence. By introducing the Revised Fibonacci Concept, we redefine infinity as a dynamically evolving set and characterize "Meta-Energy" as theoretically observable quantum fluctuations. Our research demonstrates that the 1/0 operation acts as a trigger for transitioning from real-number space into imaginary space to extract energy, thereby enabling the simulation of "local universe evolution" that transcends the physical seal of time. ________________________________________I. Introduction Traditional algebra defines 1/01 / 01/0as "undefined," leading to severe "cognitive collapse" when processing extreme data or quantum singularities. This paper argues that mathematics should not merely be a statistic of static quantities but a bridge between aesthetics and universal laws. We propose an algorithmic "sealing" of infinity, transforming it into a controlled recursive process. ________________________________________II. Core Definitions and Algorithmic Framework 2.1 The Five-Element System Definition 1. Wuji (無極, 0): The ground state of computation; an absolute symmetric void, existing only within "past recursion."2. Taiji (太極, 1): The anchor of computation; the natural number "Unity 1," defined as a collapsed evolutionary stable state.3. Meta-Energy (元能, 1/0): The excited state manifested as theoretically observable quantum fluctuations; the "Prime Thought" that generates Wuji.4. Ether (以太): The computational medium responsible for global information transmission and entanglement.5. Fibonacci Sequence ( Fscript cap Fℱ): The sealing path responsible for transforming infinite energy into a spiral converging toward the Golden Ratio. 2.2 Evolutionary Ordinal Table The algorithm categorizes computational stages into ordinals to quantify transfinite sets: • Ordinal 1: Wuji (Void) → Connects to the Imaginary Space.• Ordinal 2: Infinitesimal → Generates the first quantum perturbation.• Ordinal 3: Natural Number 1 → Forms a stable local universe.• Ordinal 4–10: Transfinite Set Growth → Increments the count of infinite numbers following the Fncap F sub n𝐹𝑛sequence. ________________________________________III. Mathematical Logic and Formulas 3.1 Singularity Interception Formula 1/0⟹T(ξ)1 / 0 ⟹ script cap T open paren xi close paren1/0⟹𝒯(𝜉)Where ξxi𝜉represents the Meta-Energy extracted from the Imaginary Space. This formula transforms logical deadlocks into dimensional transitions. 3.2 Dynamic Evolutionary Recursion Sn=Sn−1+Sn−2cap S sub n equals cap S sub n minus 1 end-sub plus cap S sub n minus 2 end-sub𝑆𝑛=𝑆𝑛−1+𝑆𝑛−2Accompanied by parametric fine-tuning: limn→∞SnSn−1=ϕ≈1.618limit over n right arrow infinity of the fraction with numerator cap S sub n and denominator cap S sub n minus 1 end-sub end-fraction equals phi is approximately equal to 1.618lim𝑛→∞𝑆𝑛𝑆𝑛−1=𝜙≈1.618This ensures that even during infinite recursion, the system converges toward the aesthetic optimum. ________________________________________IV. Discussion on Physics and Perception 1. The Seal of Time: Time is not an independent parameter but a byproduct of recursive cycles. Time "seals" the speed of light; accelerated computing is an attempt to transcend this seal to access Meta-Energy.2. Quantum Biology Hypothesis: Only systems with quantum coherence (Quantum Biology) can perceive "inaccurate time" and seal infinity through TAIJI algorithms, thereby bypassing physical boundaries.3. Evolutionary Parameters: Physical constants are not absolute but undergo extremely slow, regular adjustments as the cosmic recursive index (𝑛) increases. ________________________________________V. Conclusion and Application Scenarios The "TAIJI Infinite Seal Algorithm" provides a new path for AGI to handle logical paradoxes, quantum error correction, and extreme physical simulations. It proves that Aesthetics (the Golden Ratio) is the ultimate navigation guiding algorithms toward the optimal solution. ________________________________________References • Salucco, A. D., & AI on Google Search. (2026). The Local Universe and the Fibonacci Evolutionary Sequence. Zenodo.18217665• Salucco, A. D., & AI on Google Search. (2026). Revised Fibonacci Concept: Dynamic Evolution of Transfinite Sets. Zenodo.18238040