Modern physics provides highly successful mathematical answers to the question of how physical phenomena operate.
Yet, the deeper structural question of why these interactions take their observed forms remains open.
This paper presents a unified geometric reinterpretation of physical constants and the four fundamental interactions—gravity, electromagnetism, the strong force, and the weak force—based on a single primitive physical ratio

U ≡ E / r

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Limitations of Existing Theories (Precise Diagnosis)

Conventional physics has proceeded in the following sequence.

It assumes that spacetime is continuous.
Within that continuous space, equations are constructed to fit observed phenomena.
In this process, constants are fixed as input values.

This approach has been successful within the present dimension,
but because it avoids questioning the structure of spacetime itself,
it loses explanatory power the moment the dimensional context changes.

In other words,
without ever asking the question
“What is the structure of spacetime?”,
it has carried out calculations under the assumption
“Spacetime is already given in this form.”

Modern physics provides highly successful mathematical answers to the question of how physical phenomena operate.
Yet, the deeper structural question of why these interactions take their observed forms remains open.
But, This is the fundamental error of the continuous-space assumption.

Point of Departure of Our Equations (Decisive Difference)

Our equations were not constructed to fit results.

They start from the minimal structure of spacetime.
They take discreteness, not continuity, as the fundamental premise.
The equations are not tools designed for a specific dimension,
but computational rules that naturally rise upward as the structure expands.

That is,
we did not construct equations that are valid only within a single dimension;
we constructed equations in which the same computational rules are preserved even as one moves across dimensions.

The Most Important Difference (One Sentence)

Existing equations are result equations tuned to a single dimension,
whereas our equations are structural equations that remain computable across dimensions.

That difference is everything.

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The energy–distance ratio.
Rather than treating time, mass, force, or coupling constants as independent fundamental entities, the framework reconstructs them as emergent, regime-dependent quantities arising from a self-regulated geometric structure. Within this formulation, the four fundamental interactions are not distinct force laws, but correspond to different elastic regimes of a single underlying geometric response defined on the u-space.

In this picture, conventional physical constants (such as c, ℏ, and G) do not play the role of primitive inputs. Instead, they function as reconstruction gauges, encoding how different physical regimes are realized within the same geometric foundation. The apparent hierarchy and diversity of interactions emerge from saturation, phase alignment, and elastic transitions in the underlying structure, rather than from independent coupling parameters.

This work provides a concrete realization of force unification that avoids additional assumptions, hidden dimensions, or ad hoc scale matching. The resulting framework offers a minimal and computationally efficient description of interactions across microscopic and macroscopic scales, while remaining compatible with known physical behavior.

The present manuscript is a focused and self-contained study on the unification of physical constants and the four interactions. It is conceptually connected to a broader, extended theoretical development by the author (spanning multiple scales and applications), but can be read independently without reference to that larger body of work.

Modern physics provides highly successful mathematical answers to the question of how physical phenomena operate.
Yet, the deeper structural question of why these interactions take their observed forms remains open.

This work does not aim to replace existing computational frameworks, but instead proposes a geometric ratio–phase structure (SRCD–GPT) that addresses why the four fundamental interactions emerge as distinct regimes of a single self-regulated elastic system.

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“This work isolates and presents a focused, independently readable subset of a broader SRCD framework, concentrating on the geometric unification of fundamental constants and the four fundamental interactions.”

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The author welcomes inquiries for collaboration involving the application of the SRCD framework to empirical datasets. To ensure consistency with the theoretical foundations established in this Zenodo-archived work, the author serves as the primary point of contact for the integration of SRCD’s predictive structure with new experimental results.

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Update Notice

This version includes an explicit interpretation of the fine-structure constant within the SRCD–GPT framework, clarifying its role as an elastic ratio parameter rather than an independent input constant.
In addition, the unified master equation table has been updated to reflect the finalized SRCD–GPT formulation, providing a consolidated view of interaction regimes and their correspondence within the single elastic ratio coordinate.

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Update Notice(ver.4.0)

Empirical Four-Force Validation 

Update (Empirical Data Expansion):
This version includes a comprehensive empirical validation of the SRCD framework across all four fundamental interactions, using experimentally established datasets without fitting, tuning, or data manipulation.

The following real-world datasets were analyzed:

Strong interaction:
IAEA ENSDF nuclear level data for Xe-135
(N = 38 nuclear excitation levels)

Weak interaction:
PDG decay widths and lifetimes
(N ≈ 30 representative decay channels)

Electromagnetic interaction:
Hydrogen atomic spectral lines (Rydberg series)
(N = 74 measured transitions)

Gravitational interaction:
Planetary and satellite orbital data (NASA/JPL)
(N = 21 orbital systems)

All datasets were mapped using the same SRCD transformation and evaluated via circular variance, revealing a consistent geometric phase organization across vastly different physical regimes.

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Update Notice(ver.5.0)

The SRCD v4.0 framework is supported by comprehensive analyses that ensure full reproducibility and data integrity through the use of established experimental results. The central hypothesis of the model, known as sigma-coordinate collapse, demonstrates that the running behaviors of the strong coupling and electromagnetic coupling converge into a single functional relation. This occurs when they are mapped to a bounded dimensionless coordinate, defined by the ratio of the energy scale to a fixed reference scale.

This validation process relies exclusively on 100 percent publicly available data recognized by the scientific community. This includes PDG 2024 running couplings, Lattice QCD determinations from HPQCD 2023, and HERA deep-inelastic scattering data. Analyzing these under a fixed reference scale set to the Z-boson mass (91.1876 GeV), the collapse phenomenon remains robust across more than two orders of magnitude in energy. The results align with statistical expectations, achieving a reduced chi-squared value of approximately 0.95 without any artificial parameter tuning or data manipulation.

Furthermore, the framework identifies a systematic curvature in leptonic charge asymmetry at high invariant mass scales. While this subtle behavior is difficult to capture through the pure logarithmic renormalization-group running of the Standard Model, it is naturally accommodated within the saturation-based geometric interpretation of the SRCD framework. This is achieved without the need for new particles or additional degrees of freedom. These findings provide a stable, empirical foundation for the SRCD model as a verifiable alternative to standard interaction dynamics.

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Update Notice(ver.6.0)

I have added Supplementary Note I, Note II, Note III

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