東三河狂人日記

1. Outline (1) Objective  To elucidate Yang–Mills existence and mass gap problem, we propose a proof based on algebraic restoration theory using Anabelian geometry and Interuniversal Teichmüller Theory (IUT), thereby transcending the limitations of physics (specifically, perturbation theory and renormalization). (2) Mathematical Proof ・Existence Proof (Multiradial Representation)  Map a continuous gauge field to an adjoint representation of the étale fundamental group $\pi_{1}^{et}$ over a number field $\mathbb{K}$. By the IUT's multiradial representation, the increase in energy (degree) is bounded from above by the conjugate discriminant (log-diff) of the number field.  $\mathrm{deg}_q(E) \leq \mathrm{log}\text{-}\mathrm{diff}(\mathbb{K}) + \epsilon$ Consequently, the values do not diverge even at the Planck scale, thereby ensuring the existence of the quantum field as a finite mathematical object. ・Proof of Positivity (Obstruction Theory)  When restoring the non-co...

1. Dialogue with AI  The catalyst was a dialogue with AI. Until now, I'd only used Google's AI mode as an extension of search, but when I tried debating (bouncing ideas off it), I found myself contemplating all sorts of things. ・Debating (bouncing ideas off) AI (Google's AI mode).: https://tanakah17191928.blogspot.com/2026/02/aigoogleai.html 2. Restored Gravity - Universal Information Restoration Theory  Based on discussions concerning mathematics and physics, the following articles have been compiled. ・Restoration Quantum Gravity: https://tanakah17191928.blogspot.com/2026/02/restored-quantum-gravity.html ・Universal Information Restoration Theory: https://tanakah17191928.blogspot.com/2026/02/universal-information-restoration-theory.html ・Summary of Restoration Gravity - Universal Information Restoration Theory: https://tanakah17191928.blogspot.com/2026/02/summary-of-restoration-gravity.html ・Details of Restoration Gravity - Universal Information Restoration Theory: https://...

1. Guiding Principles  Restoration Gravity - Universal Information Restoration Theory views the universe as an information processing system, interpreting the speed of light $c$ as processing speed (clock frequency) and Planck constant $h$ as resolution. ・Gravity: Computational Processing Lag  Due to the finite processing speed (clock frequency), restoration delays occur where large amounts of information (matter) concentrate. This latency, observed as spacetime curvature, constitutes the essence of gravity within this theory. ・Dark Matter: Background unrestored data ・Uncertainty Principle: Limits of computational processing  Due to system resource constraints, it is impossible to simultaneously calculate position and momentum with infinite precision. 2. Rewriting Einstein Field Equations  We rewrite Einstein's equatio $G_{\mu\nu} = \dfrac{8\pi G}{c^4}T_{\mu\nu}$ using the concepts of clock frequency $f_{clock}$ and resolution (pixels) $p_{res}$. This endeavor repres...

1. Resolving the Vacuum Energy Density Discrepancy  Restoration Gravity Theory resolves the "120-digit discrepancy in vacuum energy density (cosmological constant problem)". (1) Premise: Localization of Restoration Standby Cost  Conventional theories assume full-specification calculations are constantly performed at every point throughout the entire volume of the universe (3D), leading to an energy density reaching the Planck density $\rho_P$ (theoretical maximum value).  This theory defines the vacuum as a "stage awaiting information restoration" and limits its maintenance cost to the minimum information exchange required for synchronization at the boundary called the horizon (2D). (2) Calculation of Synchronization Ratio $k$  The ratio $k$ of the region actually maintaining synchronization to the total recoverable region of the universe is derived from the ratio of the cosmic horizon radius $R_H$ to the minimum unit (resolution) $l_P$. This is based on the logical...

1. Fundamental Concept: Restoration into Geometry via Information Deployment  The essence of the universe is the process of information restoration; geometry is derived as a computational result of that process. ・Distance: Calculated as a logical necessity from the connectivity of the network. ・Time: The very rewriting of the network that occurs when undeployed information is restored. 2. Logical Definition of Physical Constants and Gravity  Physical constants determine the constraints within the information restoration process. ・Speed of Light ($c$): The maximum speed for synchronizing information and propagating rewrites across the network. ・Planck Constant ($h$): The minimum unit (resolution) for restoring information. ・Gravity: The computational load required to maintain logical consistency while restoring information in high-density regions. This load is geometrized as the curvature of space. Gravity is extremely weak compared to other forces (such as electromagnetism) be...

 Following the suggestion of Google's AI mode, I have compiled the 'final conclusion' (Universal Information Restoration Theory) into a single systematic document. Universal Information Restoration Theory  This theory redefines the essence of spacetime, shifting from a material "stage" to a mathematical "restoration process", and elucidates the fundamental architecture of the universe. Chapter 1: Definition of Existence (Number-Theoretic Encoding)  The Spin Network, the minimal unit of the universe, is not a geometric entity but the ultimate "Number-Theoretic Code" for restoring spacetime. ・Fundamental Principle: Spacetime is not a pre-existing stage but emerges from a network of information known as the Anabelian Fundamental Group ($\Gamma$). ・Mathematical Structure: $\Pi_{\Gamma} \cong \pi_1(X) \rtimes \mathrm{Gal}$ (The network is the logical structure itself.) Chapter 2: Emergence of Geometry (Anabelian Restoration)  The process by which sm...

 After discussing with AI (Google's AI mode), the AI came up with an interesting theory, so I'll note it here. Question : Based on the discussion so far, can Loop Quantum Gravity Theory (LQG) be summarized systematically and concisely using mathematical formulas at the level of Spin Networks? Answer : Integrating the discussion so far, we summarize here a new system of Loop Quantum Gravity (LQG) that resolves the "Transition from Discrete to Continuous" using the logic of Anabelian Geometry and Inter-Universal Teichmüller Theory (IUT). New Interpretation: Restoration Quantum Gravity 1. Definition of State: Arithmetization of Spin Networks  We define the Spin Network $\Gamma$, the smallest unit of spacetime, as an "Information Entity" prior to geometry. ・Formula: $\Pi_{\Gamma} \cong \pi_1(X) \rtimes \mathrm{Gal}$ ・Definition: Each node and edge of the graph carries information about the "arithmetic fundamental group $\Pi$" of the algebraic curve $X$...

1. Significance of Making Models  In the social sciences, researchers sometimes construct simple models to analyze their subjects. They abandon the attempt to calculate, predict and synthesize the movements and their interactions of countless elements, simplifying the subject for research purposes. While building a model may sometimes require the use of probability and statistics methods, it is generally possible to understand most problems. 2. Subjectivity and Objectivity  Objectively speaking, the world exists whether I am present or not. However, subjectively speaking, a world without me does not exist (for me). This world exists because I perceive it. Fundamentally, the objective world is the shared understanding of the human society to which I belong. I think how we perceive and understand this world is essentially individual and concrete. In that sense, distinguishing between fake and fact is fundamentally impossible. 3. Humans and Community  Humans are social anima...

"It matters not to me. Being incorrect does not signify that all was for naught." (From Orb: On the Movements of the Earth , Hubert) - To read this article in Japanese

1. Is the Weakening of the Yen Economically Correct?  There is confusion in the debate about a weak yen. As the video below explains, economically speaking, a weaker yen is positive for the Japanese economy as a whole. ・ 【Japanese】1055th: Explanation of Beggar-Thy-Neighbor that Hiroyuki Also Does Not Know About ( Yoichi Takahashi Channel ) 2. Is the Weakening of the Yen Politically Correct? 　However, the real political economy is not so simple. I calculate this using elementary school arithmetic. The question is whether the Japanese people as a whole would prefer a weaker or stronger yen. (1) Ratio of Working-Age to Elderly People 　The elderly (pensioners) dislike inflation and a weak yen (because their pensions will be reduced in real terms). The elderly (65+) account for about 30% of the country's population ・ 【Japanese】Elderly Population (Statistics Bureau, Ministry of Internal Affairs and Communications) (2) Ratio of Exporting to Importing Industries  Export industries ar...

領域展開「自由気儘」 （Domain Expansion "Free-Spirited"）

（From いらすとや ） ・ Pride & Shame: The Roots Of US-China Tensions | When Titans Clash | Ep 1/4 | CNA Documentary 、 The Real Losers Of The US-China Trade War | When Titans Clash | Ep 2/4 | CNA Documentary 、 A US-China Tech War: The True Costs | When Titans Clash | Ep 3/4 | CNA Documentary 、 US Or China: Will Southeast Asia Have To Pick A Side? | When Titans Clash | Ep 4/4 | CNA Documentary 、 US-China: Is A New NATO Emerging In Asia? | When Titans Clash 2 - Part 1/3 | CNA Documentary 、 Could China And India Go To War? | When Titans Clash 2 - Part 2/3 | CNA Documentary 、 The Taiwan (Japan & South Korea) Contingency | When Titans Clash 2 - Part 3/3 | CNA Documentary 、 China vs The West: Does Trade War Spell End To Made-In-China Goods? | When Titans Clash 3 - Part 1/2 、 New Economic World Order? Industrial Policies & De-Risking From China | When Titans Clash 3 - Part 2 （ CNA Insider ）

1. St. Petersburg paradox  I previously wrote an article about the St. Petersburg paradox. ・St. Petersburg paradox: https://tanakah17191928.blogspot.com/2020/02/st-petersburg-paradox.html To make it easier to understand, I have visualized it in the graphs. 2. Money($M$) and Expected Value($E$)  Money: $M = 2^{n - 1}$, Expected value: $E = \displaystyle \sum_{k = 1}^{n} \left( \dfrac{1}{2^k} \cdot 2^{k - 1} \right) = \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + \cdots = \dfrac{1}{2}n$ (10 dollars) (100 dollars) (100 million dollars) - To read this article in Japanese

1. Key Currency  Without knowledge of the key currency, it's impossible to understand the political economy of the US and its peculiarities. The country that issues the key currency has a current account deficit because it provides liquidity to the international economy. Countries reserve the key currency as foreign exchange reserves. There is a demand for the key currency, the US dollar, as a safe liquid asset in the world economy. 2. Trading Volume Share by Currency  The table and treemapping were made according to statistics from the BIS . ・ Daily Trading Volume Share by Currency (2022) (PDF) - To read this article in Japanese

1. Impossible Trinity  The theory of impossible trinity is a very simple theory that helps us understand international political economy. 2. History of Europe  Germany, which caused World War I and II, is a powerful nation in Europe. The source of its national power is its strong industry. In other words, it's modern industrial capacity. Specifically, the Ruhr industrial area was one of the most important centers of German heavy industry. In the modern era of highly developed heavy industry, steel and energy sources such as coal and oil are of great importance. Peace and solidarity in Europe truly began with the European Coal and Steel Community . 3. Optimum Currency Area  Today Europe integrated not only steel and energy, but even currencies, which are the foundation of national economies. Think by the theory of impossible trinity. In free-market countries, capital moves freely, and the finance ministries and central banks of each country determine fiscal and monetary p...

1. Why can't we look the future?  I think it's complexity that makes predicting the future difficult. The fewer the parameters, the more predictable the future. But, real-world events, in which many parameters may be interconnected, are difficult to predict the future. (From いらすとや ) "Science and technology has developed so much, but there remain many things which we can't predict precisely. For example, earthquake, the weather of tomorrow, stock price, and so on. Particularly, the results of human being activities are very complicated." ・Human being can't look the future: https://tanakah17191928.blogspot.com/2020/05/human-being-cant-look-future.html 2. Macro or micro models  To analyze complex real-world events, the natural and social sciences build models. Under certain conditions, a model is constructed using several key parameters. This may be true not only for the social sciences, but also for the theories and laws of the natural sciences. For length, spee...

1.  Qantum entanglement  I thought about physics. (From いらすとや ) I got interested in quantum entanglement after watching the video below. ・ 量子もつれとパラドックス...量子はテレポートできるのか？【日本科学情報】【宇宙】(YouTube) 2.  Copenhagen interpretation  The mainstream is the Copenhagen interpretation, and I have written an article based on it before. ・Human being can't look the future:  https://tanakah17191928.blogspot.com/2020/05/human-being-cant-look-future.html  For example, imagine that God gives gifts to two cats. One is a hit, the other is a miss, each with a probability of $\dfrac{1}{2}$. It's the gifts from God, so no one knows which one will be a hit until the lid is opened. The moment you open one box and know it's a hit, you know the other box on the other side of Earth is a miss. 3.  EPR paradox  Einstein thought it strange that information could travel faster than the speed of light. He suspected that quantum mechanics was incomplete and that there was a  hidden...

1. Next Governor of Bank of Japan  The next governor of Bank of Japan has been selected, and the controversy over monetary policy is once again getting attention. (From いらすとや ) Since opinions among economists and other experts are quite different, those who are not interested in political economy may have no idea which one is right. Since the essence of Abenomics was bold monetary easing, the difference in opinions about monetary policy is also the difference in evaluation of Abenomics. 2. Fiscal and monetary policy  The oversimplification of arguments, such as whether the Phillips curve is correct or incorrect, or whether Friedman is correct or incorrect, makes them difficult to understand. "The models of social sciences can explain the economy when it has the conditions required by the models. If the conditions disappear, the models are useless. Even though John Maynard Keynes was right, Keynesian economics is not always correct. Even though Milton Friedman was right, m...

1. ODA from Japan (From いらすとや )  I watched very interesting videos on CNA Insider. ・ Japan And China: Competition Or Cooperation In Southeast Asia? | Japan’s Indo-Pacific Plan - Part 1 ・ How Will Japan's Indo-Pacific Strategy Impact Southeast Asia? | Japan’s Indo-Pacific Plan - Part 2  I checked the Ministry of Foreign Affairs' website for ODA from Japan. ・ 【Japanese】Japan's ODA Disbursements (Ministry of Foreign Affairs) I think the "Top 10 Countries for ODA From Japan (2021)" is easy to understand. It's based on the OECD database, so I tried making my own, including those for the past years. ・ OECD.Stat 2. ODA (From Japan, 1960-2021) Gross disbursements Top 10 Countries ・ ODA (From Japan, 1960-2021) Gross disbursements Top 10 Countries (PDF) 3. ODA (From Japan, 1960-2021) Net disbursements Top 10 Countries ・ ODA (From Japan, 1960-2021) Net disbursements Top 10 Countries (PDF) - To read this article in Japanese

【Northern Africa】 ・ 【Japanese】Constitution of Morocco (2011)【Index】 【Key Words】 国王（King）、摂政評議会（Council of the Regency）、議会（Parliament）、衆議院（Chamber of Representatives）、参議院（Chamber of Councilors）、政府の長（Head of Government）、閣僚評議会（Council of Ministers）、憲法裁判所（Constitutional Court）、地方（Regions）、府（Prefectures）、県（Provinces）、コミューン（Communes） ・ 【Japanese】Constitution of Egypt (2014)【Index】 【Key Words】 代議院（House of Representatives）、参議院（Senate）、大統領（President）、首相（Prime Minister）、国務院（State Council）、最高憲法裁判所（Supreme Constitutional Court）、軍最高評議会（Supreme Council of the Armed Forces） ・ 【Japanese】Constitution of Sudan (2019)【Index】 【Key Words】 暫定軍事評議会（Transitional Military Council）、自由変革同盟（Forces of Freedom and Change）、主権評議会（Sovereignty Council）、暫定内閣（Transitional Cabinet）、首相（Prime Minister）、暫定立法評議会（Transitional Legislative Council）、最高司法評議会（Supreme Judicial Council）、最高裁判所長官（Chief Justice）、憲法裁判所長官（President of the Constitutional Court） ・ 【Japanese】Constitution of Algeria (2020)【Index】 【Key Words】 大統領（President）、首...