What question did this study set out to answer?

Derive the dimensionless fine-structure constant (alpha^-1 ≈ 137.035999) from pure first-principles geometry within the framework of Helical Holographic Quantum Mechanics (H3QM).

August 16, 2026Open Access

Pure Geometric First-Principles Derivation of the Fine-Structure Constant alpha^-1 ≈ 137. 035999 via 3D Holographic Topology and the 2^-24 Machine Epsilon Theorem

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CCChou Cosmo

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Overview

Theoretical analysis demonstrates exact geometric derivation of the fine-structure constant in electromagnetic theory, indicating fundamental physical constants emerge from topological packing...

Key Points

Derive the dimensionless fine-structure constant (alpha^-1 ≈ 137.035999) from pure first-principles geometry within the framework of Helical Holographic Quantum Mechanics (H3QM).
Formulated an analytical limit polynomial utilizing 3D maximum contact packing geometry (kissing number K = 12) and closed topological phase winding constraints.
Integrated 3D Kakeya Fourier restriction theorems (spatial pruning factor kappa = 2^-3), random tensor operator damping, and L1 Topological Attention Residuals into an 8-step dynamic convergence model.
Yielded an initial analytical baseline of alpha^-1_(0) = 4pi^3 + pi^2 + pi ≈ 137.036303, achieving 99.99977% agreement with experimental measurements.
Achieved exact convergence to the CODATA recommended value of 137.035999 within 8 dynamic steps, with a residual of 5.96 x 10^-7 saturating the IEEE 754 float32 machine epsilon (2^-24) and reaching exact zero residual under fixed-point integer sign-operator arithmetic.

Cite This Study

Chou Cosmo (2026) studied this question.

synapsesocial.com/papers/6a817a72f2fb91fc834ae440 https://doi.org/10.5281/zenodo.21947797

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August 16, 2026Open Access

Pure Geometric First-Principles Derivation of the Fine-Structure Constant alpha^-1 ≈ 137. 035999 via 3D Holographic Topology and the 2^-24 Machine Epsilon Theorem

View Full Paper

Ask AI

Bookmark

Authors

CCChou Cosmo

Discussion

Member takes

Overview

Theoretical analysis demonstrates exact geometric derivation of the fine-structure constant in electromagnetic theory, indicating fundamental physical constants emerge from topological packing...

Key Points

Derive the dimensionless fine-structure constant (alpha^-1 ≈ 137.035999) from pure first-principles geometry within the framework of Helical Holographic Quantum Mechanics (H3QM).
Formulated an analytical limit polynomial utilizing 3D maximum contact packing geometry (kissing number K = 12) and closed topological phase winding constraints.
Integrated 3D Kakeya Fourier restriction theorems (spatial pruning factor kappa = 2^-3), random tensor operator damping, and L1 Topological Attention Residuals into an 8-step dynamic convergence model.
Yielded an initial analytical baseline of alpha^-1_(0) = 4pi^3 + pi^2 + pi ≈ 137.036303, achieving 99.99977% agreement with experimental measurements.
Achieved exact convergence to the CODATA recommended value of 137.035999 within 8 dynamic steps, with a residual of 5.96 x 10^-7 saturating the IEEE 754 float32 machine epsilon (2^-24) and reaching exact zero residual under fixed-point integer sign-operator arithmetic.

Cite This Study

Chou Cosmo (2026) studied this question.

synapsesocial.com/papers/6a817a72f2fb91fc834ae440 https://doi.org/10.5281/zenodo.21947797

View Full Paper

Ask AI

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