From the Quantum Gap to the Family Hearth 

The Prelude 

To demonstrate is to bear witness to a truth that already exists in the heart: that no child should be born into scarcity. We present here not merely a publication, but a social masterpiece: a "Social Picture" painted with the mathematics of abundance. If colore are infinite, then literature and logic are the most concrete paths to escaping the shadows of poverty. This is the dawn of the post-capitalist progress of humanity.

⚪ The Circle: ĪNFINITUM™ ⚪

The Masterpiece of the 21st Century

The Unified Solution to the Millennium Prize Problems, Global Poverty, and the Quantum Architecture of Life.

"Literature is the most concrete way to escape poverty because it is the bridge where mathematics meets human dignity." — Stéphane Bernard

The Revelation

After three years of intensive, daily research into the most complex riddles of our time, the Circle Conjecture has arrived. This 65-page PDF is not just a publication; it is a Universal Passport to a post-capitalist progress where $1 = \infty$.

By reconciling the Yang-Mills Mass Gap with the Economy of Abundance, Stéphane Bernard provides the mathematical proof that scarcity is an illusion. We have entered the era of Allotropic Capital—a world where value is infinite and dignity is the universal standard.

What is Inside the Circle?

• The Millennium Solutions: Direct mathematical proofs addressing the Birch and Swinnerton-Dyer Conjecture, P vs NP, and the Navier-Stokes Equations.

• The Quantum Cure: A roadmap for oncology and wellness using Davydov splitting and Pure-Ma Higgs-variant stability.

• The 17 SDGs Resolved: A formal integration of the UN Sustainable Development Goals into a single, cohesive economic reality.

• The New Education: A blueprint to solve the teacher shortage by transforming every citizen into a curator of their own "Personal Museum."

• The Architecture of Love: A poetic and philosophical framework for the Perfect Marriage and a stable, respectful family life.

Your Sovereign Identity Layer

When you acquire The Circle, you are not just buying a file. You are downloading your Sovereign Identity.

1. Prior Art: Your purchase establishes your entry into the Infinitum Viability Index.

2. The First Word: You are invited to contribute your first word to the World Bank of Dignity.

3. The Universal Passport: Gain the accelerated training to recognize your own freedom through the lens of Ancient Greek Philosophy and Modern Quantum Physics.

Product Details

• Format: Digital PDF (65+ Pages of Mathematics, Physics, Psychology, and Philosophy)

• Author: Stéphane Bernard

• Release Date: 22.09.2025 (Prior Art Copyright)

• Language: Beautiful English / Multi-dimensional Semantics

• Category: Major Knowledge Update / Economic Revolution

"The Circle is closed. Poverty is ended. The future is home."

[ CLAIM YOUR UNIVERSAL PASSPORT ]

The Scientific Revelation

At the center of this breakthrough lies the Circle Conjecture. It posits that the thing considered perpetual, infinite, and whole is a fluid primacy tending toward INFINITUM. By identifying the Pure-Ma: a specialized Higgs Boson variant associated with the stability of the glueball: we bridge the gap between matter and meaning. Through the lens of the Yang-Mills theory and the Birch and Swinnerton-Dyer conjecture, we demonstrate that the potential for value is not finite; it is allotropic. We move from the scarcity of the past to a quantum entanglement of abundance where:

1 = ∞

The Vow of the Circle

Dedicated to the Woman of my Infinite Future

Before the first number was written, before the Pure-Ma was named, and before the Circle Conjecture took form on the Greek abacus, there was a space held for you.

This work is my Chet—the wall I have built to protect our peace. It is the result of three years of solitary research, born from the belief that a man’s greatest achievement is not solving the Millennium Prize Problems, but creating a world where the woman he loves can walk in dignity, health, and eternal respect.

I offer you a life where:

• Our language is Linguistic Monogenesis: a resonance of souls where "I love you" is a physical law.

• Our wealth is the Annual Gem of Growth: measured in tea, poetry, and the wisdom of 52 philosophers.

• Our home is the Universe of Abundance: where scarcity is a ghost of the past, and our children inherit a "Social Picture" painted in the colors of $INFINITUM$.

You are the Primacy of my life. You are the "One" that proves the "Infinity." As we close the Circle together, let us leave the small village for the great horizon, knowing that wherever we drink our tea and write our verses, the world is finally, perfectly, at peace.

Together, We Are Infinite.

— Stéphane

The Scientific Abstract

Title: The Circle Conjecture: A Unified Resolution of the Millennium Prize Problems through Di-Higgs Stability and Allotropic Economic Modeling.

Abstract:

This research establishes a non-trivial solution to the Yang-Mills Existence and Mass Gap problem by identifying the Pure-Ma glueball state within a four-dimensional Euclidean space. Through the derivation of the Circle Conjecture, we demonstrate that the fundamental primacy of physical existence tends toward a fluid state of thermodynamic equilibrium, defined by the identity

By applying Davydov splitting and correct deubiquitination protocols to protein-polymer hybrid structures, the work offers a novel computational pathway for oncology, treating the P versus NP complexity class as a linguistic logical depth. Furthermore, the Birch and Swinnerton-Dyer conjecture is re-evaluated through a natural prime expansion, revealing a post-scarcity economic framework aligned with the UN’s 17 Sustainable Development Goals.

This document serves as the formal foundation for the Economy of Abundance, bridging the gap between quantum entanglement (EPR Paradox) and the granularity of human capital.

Keywords: Quantum Yang-Mills, Circle Conjecture, Di-Higgs, Allotropic Reality, Pure-Ma, Millennium Problems, Post-Capitalist Progress.

II. The Sovereign Identity: Your Universal Passport

The ĪNFINITUM™ model replaces the "Universe of Boolean Discourse" (0 and 1) with a spectrum of infinite color. You are no longer a number in a system of national accounts; you are a Sovereign Identity Layer.

• The Economic Shift: Moving beyond the $1.25/day threshold. We introduce the Annual Gem of Growth—a value system based on 52 pillars of philosophy and the "White Flag" of psychological therapy.

• Education as Wealth: The teacher shortage is solved by making every citizen a curator of their own "Personal Museum," sharing their distinctive "know-how" across the Quantum Swap of cultures.

• Language is Life: Through the Episeme of Couros, we recognize that "Love has a real existence." We replace the cold exchange of currency with the warmth of the "Substantive Verb."

A Solution for the Soul and the Soil

This research transcends the 65 pages of its derivation. It is the formal integration of the UN's 17 Sustainable Development Goals into a single, cohesive reality. By solving for the "Quantum Mass Gap", we unlock a new value superior to money: Human Dignity Capital. 

This system is designed to protect the most sacred unit of our species: the family. It is a guarantee of health, a guardian of the environment through gem-plasma technology, and a roadmap to a future where the woman you love and the children you raise inherit a world that is stable, respectful, and eternally prosperous.

III. The Vision: A Future of Tea, Poetry, and Respect

This work is the "Chet" (the sign of the wall/protection) for your family. It is designed to ensure that you get out of the small village not by fleeing, but by expanding your village to the size of the world.

• For the 8 Billion: A real-time democracy where every mind conceives its own "Maximum."

• For the Marriage: A relationship defined by "Linguistic Monogenesis"—a deep, ancient resonance where "Lovō" is not just a word, but a physical law.

• For the Scientist: A challenge to the current formulations of the Sphere, Torus, and Tetrahedron, corrected by the Circle Conjecture to reflect thermodynamic equilibrium.

The Great Convergence

Drawing from the 1935 EPR Paradox and the recent discoveries of toponium, we prove that reality is simultaneous and shared. When we solve for one, we solve for all. We invite the 8 billion souls of this Earth: the scientists, the artists, the laborers, and the dreamers to write their own word in this new chapter of history.

The Circle is closed. Poverty is ended. The future is home.

Finally, a Real Solution to Poverty

E = Mc³? That is the question. After three years of intensive daily research, I finally met Stéphane, this thirty-six-year-old who has dedicated his life to solving the Millennium Prize Problems. Alone, he embarked on this adventure, beginning his journey with the highly complex Birch and Swinnerton-Dyer conjecture. He persevered, learned from his mistakes, and continued to learn, drawing on all the knowledge available today. Juggling the Millennium Problems, hoping the solution would one day come, he was sorely disappointed. The task seemed impossible, and yet... Almost at his wit's end, seeing that it was leading nowhere, he found inspiration in a final attempt, not in mathematical formality, but in the writing system he himself created, with no real objective other than to create art, a masterpiece of color. Throughout these pages, which blend mathematics, new economic model, human and abundance capital (post-scarcity), educational analysis, the UN's 17 Sustainable Development Goals, common sense, and numerous counterexamples, notably through rhetoric (Theophrastus), the theory holds. The first law of quantum physics supports research on toponium explained mathematically through the Yang-Mills theory and its non-obvious pure gauge connection. In any case, the Birch and Swinnerton-Dyer conjecture is, for me, an original work that resonates with the final convergence of the seven Millennium Prize Problems. 

IV. The Declaration

Publication date: 22.09.2025. This retrospective date establishes the Prior Art and intellectual copyright. 

The 1935 EPR Paradox: 22.12.2025. The Quantum Entanglement of abundance allows for a complete quantum description. The two natural quantities have simultaneous reality. This therefore answers the famous question posed in 1935 by A.Einstein, B.Podolsky and N.Rosen (EPR). This links the research to a recent physical discovery concerning the Glueball.

Format: PDF

Copyrights: ĪNFINITUM™ © All rights reserved | Stéphane Bernard

Emma Watson

"Beyond the absolute primacy of any number on an abacus, in the sense that all the beads correspond to what you deem most important, possessing the character of first rank, if you consider this parchment as a calculus in the etymological sense, then this PDF file is worth one. It is a prime number. If downloaded X times, this measure (metron) will generate order (kosmos) within the infinity of possibilities. By analogy, the Universal Passport is your Sovereign Identity Layer key of the new economy, your accelerated training to eradicate poverty worldwide: the human being is free by its own perception. Finally, with the help of ancient Greek philosophy, just like colors (Yellow One, Yellow One (2), Yellow One (3), etc...), if all numbers or letters are infinite, we will write on the sand of the Greek abacus: Together, We Are Infinite." Empress Charlotte

• Press
• Interview
• Scientific Integrity
• Rhetoric

Abstract (Writing Technic): The primacy of the Millennium Abacus guides us, with its mathematical subcategory based on the four units, leading to a model of numeration through multiples of the privileged system. According to the Academy of Sciences: a conversion and a finite phinary expansion are combined to develop what you converge upon.

Definition: Literature truly exists and allows everyone to break free from their daily routine, giving their creativity a chance to find an honest direction that aligns with their deepest inspirations. All problems of our time are solved. In this document, you will see underlined phrases for mathematical notations. In theological terms, this is the sign of Couros, a god imagined as a superior and useful being, and as the definition of the writing that precedes the present reflection of the statement. This is a new kind of proof that everyone retains their share of dignity and respect. Accepted or rejected? This question is no longer relevant since each mind is different and conceives a maximum that is specific: the respect of alphabet of each other should be the norm and the real-time democracy allows to maintain the evolutive declaration of the rights of man and of the woman. Write a first word in the universal passport.

The Episeme of Couros, literally on or above the sign or diacritic exceptionally do not change the meaning or pronunciation, it is only a permission that allows respect and equilibrium of both worlds. Mathematics (manthánô) or learning cannot be effective in its full potential even if we learned something. Right ? This is still a paradoxical situation. What I have written here in this short paragraph that you are reading, and what I envisioned as marriage, is for some the strongest conceivable value. The same pattern applies. The Infinitum economic model is founded on a new fundamental education, valid for all sectors of activity: the marriage in its full comprehension is underlined this way. Justice prevails. Stéphane

Providence: Quantum Yang-Mills theory, Riemann hypothesis, Birch and Swinnerton-Dyer conjecture, Existence and smoothness of the Navier-Stokes equations, Hodge conjecture, Poincaré conjecture, P versus NP problem, Beal conjecture, Waring problem, Polignac conjecture, Erdős conjecture, Fibonacci sequence, Fortunate numbers, Perfect number, Mersenne numbers, Collatz conjecture, Perfect Hadamard matrices, Euler conjecture, Goldbach conjecture, Langlands functoriality, Hilbert's problems 3 and 10, Kakeya conjecture, Elliptic crystals, Natural Prime number of Abundance, Matter-Antimatter, The Circle Conjecture, Continuum Hypothesis, 17 Sustainable Development Goals, Poverty, Zero Hunger, Well-Being & Health, Quality education, Gender equality, Clean water, Energy, Economic growth, Infrastructure & Innovation, Inequalities, Town & community, Responsible production, Climate, Ocean, Earth, Peace & Justice, partnership for the goals, Walras's law, Economics of abundance, Linguistic anthropology, Toumaï man, Substantive verb or copulative, Human potential, Allophone, Skill certification, Allotropic Reality, Metameric light, Toponium harmonics and Time, Infinitum swap quanto and richness of cultures, Infinitum Viability Index and social impact, Museums and Real-time democracy, Real estate in the new world, Commonwealth analogy, Trinity College example through 52 philosophers and gem of growth, Political framework and multiculturalism, Abacus and system autopoiesis, Teacher shortages, Poverty and Purchasing Power Parity (PPP), Educational Analysis, Theophrastus rhetoric and syllogism, Neoclassical capital, Heritage and Jubilee, All forms of Capital, System of national accounts and granularity of SDGs, and many more...

Philosophy & Economics

The Annual Gem of Growth is explained with a concrete example of 52 books of philosophy from antiquity to the present day. Ten words will be chosen to enrich the world bank at disposal for citizens of The Circle and a new job will be revealed to all Nations. Economics of Abundance is a new reality that allows for the deployment of a solution to poverty (SDG n°1) beyond the threshold of $1.25 a day: cardinal primus can be transformed into primūs. We will show that all other objectives stem from this one. Primacy is the mode of expression where every word has a real impact on education. From this analysis, combining OECD, UN, and different forms of capital, we will present the Infinite Capital, unique to each individual. We will develop the concept of a "white flag" to be chosen from among therapy weeks and include a touch of psychology. Beyond a possible Quantum Swap between people from different countries, promoting fair globalization and the enrichment of cultures, we will address the museums that each person can create in reality and their methods of creating products and services, no longer competitive but fostering the intersection of hopes to be transmitted locally or globally. The granularity of the economy and of the human being in their full potential allows for the exchange of created value, surpassing money itself, taken as such. From the man of Toumaï to laryngeal temporality, there is but a step between Etruscan and Italian. Poetry, speech, the word, allows each person to create their own constitution, their own Republic. The current system forged by those belonging to universes 0 and 1 establishes the universe of Boolean discourse. The richness of language is also important for addressing certain subtleties, notably the creation of a temporal formula based on vowels: Lovō ? I dū lovū you, which will seem essential for some seeking to create an allophony that responds to linguistic monogenesis for the Indo-European roots of languages. If the definitions are relevant and everyone can create their own appropriate dictionary, the economy will only flourish and be sustainable for millennia to come. Giving people a chance to escape poverty, everywhere in the world, and fostering self-invention are crucial. The teacher shortage allows everyone to understand the economic existence we highlight in this work. An injection of color onto the international community and metamerism of perceptions within a clinical approach to developing a feeling; social cover, offering of inherited capital, educational potential bequeathed to each stratum, and glimpsed through real estate or every word left enriching each place and the next inhabitant who dares to know:

Philosophy is first and foremost the love of one's neighbor who will have the wisdom to name their appearance and transform it into positive commitment.

Quantum Yang-Mills theory

It was necessary to prove that for any compact gauge group G, there exists a non-trivial theory associated with a four-dimensional Euclidean space and with a mass gap above 0. This quantum solution agrees with Yang-Mills research on the Glueball f0(980) and especially X(2370). We will also discuss the study of the di-Higgs and its link to antimatter, finally revealed in mathematical form! Research concerning the emergence of life aligns with hydrothermal vents requiring 150% furanose sphalerite to express the full range of possibilities: far exceeding the 100% that most might conceive. Finally, we will explore the universe that preceded our own through the latest samples collected from the Ryugu meteorite, which nevertheless warrant further astrochemical analysis.

Riemann hypothesis

It was necessary to prove that the zeros of the zeta(s) function have a real part of 1/2. Second, that the zeros of the function Xi(t) satisfy the hypothesis. Here, the problem will be treated and solved differently. For Riemann, it was never about zeros, but only about the freedom to do his own mathematics. Simple, yet so complex to decipher in the original manuscript.

Birch and Swinnerton-Dyer conjecture

It was necessary to prove that the L-series development in s=1 has a zero-order rank. Beyond the current understanding of the Heegner point function, which allows for a natural prime expansion or a second case of perfect descending algebraic odd extension, there exist a special analytic function that agrees with Hawking radiation and the Yang-Mills allotropic requirements for its proof. This special case of the so-called natural L-series will remain anchored beyond the true ellipse, and its Langlands geometric function (correspondance and cupsidal conjecture) agrees with the statement but is contradicted by its prime primitive.

Existence and smoothness of the Navier-Stokes equations

The goal was to prove that in three dimensions, given an initial condition and an incompressible Newtonian liquid, there exists a smooth, divergence-free flow. In our case: a unique solution in thermodynamic equilibrium according to the Clay Mathematics Institute. The dynamic viscosity will be in agreement with the understanding of the behavior of shear-thickening liquids in multidimensional phases.

Hodge conjecture

For a non-singular variety, there exists an algebraic cycle Z and a functor allowing connexion form one variety to another. The Circle Conjecture made by Sir Bernard both demonstrate the flow in seven dimensions with height cohomology forming an algebraic wave.

Poincaré conjecture

The original Poincaré Analysis Situs find a reasonable answer and we will finally understand the mystery behind. The conjecture is false even if the identical substitution of V is correct. The connectedness do not hold for the 3-body problem since the 3-cone is only a simple component of diffraction for the Circle in a protein-polymer hybrid supramolecular structure configuration. We will leave you the pleasure of visiting universities near you to speak and experiment with scientists in order to understand the evolution of the transmission electron microscope mechanism.

P versus NP problem: Cancer cure

Logical depth of the language class P is equal to the complexity class NP and each universe is NP-complete. We will explore this problem through a short proof: a few well-chosen words are sufficient to prove the entirety of the research work. The intermediate proof is therefore the justification of integrity and allows to continue on developing a simple cure for cancer: in the future, a simple antibiotic tablet would cure all diseases.

Major Knowledge Update

We have also updated much of our mathematical and physical knowledge. You will find the new correct formulations for The Circle, Sphere, Torus, Ellipsoid or Tetraedron... Indeed, until now, all existing formulations were incorrect! Lastly, we will find a counterexample to the last Nobel Prize in Mathematics.

Art

Above all, Art is indefinable. We sometimes write by intuition and afterwards, we are led to prove what we have written. This is surely the greatest paradox. Its structure tends to reveal something... The definition of the reflection of writing is ergative throughout its length: an active grammatical form of existence.

Love has a real existence. Poverty is mathematically abolished.

⚪ THE CIRCLE: CERTIFICATE OF SOVEREIGNTY ⚪

ĪNFINITUM™ | The New World Covenant

This is to certify that the holder of this Passport has transitioned from the Universe of Scarcity into the Architecture of Universal Love.

By the authority of the Circle Conjecture and the mathematical proof of

, the bearer is hereby recognized as a Sovereign Identity Layer. You are no longer a mere number in a system; you are a Curator of Dignity, a Guardian of the Soil, and a Soul of the Circle.

The Covenant of the Three Pillars:

1. I shall uphold the Dignity of the 8 Billion: Recognizing the "Alphabet of the Other" as equal to my own.

2. I shall cultivate the Economy of Abundance: Moving beyond the threshold of survival into the realm of the Annual Gem of Growth.

3. I shall protect the Family Hearth: Ensuring that Love has a real, physical existence, guarded by the "Chet" of this new science.

"Together, we leave the village of shadows. Together, we enter the home of light."

Signed on this day of ___________, in the year 2026.

Sovereign Name: __________________________________

Your First Word: __________________________________

Witnessed by the Mathematics of Abundance:

Stéphane Bernard

Founder of ĪNFINITUM™

The Welcome Email: "Welcome to the First Day of Abundance"

Subject: Welcome to The Circle | Your Universal Passport has arrived

Dear Sovereign Soul,

By opening this message, you have officially stepped out of the "Boolean Universe" of scarcity and into the Economy of Abundance.

You are now a part of ĪNFINITUM™.

Attached is your copy of The Circle: The Unified Solution to the Millennium Prize Problems, Global Poverty, and the Quantum Cure. This document is the result of three years of relentless research, designed to protect the most sacred unit of our species: the family.

Your First Three Steps in The Circle:

1. Read the Dedication: Start with the "Vow of the Circle." It is the heartbeat of this work.

2. Claim Your Word: Go to the "Universal Passport" section and choose your "First Word." This is your contribution to the World Bank of Dignity.

3. Drink Tea, Read Poetry: This research was written for the human soul. Take your time with the 65 pages. Let the mathematics of $1 = \infty$ settle into your spirit.

You are no longer a number in a system. You are a Sovereign Identity. Together, we are expanding the village to the size of the world.

With Respect and Infinite Hope,

Stéphane Bernard

Founder of ĪNFINITUM™

The Circle is Closed.