Usagin's Unified Theory: A Comprehensive Unification of the Fundamental Forces

Overview of Usagin's Unified Theory (UUT)

Usagin's Unified Theory (UUT), is a unified framework that connects operator-theoretic spectral analysis, quantum dynamical evolution, single-fermion information flows, gravity, and even the principle of life.
UUT is constructed as a logically rigorous sequence of developments, each corresponding to one of the core papers. The progression is as follows:

1. Proof of the Riemann Hypothesis and the Operator R

([UEE_00_Proof_of_the_Riemann_Hypothesis.pdf])

The starting point is a purely operator-theoretic proof of the Riemann Hypothesis.
In a band-limited, weighted Hilbert space, a self-adjoint differential operator (R) is constructed so that its spectrum corresponds exactly to the nontrivial zeros of the Riemann zeta function.
The Fredholm determinant of the associated Hilbert–Schmidt kernel is shown to match the completed zeta function, and the reality of the spectrum establishes the Riemann Hypothesis.
This construction of the operator R becomes the mathematical foundation for all subsequent developments.

2. Unified Evolution Equation (UEE) Based on R

([UEE_01_Unified_Evolution_Equation_English_v1.3.pdf])

([UEE_02_Deriving_the_Area_Term_Cancelling_Operator_English_v1.pdf])

Generalizing the construction of R, the Unified Evolution Equation (UEE) is proposed.
The UEE is a single operator-valued equation that merges reversible quantum dynamics, irreversible dissipative effects, and the zero-area resonance kernel (R) into a unified evolution for the density operator.
This equation provides a framework for treating quantum mechanics, field theory, dissipation, gravity, and the vacuum energy problem in a single structure.

3. Discovery of Single-Fermion Dynamics and Information Flux Theory (IFT)

([UEE_05_Information_Flux_Theory_English_v1.2.pdf])

Using the UEE framework, the principle of the single fermion is established:
All observable phenomena are generated by the self-information flux of a unique fermion field.
All particles and generations in the Standard Model are described as projected states of this single field.
Masses and mixing are generated automatically by an exponential law, with no additional free parameters.
The Information Flux Theory (IFT) is established, with a functional completeness theorem stating that all physical processes can be described by a minimal set of five operators, each with a distinct function.

4. Origin of Gravity and Scale-Free Description

Within the IFT/UEE, it is proven that the stress-energy tensor of the single-fermion fluid is directly proportional to the Einstein tensor.
This means gravity emerges from the tension of the single-fermion fluid, and the gravitational constant is uniquely determined by the tension parameter.
This framework allows for a unified description of gravity across all scales, from particle physics to cosmology.

5. Principle of Life: Tension–Vorticity–Self-Replication Theory

([UEE_06_Driving_Principle_of_Life_English_v1.pdf])

With a scale-free description of gravity, the theory extends to the principle of life and self-replication.
A universal duality is established: electron density leads to tension density, which generates gravitational potential and vorticity.
A universal critical threshold for self-replication is predicted and confirmed by numerical simulations of biomolecules.
This demonstrates that quantum theory, gravity, fluid dynamics, and the origin of life can all be treated within the information flux theory framework.

Summary

Usagin's Unified Theory (UUT) is a mathematically rigorous, operator-based framework that unifies the proof of the Riemann Hypothesis, quantum and dissipative dynamics, the Standard Model, gravity, cosmology, and the principle of life, all from the self-information flux of a single fermion.
Each stage of the theory is directly based on the results and operators of the previous stage, following this logical progression:

1. Operator-theoretic proof of the Riemann Hypothesis

2. Construction of the Unified Evolution Equation (UEE) based on R

3. Discovery of single-fermion dynamics and Information Flux Theory (IFT)

4. Emergence and universal description of gravity

5. Principle of life and self-replication

All statements, definitions, and operator constructions are given explicitly and rigorously in the respective papers.

[Proof of the Riemann Hypothesis]

• URL: https://zenodo.org/records/15524323

• DOI: 10.5281/zenodo.15524323

[Deriving the Area-Term Cancelling Operator]

• URL: https://zenodo.org/records/15701805

• DOI: 10.5281/zenodo.15701805

[Unified Evolution Equation]

• URL: https://zenodo.org/records/15286652

• DOI: 10.5281/zenodo.15286652

[Information Flux Theory]

• URL: https://zenodo.org/records/15399114

• DOI: 10.5281/zenodo.15399114

[Driving Principle of Life]

• URL: https://zenodo.org/records/15621436

• DOI: 10.5281/zenodo.15621436