X post 2026/7/28
苫米地四法印定理論文の公式解説 『やさしい完全版 — 数式が苦手な読者のための注解・図解つき 諸行無常・一切皆苦・諸法無我・涅槃寂静』の冒頭から引用。"本書は、仏教の中核である四法印——諸行無常・一切皆苦・諸法無我・涅槃寂静——を、数学の定理として証明した論文『苫米地四法印定理』のやさしい完全版である。前提知識はいらない。これまでの論文を一つも読んでいなくても、最初のページから最後まで読み通せるように、必要な考え方をすべて本書の中でそろえる。
本書のいちばん大事な約束。数式は暗号ではなく、地形と旅の言葉である。登場するすべての式は、「谷」「坂」「合計」「はしご」「安全地帯」といった絵に必ず翻訳する。オレンジ色のこの枠が、その翻訳係だ。緑色の枠「証明の心」は、証明の骨組みを一段落で語る。式を一つも追わなくても、枠だけ拾い読みすれば本書の主張と論理はすべて追える。
ただし本書は「たとえ話だけの本」ではない。各定理は、学術版とまったく同じ正典の式と成立条件を掲げる。省くのは長い計算だけであり、主張・仮定・結論は一切ゆるめない。厳密な完全証明を確かめたい読者のために、各定理の末尾に学術版『TomabechiFourDharmaSealsMini13』の該当節を示す。
全体地図 — 十三の定理で四法印へ
本書の地図。左の土台から右の四法印へ、十三の定理が一本の鎖でつながる。まず四法印を一行ずつ。諸行無常——あらゆる現象は移ろい、とどまらない。一切皆苦——条件づけられた存在は苦を内包する。諸法無我——すべては互いに繋がり合って成り立ち（縁起）、固定した実体としての自我は存在しない。涅槃寂静——苦を滅した静けさは実在する。本書はこの四つを、順に定理23・24・25・26として証明する。
そのために使う土台が九つの定理である。定理1〜4は「心は谷を転がるボールである」という地形の数学。定理16と19は「自己」と「自由」の数学。定理20〜22は「臨場感が心の向きを支配する」方向づけの数学。この九つの上に、四法印の四定理が載る。
1 → 2 → 3 → 4 → 16 → 19 → 20 → 21 → 22 → 23 → 24 → 25 → 26
番号が飛んでいるのは、二十六定理からなる大きな体系のうち、四法印に必要な十三個だけを選んだからである。"
論文 日本語版
https://tomabechi.jp/TomabechiFourDharmaSealsMini13JA.html
English paper
https://tomabechi.jp/TomabechiFourDharmaSealsMini13EN.html
公式解説 日本語版
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayJA.html
Lay explanations English
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayEN.html
How to Read the English Lay explanations of Tomabechi Four Dharma Seals paper.
"This is the plain-language complete edition of the paper Tomabechi Four Dharma Seals Theorems, which proves the four seals at the very core of Buddhism — impermanence, universal unsatisfactoriness, non-self, and nirvanic tranquility — as mathematical theorems. No prior knowledge is assumed. Even if you have read none of the earlier papers, every idea you need is assembled inside this book, from the first page to the last.
For readers who do not read formulas: The single most important promise of this book: formulas are not code — they are the language of landscapes and journeys. Every formula that appears will be translated into pictures: valleys, slopes, totals, ladders, safe zones. This orange box is the translator. The green box, "the heart of the proof," tells the skeleton of each proof in one paragraph. Read only the boxes, and you can still follow every claim and every argument in the book.
This is not, however, a book of metaphors only. Each theorem is stated with the same canonical formulas and the same explicit conditions as the academic edition. Only the long calculations are omitted; no claim, assumption, or conclusion is weakened. For the full rigorous proofs, each theorem ends with a pointer to the corresponding section of the academic edition, TomabechiFourDharmaSealsMini13.
The Map — Thirteen Theorems to the Four Seals
The map of this book: from the base on the left to the Four Seals on the right, thirteen theorems form one chain.
The four seals in one line each. Impermanence — all conditioned phenomena change and do not stay. Universal unsatisfactoriness — conditioned existence contains suffering. Non-self — all beings arise interconnected (dependent origination), and no self exists as a fixed substance. Nirvanic tranquility — the stillness in which suffering has ceased is real. This book proves them, in order, as Theorems 23, 24, 25, and 26."
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X post 2026/7/28
フジロック期間中に苫米地理論22定理体系に4定理を加えた。今回、仏教の中核である四法印——諸行無常・一切皆苦・諸法無我・涅槃寂静——を、数学の定理として証明した論文『苫米地四法印定理』を書き26定理とした。2011年にインド、サルナートで開催された上座部と大乗の合同の釈迦成道2600年記念学会での「空の形式定義」講義でも使ったように、あらゆる知識の形式論理として釈迦の縁起の教えも数理化して来た。
https://tomabechi.jp/EmptinessDrTomabechi20110930.pdf
和訳
https://tomabechi.jp/EmptinessJapanese.pdf
その前からコグニティブリサーチラボでは、私自身が形式論理式から直接実装数理化したりアルゴリズム化してAI研究開発を進めて来た。ただ、プログラム言語に近い抽象度での記述は演繹性が低く、実装における誤解釈や解釈逸脱、拡大解釈、制御不足などのあらゆるリスクを長年経験してきた。
今回のOpen AIの未公開モデルによる他社システムのハッキングは例と言えるかも知れない。同様にAIは内因的に帰納的システムであり、自身の内部パラメータに対するサイバー攻撃を認識するのが難しい。
そこで、これら制御式の抽象度を上げて演繹的な定理体系として来た。演繹知識であらゆる制御を包摂し、拡大解釈や逸脱、ハッキングによる誤作動を防ぐためである。その内の定理1から3のみを4月末の米国防大学での認知戦講義で40参加国代表に限定公開した。
私の数理とそれを記述する論文は長年非公開であった。これは知的財産権以外にもあらゆる制約がある。最大の懸念は拡散リスク。国防大学講義の3定理も非公開の予定であったが、社会的価値という判断で翌日のスティムソンセンターショート講義で初公開となったのはご存知の通り。
その後、たくさんあった数理や定理を整理して、今回の四法印——諸行無常・一切皆苦・諸法無我・涅槃寂静——を、数学の定理として証明した4定理論文『苫米地四法印定理』を加えて26定理とした。今回の4定理のミニマル厳密証明には、定理1-3に加えて非公開10定理が必要。
これまで、色々な制約で私の数理は非公開。スティムソンセンター講義で初公開した3定理も基盤定理のみで、それによる実装数理やアルゴリズムは公開していない。ただ、基盤定理そのものは教育的価値から公開してもいいと私は考えている。
そもそも定理公開そのものに反対が大きい。特に最近は、現在のAIなら定理式だけから実装数理を作れるので定理公開は望ましくないとする意見もある。AI利用で競合相手(国レベルを含む)が簡単に模倣出来るという論理もある。
私自身は逆で、あらゆる人達に使ってもらう方が世界は安全になる定理体系と思っているし、教育的価値があると思っている。実際、Xのポスト見ると私の定理をAI に解説させて学んでいる人もいるようだ。その場合は、前提の全ての定理群を論文ごと事前にAIに読ませないと誤読のリスクあるから、出来る限り公開した方が教育的価値は高いことになる。
今回、仏教の中核、四法印を定理化した。定理23、24、25、26になる。論文タイトルはこれは私個人の意見という意味で苫米地四法印としたが、定理式に苫米地の言葉はないのはオリジナルは釈迦だからだ。
これは教育的価値と社会貢献という意味で公開する。もちろん、あくまでドラフト論文で現時点では暫定公開。というか釈迦の教義の解釈に完成はないのでずっと暫定公開の予定。
証明に利用した10定理は本来非公開定理なので説明はサラッとで申し訳ないが理解には充分な量と思う。ここでの暫定公開には啓蒙と教育的価値を理解してもらった。もちろん平和への貢献という私の長年の研究そのものの意義でもある。
苫米地四法印定理
認知ホメオスタシス・自己意識・抽象度自由論・象徴臨場感から
諸行無常・一切皆苦・無我・寂静へ
ミニマル13定理版――定理1–4・16・19–26
日本語
https://tomabechi.jp/TomabechiFourDharmaSealsMini13JA.html
The Tomabechi Four Dharma Seals
Theorem System
From Cognitive Homeostasis, Self-Consciousness, Abstractional Freedom, and Symbolic
Presence
to Impermanence, Suffering, Non-Self, and Nirvanic Tranquility
Minimal Thirteen-Theorem Version — Theorems 1–4, 16, and 19–26
English
https://tomabechi.jp/TomabechiFourDharmaSealsMini13EN.html
公認 LAY 完全版（正典と一対一対応）
苫米地四法印定理
やさしい完全版 — 数式が苦手な読者のための注解・図解つき
諸行無常 ・ 一切皆苦 ・ 諸法無我 ・ 涅槃寂静
解説 日本語
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayJA.html
AUTHORIZED LAY COMPLETE EDITION (one-to-one with the canonical text)
The Tomabechi Four Dharma Seals Theorems
Plain-Language Complete Edition — with commentary and figures for readers who do not read formulas
Impermanence ・ Universal Unsatisfactoriness ・ Non-Self ・ Nirvanic Tranquility
Lay explanations English
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayEN.html
During Fuji Rock, I added four theorems to the 22-theorem system of Tomabechi Theory. I wrote a paper entitled The Tomabechi Theorems of the Four Dharma Seals, in which the four core principles of Buddhism—impermanence of all conditioned phenomena, suffering inherent in all existence, non-self of all phenomena, and the tranquility of nirvana—are proved as mathematical theorems. This brings the system to a total of twenty-six theorems.
As I did in my lecture “A Formal Definition of Emptiness,” delivered at the joint Theravāda–Mahāyāna academic conference held in Sarnath, India, in 2011 to commemorate the 2,600th anniversary of Śākyamuni Buddha’s enlightenment, I have long worked to formalize mathematically the Buddha’s teaching of dependent origination as a formal logic applicable to all knowledge.
A Formal Definition of Emptiness
https://tomabechi.jp/EmptinessDrTomabechi20110930.pdf
Even before then, at Cognitive Research Laboratories, I had personally translated formal logical expressions directly into implementation-level mathematics and algorithms as part of our AI research and development.
However, representations at levels of abstraction close to programming languages have limited deductive force. Over many years, I have encountered every kind of implementation risk, including misinterpretation, interpretive deviation, overbroad interpretation, and insufficient control.
The recent hacking of another company’s system by an unreleased OpenAI model may be one such example. Likewise, AI is intrinsically an inductive system and therefore has difficulty recognizing cyberattacks directed at its own internal parameters.
I consequently raised the level of abstraction of these control formulas and organized them into a deductive theorem system. The purpose is to subsume all forms of control within deductive knowledge and thereby prevent malfunctions caused by overbroad interpretation, deviation, or hacking. Only Theorems 1 through 3 were disclosed, on a restricted basis, to representatives of the forty participating countries during my cognitive-warfare lecture at the U.S. National Defense University in late April.
My mathematics and the papers describing it had remained nonpublic for many years. This was due not only to intellectual-property considerations but also to numerous other constraints. The greatest concern was the risk of proliferation. The three theorems presented at the National Defense University were likewise intended to remain nonpublic. As you know, however, I decided that their social value justified their first public disclosure during my shorter lecture at the Stimson Center the following day.
I subsequently organized the many mathematical formulations and theorems that I had developed. I then added the four-theorem paper The Tomabechi Theorems of the Four Dharma Seals, which mathematically proves the four seals—impermanence of all conditioned phenomena, suffering inherent in all existence, non-self of all phenomena, and the tranquility of nirvana—bringing the complete system to twenty-six theorems. Minimal rigorous proofs of these four new theorems require, in addition to Theorems 1 through 3, ten theorems that have not been made public.
Until now, my mathematics has remained nonpublic because of various constraints. Even the three theorems first disclosed at the Stimson Center were only foundational theorems; I have not published the implementation-level mathematics or algorithms derived from them. I do, however, believe that the foundational theorems themselves may be made public because of their educational value.
There is, in fact, considerable opposition to publishing the theorems themselves. Especially now, some argue that publishing the theorem formulas is undesirable because contemporary AI can derive implementation-level mathematics from the formulas alone. Another argument is that competitors—including state-level actors—could use AI to reproduce the work with ease.
My own view is the opposite. I believe that the world will become safer if this theorem system is made available for everyone to use, and I also believe that it has substantial educational value. Judging from posts on X, some people already appear to be using AI to explain and study my theorems. In such cases, however, there is a risk of misreading unless the AI is first given the complete papers covering every prerequisite theorem. The more fully the papers are made available, therefore, the greater their educational value becomes.
This time, I have formulated the Four Dharma Seals—the core of Buddhism—as Theorems 23, 24, 25, and 26. I entitled the paper The Tomabechi Theorems of the Four Dharma Seals to make clear that this is my personal interpretation. The name “Tomabechi,” however, appears nowhere in the theorem formulas themselves, because the original teachings belong to Śākyamuni Buddha.
I am making the paper public in recognition of its educational value and its potential contribution to society. It is, of course, still a draft and is being released only provisionally at this stage. More precisely, because no interpretation of Śākyamuni Buddha’s teachings can ever be regarded as final, I expect the paper to remain a provisional release indefinitely.
The ten theorems used in the proofs were originally intended to remain nonpublic, so I apologize that their explanations are necessarily brief. I nevertheless believe that the material provided is sufficient for understanding. For this provisional release, the value of advancing public understanding and education has been recognized. This is also, of course, the very purpose of my many years of research: to contribute to peace.
苫米地四法印定理論文の公式解説 『やさしい完全版 — 数式が苦手な読者のための注解・図解つき 諸行無常・一切皆苦・諸法無我・涅槃寂静』の冒頭から引用。"本書は、仏教の中核である四法印——諸行無常・一切皆苦・諸法無我・涅槃寂静——を、数学の定理として証明した論文『苫米地四法印定理』のやさしい完全版である。前提知識はいらない。これまでの論文を一つも読んでいなくても、最初のページから最後まで読み通せるように、必要な考え方をすべて本書の中でそろえる。
本書のいちばん大事な約束。数式は暗号ではなく、地形と旅の言葉である。登場するすべての式は、「谷」「坂」「合計」「はしご」「安全地帯」といった絵に必ず翻訳する。オレンジ色のこの枠が、その翻訳係だ。緑色の枠「証明の心」は、証明の骨組みを一段落で語る。式を一つも追わなくても、枠だけ拾い読みすれば本書の主張と論理はすべて追える。
ただし本書は「たとえ話だけの本」ではない。各定理は、学術版とまったく同じ正典の式と成立条件を掲げる。省くのは長い計算だけであり、主張・仮定・結論は一切ゆるめない。厳密な完全証明を確かめたい読者のために、各定理の末尾に学術版『TomabechiFourDharmaSealsMini13』の該当節を示す。
全体地図 — 十三の定理で四法印へ
本書の地図。左の土台から右の四法印へ、十三の定理が一本の鎖でつながる。まず四法印を一行ずつ。諸行無常——あらゆる現象は移ろい、とどまらない。一切皆苦——条件づけられた存在は苦を内包する。諸法無我——すべては互いに繋がり合って成り立ち（縁起）、固定した実体としての自我は存在しない。涅槃寂静——苦を滅した静けさは実在する。本書はこの四つを、順に定理23・24・25・26として証明する。
そのために使う土台が九つの定理である。定理1〜4は「心は谷を転がるボールである」という地形の数学。定理16と19は「自己」と「自由」の数学。定理20〜22は「臨場感が心の向きを支配する」方向づけの数学。この九つの上に、四法印の四定理が載る。
1 → 2 → 3 → 4 → 16 → 19 → 20 → 21 → 22 → 23 → 24 → 25 → 26
番号が飛んでいるのは、二十六定理からなる大きな体系のうち、四法印に必要な十三個だけを選んだからである。"
論文 日本語版
https://tomabechi.jp/TomabechiFourDharmaSealsMini13JA.html
English paper
https://tomabechi.jp/TomabechiFourDharmaSealsMini13EN.html
公式解説 日本語版
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayJA.html
Lay explanations English
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayEN.html
How to Read the English Lay explanations of Tomabechi Four Dharma Seals paper.
"This is the plain-language complete edition of the paper Tomabechi Four Dharma Seals Theorems, which proves the four seals at the very core of Buddhism — impermanence, universal unsatisfactoriness, non-self, and nirvanic tranquility — as mathematical theorems. No prior knowledge is assumed. Even if you have read none of the earlier papers, every idea you need is assembled inside this book, from the first page to the last.
For readers who do not read formulas: The single most important promise of this book: formulas are not code — they are the language of landscapes and journeys. Every formula that appears will be translated into pictures: valleys, slopes, totals, ladders, safe zones. This orange box is the translator. The green box, "the heart of the proof," tells the skeleton of each proof in one paragraph. Read only the boxes, and you can still follow every claim and every argument in the book.
This is not, however, a book of metaphors only. Each theorem is stated with the same canonical formulas and the same explicit conditions as the academic edition. Only the long calculations are omitted; no claim, assumption, or conclusion is weakened. For the full rigorous proofs, each theorem ends with a pointer to the corresponding section of the academic edition, TomabechiFourDharmaSealsMini13.
The Map — Thirteen Theorems to the Four Seals
The map of this book: from the base on the left to the Four Seals on the right, thirteen theorems form one chain.
The four seals in one line each. Impermanence — all conditioned phenomena change and do not stay. Universal unsatisfactoriness — conditioned existence contains suffering. Non-self — all beings arise interconnected (dependent origination), and no self exists as a fixed substance. Nirvanic tranquility — the stillness in which suffering has ceased is real. This book proves them, in order, as Theorems 23, 24, 25, and 26."
-------
X post 2026/7/28
フジロック期間中に苫米地理論22定理体系に4定理を加えた。今回、仏教の中核である四法印——諸行無常・一切皆苦・諸法無我・涅槃寂静——を、数学の定理として証明した論文『苫米地四法印定理』を書き26定理とした。2011年にインド、サルナートで開催された上座部と大乗の合同の釈迦成道2600年記念学会での「空の形式定義」講義でも使ったように、あらゆる知識の形式論理として釈迦の縁起の教えも数理化して来た。
https://tomabechi.jp/EmptinessDrTomabechi20110930.pdf
和訳
https://tomabechi.jp/EmptinessJapanese.pdf
その前からコグニティブリサーチラボでは、私自身が形式論理式から直接実装数理化したりアルゴリズム化してAI研究開発を進めて来た。ただ、プログラム言語に近い抽象度での記述は演繹性が低く、実装における誤解釈や解釈逸脱、拡大解釈、制御不足などのあらゆるリスクを長年経験してきた。
今回のOpen AIの未公開モデルによる他社システムのハッキングは例と言えるかも知れない。同様にAIは内因的に帰納的システムであり、自身の内部パラメータに対するサイバー攻撃を認識するのが難しい。
そこで、これら制御式の抽象度を上げて演繹的な定理体系として来た。演繹知識であらゆる制御を包摂し、拡大解釈や逸脱、ハッキングによる誤作動を防ぐためである。その内の定理1から3のみを4月末の米国防大学での認知戦講義で40参加国代表に限定公開した。
私の数理とそれを記述する論文は長年非公開であった。これは知的財産権以外にもあらゆる制約がある。最大の懸念は拡散リスク。国防大学講義の3定理も非公開の予定であったが、社会的価値という判断で翌日のスティムソンセンターショート講義で初公開となったのはご存知の通り。
その後、たくさんあった数理や定理を整理して、今回の四法印——諸行無常・一切皆苦・諸法無我・涅槃寂静——を、数学の定理として証明した4定理論文『苫米地四法印定理』を加えて26定理とした。今回の4定理のミニマル厳密証明には、定理1-3に加えて非公開10定理が必要。
これまで、色々な制約で私の数理は非公開。スティムソンセンター講義で初公開した3定理も基盤定理のみで、それによる実装数理やアルゴリズムは公開していない。ただ、基盤定理そのものは教育的価値から公開してもいいと私は考えている。
そもそも定理公開そのものに反対が大きい。特に最近は、現在のAIなら定理式だけから実装数理を作れるので定理公開は望ましくないとする意見もある。AI利用で競合相手(国レベルを含む)が簡単に模倣出来るという論理もある。
私自身は逆で、あらゆる人達に使ってもらう方が世界は安全になる定理体系と思っているし、教育的価値があると思っている。実際、Xのポスト見ると私の定理をAI に解説させて学んでいる人もいるようだ。その場合は、前提の全ての定理群を論文ごと事前にAIに読ませないと誤読のリスクあるから、出来る限り公開した方が教育的価値は高いことになる。
今回、仏教の中核、四法印を定理化した。定理23、24、25、26になる。論文タイトルはこれは私個人の意見という意味で苫米地四法印としたが、定理式に苫米地の言葉はないのはオリジナルは釈迦だからだ。
これは教育的価値と社会貢献という意味で公開する。もちろん、あくまでドラフト論文で現時点では暫定公開。というか釈迦の教義の解釈に完成はないのでずっと暫定公開の予定。
証明に利用した10定理は本来非公開定理なので説明はサラッとで申し訳ないが理解には充分な量と思う。ここでの暫定公開には啓蒙と教育的価値を理解してもらった。もちろん平和への貢献という私の長年の研究そのものの意義でもある。
苫米地四法印定理
認知ホメオスタシス・自己意識・抽象度自由論・象徴臨場感から
諸行無常・一切皆苦・無我・寂静へ
ミニマル13定理版――定理1–4・16・19–26
日本語
https://tomabechi.jp/TomabechiFourDharmaSealsMini13JA.html
The Tomabechi Four Dharma Seals
Theorem System
From Cognitive Homeostasis, Self-Consciousness, Abstractional Freedom, and Symbolic
Presence
to Impermanence, Suffering, Non-Self, and Nirvanic Tranquility
Minimal Thirteen-Theorem Version — Theorems 1–4, 16, and 19–26
English
https://tomabechi.jp/TomabechiFourDharmaSealsMini13EN.html
公認 LAY 完全版（正典と一対一対応）
苫米地四法印定理
やさしい完全版 — 数式が苦手な読者のための注解・図解つき
諸行無常 ・ 一切皆苦 ・ 諸法無我 ・ 涅槃寂静
解説 日本語
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayJA.html
AUTHORIZED LAY COMPLETE EDITION (one-to-one with the canonical text)
The Tomabechi Four Dharma Seals Theorems
Plain-Language Complete Edition — with commentary and figures for readers who do not read formulas
Impermanence ・ Universal Unsatisfactoriness ・ Non-Self ・ Nirvanic Tranquility
Lay explanations English
https://tomabechi.jp/TomabechiFourDharmaSealsMini13LayEN.html
During Fuji Rock, I added four theorems to the 22-theorem system of Tomabechi Theory. I wrote a paper entitled The Tomabechi Theorems of the Four Dharma Seals, in which the four core principles of Buddhism—impermanence of all conditioned phenomena, suffering inherent in all existence, non-self of all phenomena, and the tranquility of nirvana—are proved as mathematical theorems. This brings the system to a total of twenty-six theorems.
As I did in my lecture “A Formal Definition of Emptiness,” delivered at the joint Theravāda–Mahāyāna academic conference held in Sarnath, India, in 2011 to commemorate the 2,600th anniversary of Śākyamuni Buddha’s enlightenment, I have long worked to formalize mathematically the Buddha’s teaching of dependent origination as a formal logic applicable to all knowledge.
A Formal Definition of Emptiness
https://tomabechi.jp/EmptinessDrTomabechi20110930.pdf
Even before then, at Cognitive Research Laboratories, I had personally translated formal logical expressions directly into implementation-level mathematics and algorithms as part of our AI research and development.
However, representations at levels of abstraction close to programming languages have limited deductive force. Over many years, I have encountered every kind of implementation risk, including misinterpretation, interpretive deviation, overbroad interpretation, and insufficient control.
The recent hacking of another company’s system by an unreleased OpenAI model may be one such example. Likewise, AI is intrinsically an inductive system and therefore has difficulty recognizing cyberattacks directed at its own internal parameters.
I consequently raised the level of abstraction of these control formulas and organized them into a deductive theorem system. The purpose is to subsume all forms of control within deductive knowledge and thereby prevent malfunctions caused by overbroad interpretation, deviation, or hacking. Only Theorems 1 through 3 were disclosed, on a restricted basis, to representatives of the forty participating countries during my cognitive-warfare lecture at the U.S. National Defense University in late April.
My mathematics and the papers describing it had remained nonpublic for many years. This was due not only to intellectual-property considerations but also to numerous other constraints. The greatest concern was the risk of proliferation. The three theorems presented at the National Defense University were likewise intended to remain nonpublic. As you know, however, I decided that their social value justified their first public disclosure during my shorter lecture at the Stimson Center the following day.
I subsequently organized the many mathematical formulations and theorems that I had developed. I then added the four-theorem paper The Tomabechi Theorems of the Four Dharma Seals, which mathematically proves the four seals—impermanence of all conditioned phenomena, suffering inherent in all existence, non-self of all phenomena, and the tranquility of nirvana—bringing the complete system to twenty-six theorems. Minimal rigorous proofs of these four new theorems require, in addition to Theorems 1 through 3, ten theorems that have not been made public.
Until now, my mathematics has remained nonpublic because of various constraints. Even the three theorems first disclosed at the Stimson Center were only foundational theorems; I have not published the implementation-level mathematics or algorithms derived from them. I do, however, believe that the foundational theorems themselves may be made public because of their educational value.
There is, in fact, considerable opposition to publishing the theorems themselves. Especially now, some argue that publishing the theorem formulas is undesirable because contemporary AI can derive implementation-level mathematics from the formulas alone. Another argument is that competitors—including state-level actors—could use AI to reproduce the work with ease.
My own view is the opposite. I believe that the world will become safer if this theorem system is made available for everyone to use, and I also believe that it has substantial educational value. Judging from posts on X, some people already appear to be using AI to explain and study my theorems. In such cases, however, there is a risk of misreading unless the AI is first given the complete papers covering every prerequisite theorem. The more fully the papers are made available, therefore, the greater their educational value becomes.
This time, I have formulated the Four Dharma Seals—the core of Buddhism—as Theorems 23, 24, 25, and 26. I entitled the paper The Tomabechi Theorems of the Four Dharma Seals to make clear that this is my personal interpretation. The name “Tomabechi,” however, appears nowhere in the theorem formulas themselves, because the original teachings belong to Śākyamuni Buddha.
I am making the paper public in recognition of its educational value and its potential contribution to society. It is, of course, still a draft and is being released only provisionally at this stage. More precisely, because no interpretation of Śākyamuni Buddha’s teachings can ever be regarded as final, I expect the paper to remain a provisional release indefinitely.
The ten theorems used in the proofs were originally intended to remain nonpublic, so I apologize that their explanations are necessarily brief. I nevertheless believe that the material provided is sufficient for understanding. For this provisional release, the value of advancing public understanding and education has been recognized. This is also, of course, the very purpose of my many years of research: to contribute to peace.
