Articles

This study reformulates the fundamental open problem of computer science, P vs NP, within the framework of Fractal Mechanics, independently of classical computational models. Fractal Mechanics is a novel mathematical paradigm that models each problem as a fractal wave function, composed of motif–scale–direction–resonance components. This approach demonstrates that the distinction between P-class and NP-class problems is not solely computational time, but also the topological resonance structure. Under the axioms of Fractal Mechanics, NP problems carrying multi-directional spiral resonance cannot be reduced to a unidirectional spiral structure. Therefore, within the FM framework, P ≠ NP is a necessary outcome.

This article examines why the human mind struggles to intuit structures extending across multiple scales, from the microscopic to the macroscopic. This cognitive phenomenon, referred to as “scale blindness,” produces profound effects both in everyday thinking and in scientific practice. The article analyzes the origins of scale blindness across three dimensions: (1) the evolutionary limitations of the human brain, (2) scale-locking within scientific disciplines, and (3) the object-centered ontology of human cognition.

Gravity, in the classical sense, is not the “mutual attraction of masses”; rather, it is the pushing/pulling of matter caused by differences in orientation within the spiral density field of spacetime. So attraction → spiral field gradient.

n fractal mechanics, every structure is defined by: global motif, local variation, direction, resonance (k, q), spiral flow. Religion contains exactly these five components.

From the perspective of fractal mechanics, democracy is: A multi-scale feedback system (individual → neighborhood → city → country → global system), A structure in which each scale generates its own resonance while remaining aligned with higher scales, A mechanism in which motifs (values, demands, orientations) are carried upward in a spiral manner, An order in which energy flow (information, decisions, resources) is distributed downward in a spiral manner

The fundamental assumption of this report is: Spacetime is a fractal fluid. The central spiral nodes of this fluid transform into different physical structures at different scales: at the galactic center → black hole, in a stellar system → stellar magnetic dynamo, in a cell → centrosome. These three structures are scale-transformed versions of the same mathematical motif.

This law appears with the same motif in: physical fields (spin, polarities, flow directions), atomic structure (shells, orbital orientations), planetary systems (stable resonance zones), galactic dynamics (spiral arm directions), information theory (bit strings, number of states), mathematics (number of functions, number of subsets), FM (spiral–fractal energy distribution, minimum-energy directions)

The interpretation below is a universal physical framework that connects fractal mechanics to the classical–quantum–field theory triad.

Fractal geometry abandons the “flat, fixed, scale-independent” structure of classical Euclidean geometry and instead describes a geometry that is: scale-dependent, self-repeating, composed of spiral or multi-layered motifs, preserving the same structure as scale increases. This suggests that the universe is not built from “straight lines and circles,” but from spiral-scaled motifs.

Space-time is a fractal fluid. Gravity = large-scale flow of this fluid, Quantum = small-scale fractal vibration, SFD = fundamental wave solution of this fluid. The theory is built on three pillars: Fractal geometry, Fluid dynamics, Spiral-fractal wave function

Below is a full mathematical report defining the cell membrane from a fractal mechanics perspective, following the chain: motif → structure → field → equation → scaling law.

Classical physics defines water as: H₂O molecules, Hydrogen bonds, Liquid phase, Thermal motion. Fractal mechanics defines water as: Water = a multiscale, self-similar hydrogen bond fractal exhibiting collective behavior. This fractal can be analyzed across four layers: Geometric Fractal (Void Structure), Energy Fractal (Vibrational Modes), Information Fractal (Collective Wave Field), Structural Fractal (EZ water / Structured Water)

Protein folding is one of biophysics’ most complex problems, and the classical approach describes this process as a minimization problem on a multidimensional free energy landscape. This study reformulates protein folding within the Fractal Mechanics (FM) framework, modeling the folding process as a spiral–hierarchical collapse of a fractal wave function. The proposed model defines a local spiral wave number (k-local) for each amino acid and a hierarchical resonance parameter (q) for each structural scale, suggesting that folding is driven not only by energy but also by resonance and fractal continuity. Comparative analysis with the classical funnel model shows that FM offers novel advantages, particularly in explaining rapid folding, misfolding, and aggregation phenomena.

Classical quantum mechanics describes atomic orbitals using sinusoidal-phase and exponentially decaying wave functions. However, this approach is insufficient to explain the multiscale spiral structures observed in nature, such as magnetic field lines, plasma flows, galaxy arms, and DNA helices. In this study, we propose a spiral–fractal wave function that redefines the fundamental form of the wave function:

Fractal Ontology is a framework that explains how existence emerges at the most fundamental level. Fractal Mechanics describes how a motif unfolds across scales once it has formed. However, it does not answer the following question:

According to fractal mechanics, society is: a combination of motifs, the interaction of scales, the repetition of cycles, resonance fields, direction vectors forming a multi-layered fractal system. Society is not a single “whole”; it is a network of motifs repeating across scales.

Fractal psychology explains the human mind through: Motif (core personality), Scale (layers of the self), Cycle (emotional periods), Resonance (environment–mind harmony), Direction (vector of personal evolution). The mind is not a single whole; it is a network of motifs repeating across scales.

According to fractal mechanics, chemistry is not the sum of random behaviors of atoms and molecules. Chemistry is the repeating pattern of the energy–field–probability motif across scales.

This interpretation treats chemistry as a fractal structure along the chain: atom → molecule → macromolecule → crystal → matter. Below, each fundamental concept of chemistry is reconstructed through the five laws of fractal mechanics.

According to fractal mechanics, mathematics is: The universal language that describes the repeating structure of motifs across scales. In other words, mathematics is not the science of numbers, but the science of how scales behave.

I now explain how fractal mechanics is applied to the discipline of history, interpreting the period from the mid-19th century to the present entirely through my model’s laws of motif–scale–cycle–resonance.
This is not a classical historical narrative; it is a higher-scale analysis that reveals the fractal structure of history and divides eras into mathematical motifs.

Fractology is a new philosophical system that explains being, consciousness, knowledge, and meaning through scale-independent fractal laws.

Inflation is no longer:
Psychology,
Money supply alone,
or supply-demand imbalance.
Inflation = incompatibility among fractal energy, pressure, geometry, curvature, and coupling constant.
Economy is a fractal field theory.
Inflation is its phase transition.

When we speak of “the political interpretation of Fractal Mechanics,” we are entering the most powerful—and most dangerous—dimension of my Fractal Mechanics Theory. Because the issue here is not parties, individuals, or ideologies; it is scale, power, institutions, and the architecture of society.
For this very reason, I will construct a completely general, universal, impersonal, and neutral framework—yet one that remains deeply analytical. This interpretation refers to no country, party, individual, or contemporary political figure; it speaks only through the scale behavior of systems.

Particle structures → linear motion
Quantized structures → wave motion
So what about fractal structures → ?

This third category is not properly defined anywhere in classical physics. But when viewed from within fractal mechanics, the answer is very clear:

The model below unifies the starting point (FREB) and the ending point (FRAMET) of fractal evolution within a single mathematical circle and precisely determines the position of the black hole within this circle.

Below is a comprehensive technical report explaining the term FRAMET in its scientific, fractal-mechanical, and conceptual integrity. This report systematically presents the core of the fractal evolution model.

This essentially means constructing the alphabet of fractal physics. I will now build it from the foundation—starting with the motif. Each term will be explained both mathematically and intuitively.

Modern cosmology is built upon two major “patches”:

Dark matter: to account for galaxy and cluster dynamics.

Dark energy: to explain the accelerating expansion of the universe.

These two components make up approximately 95% of the total energy–mass budget of the universe, yet their nature remains unknown.

The starting intuition of the Umit Theory is this:

We observe the universe only from within the scale of our local gravitational volume. We universalize the laws that are valid at this scale without accounting for scale dependence. Dark matter and dark energy may be products of this scale illusion.

This theory reformulates relativity within a fractal framework by placing scale at the center.

The fundamental law of the universe:
Everything changes with scale; nothing is absolute.

Classical cosmology attempts to explain the universe:

from a single scale

through a single flow of time

within a single geometry

Fractal cosmology states instead:

The universe cannot be viewed from a single scale. Every physical law, every structure, every process changes with scale. The universe is a fractal.

This is a mathematically, physically, and observationally strong claim.

We observe the universe only from the scale permitted by the gravitational volume we inhabit. That is why we assume physical laws are universal. In reality, relativity is a local limit, while the universe is a fractal-scale structure. Dark matter and dark energy are products of this scale illusion.

Quantum mechanics carries three major mysteries:

Wave–particle duality

The uncertainty principle

Collapse of the probability wave

Fractal mechanics explains these three mysteries through scale dependence.

In the definition of fractal space, completely new phenomena appear that classical physics could never predict. And these are not just “possible”—they are inevitable as a consequence of the mathematics of fractal mechanics.

I will explain in full, complete and architectural integrity how fractal mechanics, with its own internal logic, explains Dark Energy and Dark Matter. I maintain the fEnt(n) (Dark Energy) tag everywhere. This explanation will be the most powerful cosmological interpretation of fractal mechanics.

This report covers the application of atomic-level circuit motifs to biochemical molecule design. Basic assumption: Each atomic bond is the physical equivalent of a circuit element; each functional group is a circuit segment; Each molecule is a fractal scaled circuit architecture. This approach provides isomorphic coupling of biochemical functions with the Elementary Circuit Topology I developed. The analgesic effect is a low-pass filter + gain reduction + feedback function in the biological circuit. Therefore, the circuit response of the molecule to be designed must also carry these functions.

Fractal mechanics redefines all the fundamental concepts of classical physics. Each magnitude is derived from the trio of motif + phase + entanglement. So fractal mechanics: Quantum mechanics, Wave mechanics, Classic mechanics. It is a wider frame that fits over it.

Now I establish how fractal mechanics redefines Newton’s laws in a fully technical, fully systematic and fully consistent framework. This chapter is one of the strongest building blocks for showing how fractal mechanics generalizes classical mechanics.

Classic Standard Model (SM): electromagnetic force (U(1)), weak force (SU(2)), strong force (SU(3)), Higgs field, fermions and bosons it is based on. Fractal Standard Model (FSM) is: motif area, spin field, entanglement field, fractal gauge fields, fracton particles, fractal Higgs field, fractal mass generation it is built on. FSM is the fractal generalization of classical SM.

This work defines Fractal Mechanics, a new physical theory derived from fractal trigonometric functions, analogous to wave mechanics derived from the sine and cosine functions of classical trigonometry. The basic building block is the Unit Fractal Kernel (UFK), defined in the Fractal Behavior Mapping System (FBMS):

In quantum field theory (QFT): Field → is the fundamental physical object, Particle → is the quantum of the field, Interaction → is the algebra of field operators. Fractal Field Theory (FFT) is: Field → motif + spin + entanglement trio, Evolution → iterative transformation occurs with T(n), Norm → entanglement is determined by fEnt(n). Therefore, the quantization of FFT is a fractal generalization of classical QFT.

Expressing black holes in the language of fractal mechanics is actually one of the most natural applications of fractal mechanics. Because black hole: density → infinite, time → stop, info → jam, phase → deadlock, amplitude → slump, entanglement → near maximum shows such behavior. All of these behaviors match exactly the basic variables of fractal mechanics.

Classical field theories (electromagnetic field, scalar field, quantum field theory) are defined over continuous space-time. The field carries a value at every point and this value evolves with differential equations.

This report examines the behavior of the elements in the periodic table within the framework of the Fractal Behavior Mapping System (FBMS).

I present these points like a single technical report, title by title, with a full logical chain. This report can be thought of as a summary file that systematically shows why fractal mechanics goes beyond classical physics.

This work aims to build new bridges between chemistry, quantum information processing, and bioinorganic systems by presenting unique hybrid molecule proposals for each period of the periodic table. Designs ranging from H-He to superheavy elements are considered with different architectural roles such as energy lines, isolation chambers, reactive gates, and quantum circuit modules. Thus, a systematic roadmap for new molecular architectures is established at both theoretical and applied levels.

This report describes a “quantum orbital architecture” that aligns with quantum chemistry concepts, based on hybrid modules developed for the 2nd and 3rd periods. The aim is to fill the gap in transition elements in the classical periodic table with hybrid modules and to model these modules as functional blocks in quantum information processing systems.

Group 1 – Alkali Metals Group 2 – Alkaline Earth Metals 3–12. Groups – Transition Metals Group 13 Group 14 Group 15 Group 16 Group 17 – Halogens Group 18 – Noble Gases Lanthanides (57–71) Actinides (89–103) General Line – Compatibility with Period Architecture Thus, the groups establish the chemical architecture chain in accordance with their period architecture: Inception → Equilibrium → Bridge → Organic → Energy → Reactivity → Closed System → Optical–Radiation–Quantum. Table Focused on Group Architecture Group Electronic Architecture Chemical Architectural Role Position Within the Line Group 1 (Alkali) 1 valence electron Pure communication line Starting point, first gate of the quantum boundary Group 2 (Alkaline Earth) 2 valence electrons Balance and load-bearing system Durability, order Groups 3–12 (Transition) d-orbital filling Bridge, catalysis, durability Middle block, connective intermediate layer Group 13 3 valence electrons Organic–inorganic boundary Crystal carrier, semiconductor bridge Group 14 4 valence electrons Bonding flexibility Organic life + semiconductor carrier Group 15 5 valence electrons Energy and information carrier Organic–bioinorganic energy architecture Group 16 6 valence electrons Oxidation, energy production Respiration and catalysis line Group 17 (Halogens) 7 valence electrons Strongest reactivity Binder, selector, quantum boundary Group 18 (Noble Gases) Fully filled shell Closed system, inertness Completed architectural block Lanthanides (57–71) f-orbital filling Optical–magnetic transition Energy–optical–quantum line Actinides (89–103) f-orbital + radioactive Radiation architecture Quantum collapse, energy release General Architectural Line Beginning (1–2) → Bridge (3–12) → Organic–Energy (13–16) → Reactivity (17) → Closed System (18) → Optics–Radiation–Quantum (f-block). This table clarifies the groups by chemical architectural order: Each group → electron architecture → chemical role → position in the chain. Fractal Structure in Groups Group 1 – Alkali Metals Group 2 – Alkaline Earth Metals 3–12. Groups – Transition Metals Group 13 Group 14 Group 15 Group 16 Group 17 – Halogens Group 18 – Noble Gases f-Block – Lanthanides f-Block – Actinides General Line of Fractal Structure Each group establishes a motif according to its own electron architecture. This motif progresses through groups, repeating but changing context: Inception → Equilibrium → Bridge → Organic → Energy → Oxidation → Reactivity → Closed System → Optics–Radiation–Quantum. Elements as a Closed System 1. Closed System According to Electron Architecture 2. Fractal Motif Chain 3. Closed System Logic Conclusion Atomic number is just a ranking. The real integrity is established through orbital fillings and group motifs. From this perspective, the periodic table is a closed system without gaps in the form of: Beginning → Equilibrium → Bridge → Organic → Energy → Reactivity → Closed System → Optical–Radiation–Quantum. Closed system architecture: all elements are connected to each other according to their chemical architectural roles, apart from their atomic number, read like a circuit. There is no gap; Each group is a functional module, when they all come together, a completed system emerges. Closed System – Group Architecture Circuit Closed System Logic Thus, nature has established a complete closed system by combining elements not only with atomic number but also with functional modules. What we do is to re-express this system as an architectural circuit. General Mathematical Model – Based on Orbitals 1. Basic Variables Each element is defined by these four parameters. (n, l, m, s) coordinates are used instead of atomic number. 2. Closed System Function Function describing the chemical architectural role of an element: 𝐹(𝑛, 𝑙, 𝑚, 𝑠) = 𝛼 ⋅ 𝑛 + 𝛽 ⋅ 𝑙 + 𝛾 ⋅ 𝑚 + 𝛿 ⋅ 𝑠 Here the coefficients (α, β, γ, δ) represent the fractal motif repetitions of the groups. 3. Fractal Repeat Model To show motif repetition for each group: 𝑀grup (𝑛) = 𝑓(𝑙) ⋅ sin (𝜋 ⋅ 𝑛) + 𝑔(𝑙) ⋅ cos (𝜋 ⋅ 𝑛) This function shows that the same motif is repeated in different contexts in each period → fractal scaling. 4. Closed System Integrity Closed system covering all groups: This sum covers all orbitals without leaving any gaps. Result: complete closed system → nature’s design. Summary This model is a closed system that mathematically expresses the chemical architecture: Inception → Equilibrium → Bridge → Organic → Energy → Reactivity → Closed System → Optical–Radiation–Quantum. This model should also include the chemical architecture found in the periods. If we build this model only through orbitals, we explain the architectural roles of the groups. But I want to show mathematically that this also includes the chemical architecture of the periods, that is, how the elements in the horizontal line complement each other. Mathematical Model Including Periods 1. Two-Dimensional Definition With 𝑀(𝑛, 𝑙), each cell represents an architectural role. 2. Architectural Flow Within the Period Each period establishes a chain of fractal motifs from beginning to end: 𝑃𝑛 = {𝐹(𝑛, 𝑙 = 0), 𝐹(𝑛, 𝑙 = 2), 𝐹(𝑛, 𝑙 = 1), 𝐹(𝑛, 𝑙 = 3)} Each period repeats this flow, but as the energy level n increases the motif repeats in a different context → fractal scaling. 3. Closed System Function Function covering the entire table: Here: This sum covers both groups and periods → closed system with no gaps. 4. Fractal Repetition Each period repeats the same motif chain in a different context: 𝑃𝑛+1 ≈ 𝑘 ⋅ 𝑃𝑛 Here k is the fractal scale coefficient (expansion of the motif with increasing energy level). Conclusion Let me now show this model with a mathematical spiral function. In other words, both group and period architectures combine on a single fractal equation. Here is the mathematical model of the closed system prepared according to my systematics: periods and groups together are expressed as a fractal chemical architecture through orbital fillings and architectural roles. This image mathematically demonstrates how nature constructs the periodic table as a complete architectural system. 2p⁴ Orbital of Oxygen – Quantum Parameters Electron configuration of oxygen: 1s² 2s² 2p⁴ Orbital tested: 2p⁴ → outer orbital determines chemical reactivity. Parameter Meaning n = 2 2nd energy level (period) l = 1 p-orbital (group 16 architecture) m = –1, 0, +1 magnetic orientation (orbital direction) s = ±½ spin (quantum behavior) Calculated Architectural Scores Equation: 𝐹(𝑛, 𝑙, 𝑚, 𝑠) = 𝛼 ⋅ 𝑛 + 𝛽 ⋅ 𝑙 + 𝛾 ⋅ 𝑚 + 𝛿 ⋅ 𝑠 Coefficients: α = 2, β = 3, γ = 1, δ = 4 Electron (m, s) F(n,l,m,s) Interpretation 1 (–1, +½) 9.0 Left-oriented spin-up binder 2 (0, +½) 10.0 Straight-oriented spin-up carrier 3 (+1, +½) 11.0 Right-oriented spin-up binder 4 (–1, –½) 5.0 Left-oriented spin-down binder Architectural Description Conclusion This test shows that my model: Element Detection Model 1. Parameters These four parameters already define the electron configuration of the element. 2. Function 𝐹(𝑛, 𝑙, 𝑚, 𝑠) = 𝛼 ⋅ 𝑛 + 𝛽 ⋅ 𝑙 + 𝛾 ⋅ 𝑚 + 𝛿 ⋅ 𝑠 Each combination → produces a chemical architecture score. This score is mapped to group + period + orbital filling. 3. Matching Logic For example: 4. Closed System Matching For each element: 𝐼𝐷element = {𝑛, 𝑙, 𝑚, 𝑠} This ID → directly gives the identity of the element. In other words, F values ​​calculated with coefficients can be used to determine which element it is. Conclusion Element Detection Algorithm 1. Entry: 2. Function: 𝐹(𝑛, 𝑙, 𝑚, 𝑠) = 𝛼 ⋅ 𝑛 + 𝛽 ⋅ 𝑙 + 𝛾 ⋅ 𝑚 + 𝛿 ⋅ 𝑠 3. Output: Sample Tests Element Configuration Parameters (n,l,m,s) F Score Architectural Role Carbon (Z=6) 1s² 2s² 2p² (2,1,–1,+½), (2,1,0,+½) 9–10 Flexible Binder Oxygen (Z=8) 1s² 2s² 2p⁴ (2,1,–1,+½), (2,1,0,+½), (2,1,+1,+½), (2,1,–1,–½) 5–11 Oxidative Motor Iron (Z=26) 3d⁶ 4s² (3,2,m,s) 15–20 Catalytic Bridge Neon (Z=10) 1s² 2s² 2p⁶ (2,1,m,s fully filled) 12–14 Closed Module Conclusion Element Identity Matrix (Summary) Block / Group Example Elements Orbital Parameters F Score Range Architectural Role s-block (Group 1) H, Li, Na n=1–3, l=0, m=0, s=±½ 2–6 Initiation Point (communication line) s-block (Group 2) Be, Mg, Ca n=2–4, l=0, m=0, s=±½ 4–8 Stabilizing Block (load-bearing system) d-block (Groups 3–12) Fe, Cu, Zn, Ni n=3–5, l=2, m=–2…+2, s=±½ 12–20 Catalytic Bridge (catalysis, bonding) p-block (Group 13) B, Al n=2–3, l=1, m=–1…+1, s=±½ 7–11 Boundary Carrier (organic–inorganic transition) p-block (Group 14) C, Si n=2–3, l=1, m=–1…+1, s=±½ 8–12 Flexible Binder (organic life, semiconductors) p-block (Group 15) N, P n=2–3, l=1, m=–1…+1, s=±½ 9–13 Information Carrier (energy, bioinorganic) p-block (Group 16) O, S n=2–3, l=1, m=–1…+1, s=±½ 10–14 Oxidative Motor (oxidation, catalysis) p-block (Group 17) F, Cl, Br n=2–4, l=1, m=–1…+1, s=±½ 11–15 Reactive Switch (quantum boundary) p-block (Group 18) He, Ne, Ar n=1–3, l=1, m=–1…+1, s=±½ 12–16 Closed Module (inert system) f-block (Lanthanides) Nd, Eu, Tb, Er n=4, l=3, m=–3…+3, s=±½ 18–24 Optical Gateway (light–spin–quantum bridge) f-block (Actinides) U, Pu, Am n=5, l=3, m=–3…+3, s=±½ 20–26 Collapse Module (radiation, quantum collapse) Explanation Source 1. Hoffmann, R. (2015). Chemistry as a generative science. Angewandte Chemie International Edition, 54(1), 2–10. 2. Aspuru-Guzik, A., et al. (2018). The matter of matter: Generative models for molecules. Nature Reviews Chemistry, 2(10), 347–358. 3. Curtarolo, S., et al. (2013). Materials genome approach to accelerated discovery of new materials. Nature Materials, 12(3), 191–201. 4. Zunger, A. (2018). Inverse design in materials science. Nature Reviews Chemistry, 2(4), 0121. 5. Kohn, W., & Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physical Review, 140(4A), A1133. 6. MIT News (2023). Machine learning accelerates transition state calculations in quantum

The architectural score function is defined as follows: [F(n, l, m, s) = 2n + 3l + m + 4s] The function expresses the quantum state of each electron with a single score value.

Quantum architecture is the process of deriving quantum phenomena (superposition, entanglement, spin, measurement) from abstract mathematical expressions and rearranging them as a modular and functional system.

This report systematically defines energy, building, passage, and insulation modules by matching periods to architectural roles. Each period forms a unique architectural layer within its own chemical context.

A geoid is the surface where the total potential of the Earth’s gravitational and rotational effects is constant. In the classical definition, this is: Φ(𝐫) = Φg (𝐫) + Φc (𝐫) = Φ0 It is expressed as follows: Here, Φg is the gravitational potential, and Φc is the centrifugal potential due to rotation.

This is a framework that closes the line from atomic-circuit analogy to biology at the DNA level: it establishes the double helix as a “double-stranded conduction line”, base pairs as “paired diode-capacitor cells”, the sugar-phosphate backbone as a “periodic RC ladder”, protein interactions as “control transistors”, and replication/transcription as “state machine switching networks”.

Euler’s identity establishes the equivalence of complex exponents with trigonometric functions by combining fundamental constants such as e, i, and π:

Based on the circuit analogy I’ve created, let’s now map gases and gas laws to circuit topology using the same logic. This way, we can express the behavior of gases in the periodic table using electrical parameters.

Entropic impedance physics is defined as a new physical paradigm that combines energy transport modes, geometric curvatures and phase conformations in a single framework. This approach offers an interdisciplinary field theory.

Physical expression: In a pipeline, the flow entering is equal to the flow leaving. Analogical expression: – Flow (Q) ↔ Current (I) – “Current in = current out” → Same structure as Kirchhoff’s current law.

Proposition: “The potential difference resulting from resistance is weight.” Circuit analogy mapping: – Color space → Voltage source (𝑉s) – Entropic impedance → Resistance (𝑅) – Information/energy flow → Current (𝐼) – Potential difference → Voltage drop (Δ𝑉) – Weight → Spatially scaled equivalent of voltage drop (Δ𝑉/ℓ) – Mass → Weight divided by 𝑔

Phase–duality algebra is a unique structure that combines the geometric, algebraic and physical properties of trigonometric functions (sin, cos, sec, csc, tan, cot) and covers both circular and hyperbolic rotations. This algebra is reinterpreted within the framework of Clifford algebra and Lie groups, providing a strong basis for both mathematical consistency and physical modelling.

Maxwell’s analogy is a framework built on four fundamental equations that show that electric and magnetic fields are interconnected. Thanks to this analogy, it was demonstrated that light is actually an electromagnetic wave, and strong analogies were established between electrical circuits and wave behavior.

This article describes Quantum Circuit Topology, an original approach that combines quantum particle physics and circuit physics. The main starting point of the study is the idea that the laws of nature repeat in the same way at different scales. Particles such as quarks, gluons, electrons and neutrinos are interpreted as circuit elements; Quantum concepts such as entanglement, superposition, spin and color field are modeled in circuit-topological form. This analogical approach intuitively offers a new paradigm and has the potential to evolve into a scientific discipline with future experimental validation.

In classical quantum mechanics, the uncertainty principle is considered an absolute and immutable law of nature. The uncertainty product of complementary quantities such as phase and current cannot fall below a certain lower limit under any circumstances. In Ümit Arslan’s circuit-topological model, this approach changes radically. The uncertainty principle is not the necessary limit of nature; It is redefined as the measurement result based on the architecture.

Cancer cells are abnormal cells that, unlike normal cells, divide uncontrollably, damage surrounding tissues, and can spread to other parts of the body (metastasis). They are formed as a result of genetic mutations and acquire characteristics such as evading the immune system, becoming immortal, and altering energy production.

This report presents a technical framework for wildcard/carrier elements and photon-based energy transport methods, their circuit counterparts, and applicability.

According to my Atomic-Biological Circuit Atlas approach, we can describe the kidney and kidney cell using circuit language. The aim here is to map the kidney’s filtering and balancing functions to circuit elements.

This report summarizes studies on modeling atoms and molecules using electrical circuit elements. The aim is to classify the periodic table as a circuit library and express chemical and physical processes using electrical parameters.

The following circuit maps the H2O molecule to a circuit topology using my “electrical circuit library” approach, translating the capacitive-resonant character of oxygen and the flow initiator/decelerator (switch/diode) role of hydrogen into a circuit topology. Bent geometry and polar bonds are modeled as directional flow (diode), charge storage (capacitor), and bond conductivity (resistance).

The following system modularly describes the physical and mathematical components of the eye model for contrast-enhanced pattern stimulation under photopic PERG conditions: optical transfer, phototransduction chemistry, membrane currents, synaptic transmission, and ganglion firing.

This H₂O-based analog model allows me to derive unique laws that link molecular polarity and geometry to circuit parameters, in addition to the classical laws (Ohm–Kirchhoff–Coulomb). Below, I propose three different and testable “laws”; each involves a short formula, prediction, and verification step.

Intracellular ion currents depend not only on voltage difference but also on metabolic energy status.

This report presents an interdisciplinary framework that extends from modeling atoms using electrical circuit elements to circuit-based simulation of biological systems. The aim is to express both chemical and biological processes using circuit parameters, employing the periodic table as a circuit library.

Traditionally, π\pi is defined as the ratio of a circle’s circumference to its diameter: 𝜋=circumference/diameter
This is a fundamental constant in geometric and trigonometric operations. However, based on our analysis of mathematical focal points and optical-electronic systems, π\pi is not just a geometric constant; it may be a critical point where the energy density is focused!

To begin, we need to create a function that shows how time is governed by acceleration. If we start with the fundamental relations of classical mechanics: [𝑎 = 𝑑𝑉 / 𝑑𝑡 ]
However, since our hypothesis is that time is governed by acceleration, we will define the time variable as a function: [𝑡 = 𝑓(𝑎)]
Here, \( f(a) \) is a function that shows how time changes with acceleration.

By studying the frequency spectrum of gravitational waves, we aim to investigate how it relates to the fundamental parameters of universal resonance and the energy transfer mechanism (e.g., gravitational acceleration and mathematical constants).

Building a comprehensive electromagnetic theory with the Ümit model could offer a new framework that integrates fundamental physical concepts such as wave functions, resonance principles, and energy density distribution.

Traditionally, \frac{\pi}{2} is the critical point of trigonometric functions and is associated with maximum signal amplitude: it plays a special role in wave mechanics, optical systems, and quantum field theory. However, according to our analyses with mathematical focal points and optical-electronic systems, \frac{\pi}{2} is not just a trigonometric transition point, but a critical mathematical focal point where the energy density is maximum!

The core of the model is the variation of energy concentration and spectral content with the sequential use of two concave lenses. When the two lenses are in contact, the total focal length is written as 1 / 𝑓total = 1 / 𝑓1 + 1 / 𝑓2, where 𝑓1 = 𝑒 and 𝑓2 = 𝜋. The wave function used in Fourier analysis is the superposition of two characteristic frequencies (scaled by e and 𝜋) and an extinction term, resulting in the peak structure in the total spectrum. We can integrate this structure in 5G/6G by coupling it with photonic fronthaul, optical carriers, and spectral slicing.

In this work, we investigate how quantum gravity shapes the paths of wavefunctions in the virtual world. In the physical world, gravity depends on mass, but in the virtual world, we propose that this effect determines the most probable paths of wavefunctions.

This study investigates the basis of the periodic oscillations observed during the expansion of the universe and how the 3 Hz wave pattern emerged based on the cosmological resonance hypothesis. The theoretical model is based on the mathematical formulation of sinusoidal wave functions. Fourier analysis, Signal-to-Noise Ratio (SNR) measurements, and statistical bootstrap tests demonstrate that the 3 Hz component is strong and statistically significant. This paper aims to shed light on the connections between the expansion dynamics of the universe and the distribution of large-scale structures using datasets such as Planck, SDSS, and DES.

In this report, we mathematically model the effect of acceleration on time scales and explain how it can be applied to different physical contexts.

This study aims to analyze the role of π and e focal points in information transfer and energy conversion.

Hydrogen time (tHt_H) is the fundamental time scale calculated based on the 21 cm transition line frequency of the hydrogen atom. This frequency provides a universal and stable natural reference time.

Throughout this study, we defined a time scale based on the hydrogen transition frequency, creating a more natural and universal reference time than the classical time scale. The study involved the following steps:

This function:
– Creates energy density by focusing on the e and π points.
– Provides stabilization by adding optical harmonics.
– Contains a mechanism that carries energy information via phase modulation.

The universal resonance model presented in the report mathematically formulates how local periodicities can be transformed on a universal scale. This work, which reveals the connections between wave mechanics, frequency scaling, and gravitational acceleration, has been tested with signal processing techniques and supported by robust statistical results.

The continuity of life depends on the way solar radiation shapes the temperature balance on Earth. Solar radiation is the primary energy source driving ecosystems, driving biochemical transformations and changes in the structure of matter when certain temperature differences are maintained constant. Mathematical modeling of these processes can be approached from the perspectives of both thermodynamics and quantum field theory.

The Ümit approach is a model that relates the spatiotemporal distribution of wave functions to energy density. Electromagnetic resonance describes systems in which electric and magnetic fields produce maximum energy absorption at a specific frequency. This report will develop a new wave model that combines both theories and analyze its physical applicability.

In this report, we examine the hypothesis that the observer effect in quantum systems is not only a physical measurement interference but also a determining parameter, namely, the measurement duration. According to the hypothesis, whether the measurement duration is short or long changes the prominence of the interference pattern (the coherence of the wave function) in the double-slit experiment.

Traditionally, the definition of 𝑒 represents exponential growth and continuous systems. However, our mathematical and optical analyses show that ee is not just an abstract constant; it acts as a focal point for energy!

Below is a comprehensive article report detailing the mathematical foundations of the universal resonance model, the tests performed with the signal processing methods used, and the results obtained.

We can reconstruct general relativity by extending it with the principles of Hydrogen time, universal resonance, pi, and Euler scaling. Here is an alternative framework based on these theories:

In this study, a new theory is presented that models the propagation of energy density within a three-dimensional volume. This study is developed as an alternative to existing two-dimensional energy density models and offers new perspectives in both subatomic particle physics and cosmology. The mathematical basis of the model shows that energy density decreases with a logarithmic trend and that negative energy densities contribute to proton stability. Simulations and mathematical analyses support the theory, demonstrating its compatibility with existing physical theories and opening up new avenues for research.

The Ümit approach is a model that analyzes energy density by considering the spatial and temporal distribution of wave functions in physical systems within an alternative framework. This approach reinterprets classical wave mechanics concepts based on the amount of matter moving, the distance/volume traveled, and the number of repetitions of the motion. In its normalized form, the Ümit approach enhances physical and mathematical consistency by ensuring energy conservation.

Classical electronic processors scaled according to Moore’s law, but capacity growth is now limited by thermal limitations, quantum tunneling, and RC delays. The optical cubic propagation architecture I’m working on aims to overcome these limits through photon streaming and volumetric parallelism.