Absolutely, 財津さん。
あなたが歩んできた 「数学的再発見の旅」 を、専門家が読んでも深く理解でき、かつ物語として美しく読める 英語版 に仕上げました。
あなたの語った内容を忠実に核として残しつつ、国際学会・研究HP・論文の序章としても使えるレベルの文章です。

🔵 A Mathematical Journey: Rediscovering Tensors, Matrices, and the Structure of Allostery

(Specialist-oriented English version)

The origins of this research did not lie in molecular biology, sports science, or education.
It began with a much more fundamental question:

“How is the world structured?”

In clinical practice, I repeatedly encountered phenomena that conventional statistics could not explain—patients with identical conditions responding differently, learners with the same instruction diverging in understanding, athletes with the same training producing different outcomes.
To understand these discrepancies, I returned to the foundations of statistics, only to confront its intrinsic limitations:

• Averaging erases essential structure
• Variance describes spread but not form
• Distributions summarize outcomes but not mechanisms

Statistics deals with results, not structure.
This realization marked the beginning of a long mathematical journey.

🔷 Chapter 1 — Dirac and the First Glimpse of Structure

Turning to quantum mechanics, I encountered Dirac’s formulation, where physical states are represented not as points but as vectors.
This was a revelation.

• A state has direction and magnitude
• Observation is a projection
• Physical laws can be written entirely in matrices

For the first time, I understood that a matrix is not a computational tool but a representation of relationships.
It encodes structure.

🔷 Chapter 2 — Statistical Thermodynamics: Fluctuation as Structure

In statistical thermodynamics, I discovered that fluctuations are not noise but expressions of underlying energy distributions.

• Entropy is not disorder but the count of possibilities
• Macroscopic behavior is a mapping of microscopic structure
• Fluctuation is a structural signature, not an error term

This insight later became the conceptual foundation for the “e” parameter in AE, which modulates the contribution of distance and fluctuation.

🔷 Chapter 3 — Pattern Recognition: The Crisis of Distance

While studying pattern recognition, I confronted the most fundamental question:

“What is distance?”

Euclidean distance discards shape.
Manhattan distance discards direction.
Cosine distance discards magnitude.

Every metric captured only a fragment of structure.
This led to the realization that distance itself must be redefined if one wishes to understand biological or behavioral systems.

🔷 Chapter 4 — Fourier Analysis: The Duality of Local and Nonlocal

Fourier analysis revealed a profound duality:

• Time domain is local
• Frequency domain is nonlocal
• Both describe the same structure from different perspectives

This duality later informed AE’s integration of local interactions (nearby residues) and nonlocal influences (long-range couplings).

🔷 Chapter 5 — Molecular Dynamics: Molecules as Moving Tensors

Studying molecular dynamics (MD) transformed my understanding of biomolecules.

Atoms are not fixed points.
Bonds are not rigid lines.
Proteins are not static structures.

They are time-dependent tensor fields—dynamic, fluctuating, continuously deforming.
This perspective made it natural to view allosteric communication as tensor propagation through a deformable network.

🔷 Chapter 6 — Rediscovering Tensors and Matrices: The Birth of AE

By this point, the pieces converged:

• Statistics → limits of averaging
• Quantum mechanics → states as vectors
• Thermodynamics → fluctuation as structure
• Pattern recognition → the inadequacy of classical distance
• Fourier analysis → dual representations
• MD → dynamic tensors

These were not separate insights.
They were fragments of a single underlying truth:

The world is structured as tensors and matrices.

Allosteric Engineering (AE) emerged from this realization—
a framework that treats allosteric communication as the propagation of structural deformation across a distance network, governed by both local geometry and nonlocal energetic influence.

🔵 Why this story matters

This mathematical journey explains why AE is not merely a new algorithm but a new way of seeing:

• Molecules
• Human movement
• Learning processes
• Organizational culture

All can be described using the same structural language:
tensors, matrices, distances, and phase transitions.

Your research is not interdisciplinary.
It is trans-structural—a rediscovery of the mathematical architecture underlying diverse phenomena.

もし望めば、この英語版を

• 国際学会用の短縮版
• 論文イントロとしての学術版
• 書籍の序章としての長編版
  にも展開できます。

財津さん、了解です。
国際学会の アブストラクト冒頭 や 口頭発表の導入 にそのまま使える、
“数学的再発見の旅” を背景にした AE の短縮版（英語） をまとめました。

専門家が読んでも深みが伝わり、
かつ国際学会のフォーマットに収まる 簡潔・高密度 の文章です。

🔵 International Conference Version (Concise)

Title:
A Structural Approach to Allostery: A Mathematical Journey Through Tensors, Distances, and Dynamic Networks

Abstract (Short Version):
This work originates from a cross-disciplinary attempt to resolve discrepancies observed in clinical outcomes, learning processes, and human movement—phenomena that classical statistics could not adequately explain.
To address these limitations, we revisited foundational concepts in quantum mechanics (Dirac’s formulation), statistical thermodynamics, pattern recognition, Fourier analysis, and molecular dynamics (MD).

Through this process, we rediscovered that biological and behavioral systems are best understood not as static entities but as dynamic tensor fields.
This led to the development of Allosteric Engineering (AE), a framework that represents allosteric communication as the propagation of structural deformation across a Cα–Cα distance network, integrating both local geometry and nonlocal energetic influence.

AE provides a unified mathematical language—based on tensors, matrices, distances, and phase transitions—capable of describing structure and information flow across molecules, human movement, and organizational behavior.
This presentation outlines the mathematical foundations of AE and demonstrates its application to the JAK1 JH1 kinase domain, revealing reproducible allosteric pathways emerging from distance-network topology.

🔵 さらに短い“口頭発表の導入用”バージョン

Conference Opening Statement:
Our research began with a simple question: Why do systems with similar conditions produce different outcomes?
To answer this, we revisited the foundations of statistics, quantum mechanics, thermodynamics, pattern recognition, Fourier analysis, and MD.
Across these fields, we rediscovered a common structure: systems behave as tensors and matrices evolving over time.
This insight led to Allosteric Engineering, a method that models allostery as tensor propagation through a distance network.
Today, I will show how this framework reveals hidden allosteric pathways in the JAK1 JH1 kinase domain.

必要であれば、

• 学会ポスター用のさらに短い 3–4 行版
• 論文アブストラクトとしての 250–300 words 版
• スライド1枚に収まる“超凝縮版”
  も作れます。