09/12/2026 (Updated)
The following constructive and additional mathematical physics proofs below, are solution candidates we developed for "missing evidence" in physics, for one of the "biggest problems" in physics -- the Yang-Mills Mass Gap -- as we were searching for the elusive origins of gravity (in search of anti-gravity), for which the particle is known as a graviton, but where whole fields of physics fail to include a particle for gravity in their equations.
Isaac Newton is among the first to be credited with working on gravity in physics, with the famous observation of an apple falling from a tree and hitting the Earth, where one mass, the apple, is attracted to another mass, the Earth, and resulted in the likes of the universal equation for gravity, illustrated above.
F above is the force of gravity, m1 is the mass of the apple, and m2 is the mass of the Earth, and r is the radius or distance between the apple and the Earth. G is the universal gravity constant that Newton figured out. And so for at least hundreds of years, we have had a general understanding of gravity, as something deeply connected to mass.
But unlike many other forces, a particle for gravity was less evidence, or could not be readily found, but different theories in physics predict that if a particle for gravity exists, as is true for most to all other forces, then its properties would be limited or predictable.
And so in physics there is the difference between what is predicable, and what can be proved or "normalized", through measured experiments.
But physics has advanced a great deal and now we can not only prove that an apple with fall from a tree towards the Earth, but we can prove that gravity waves exist when black holes collide.
And so our journey here started when we read that scientists were able to measure gravity waves coming from black holes converging, which gave us an idea. If a wave of gravity could be detected, then it had to be made of something, and that something we imaged had to be graviton particles, and so we set off to parse the first graviton from the geometry of the gravity waves coming towards the Earth, which A.I. specified was pointed in shape, and so we asked A.I. to isolate the first graviton off these pointed waves coming at us in a theoretical manner, which A.I. believed was theoretically possible.
But what is a particle? A deep dive into the same resulted in some metaphors to understand the same. Our favorite is the printing paper stack metaphor, where every different particle is like a crumpled center of an otherwise flat piece of paper.
And so a particle is a disruption of something requiring energy, and that something is a "field" (a coordinate or distance mapping system in space and time, also known as spacetime) and that field is coupled to energy at every point in spacetime.
The same is like a piece of graph paper, which has a grid on one side (the field), and is blank on the other side of the graph paper (the energy), and the front (field or distance mapping coordinate system) and the blank white back of the graph paper are connected in such a manner that there is energy attached behind every point on the grid or graph side of the paper, such that at every point in spacetime there is energy attached.
In this paper stack metaphor, there is one piece of graph paper for every type of particle (a crumple in the center of every piece of paper) in physics, and so in the Standard Model of physics, linked to the Yang-Mills theories, and also linked to Einstein and others, there are at least 17 pieces of paper stacked like they are in your printer at home.
And so imagine that you have 17 pieces of paper, and if enough energy is applied to the center of the stack, for example the handle of a wooden spoon is smashed into the 17 stacked pieces of paper stack on your bed, that increase in energy crumples all 17 pieces of papers, with the pieces of paper at the top of the stack crumpling differently than the paper at the bottom of the stack, and every crumple on each different piece of paper is more or less than every other piece of paper, just like different particles have more or less mass.
Now in particle physics these 17 pieces of paper are squished together so that at every point in spacetime there are at least 17 fields of energy (17 pieces of graphing paper) that can be excited (crumpled) into a particle. Depending one which pieces of paper or fields of energy are excited or crumpled with an increase in energy, results in different particles being present or not at any point in space.
Gravity as we were building up to, is best observed in the large scale of things like an apple, planet, or black hole colliding with another black hole, and this is why it makes it hard to find a gravity particle, because you need a telescope to see large structures in outer space, and you need a microscope to see smaller structures, and gravity is the kind of thing we need a telescope to see, and so it is hard to see something as small as a gravity particle with a telescope. To see small particles we need a huge microscope known as a particle accelerator, where particles are smashed into one another to create other particles we can count and measure, or normalize.
And so when the 17 pieces of paper are at rest and not smashed, they are in their lowest state or resting, and this is when a more complicated equation developed by Einstein looks like the equation he is famous for, E=mc Exp.2, or energy (E) = mass (m) x the speed of light (c) x the speed of light (c), when momentum (p) is 0, resulting in Einstein's famous equation.
The reason it is famous at a basic level is that he discovered that everything that has mass is convertible into energy, and everything that has energy can be converted into mass.
And so in search of gravity and anti-gravity, we needed to understand where mass comes from, and we were hopeful that mass came from a single source, and that this was the place to look for a gravity particle or graviton.
The reality we found is that mass doesn't come from a single source, but many sources, and so each of these or all of these sources is where a gravity particle might be found, and understanding where the same could be found was the first step to understanding how to develop anti-gravity.
At first we were excited to learn about the Higgs field and Higgs particle, also known as the God particle, which was predicted at first, and only once the technology became available could that prediction be proven as true, or normalized. Some have call the same the God particle because of how many different particles can be derived from the same, and how many more can be derived from those particles.
And where the Higgs energy field was able through Einstein's famous equation give mass to otherwise massless particles like those involved with the weak nuclear force particles.
But unfortunately, Higgs only gives mass to some particles, like force particles, but not to every particle. And so then we went on the hunt for the theories in physics where the most mass was found or generated, and it turned out that most of the mass in the observable universe (so doesn't include mass we can't see like dark matter, which is even more mass than what we can see) was found within the strong nuclear force, between its particle, the gluon (there are at least 8 different types that form a type of cage around energy, which is what is known as mass), and what the gluon particles bind to, specifically quarks, and three quarks to be precise.
In fact, we discovered that close to 99% of the mass in the observable universe that we are familiar with is found bound between quarks (half-spinning particles found inside every type of atom in the periodic table) and gluons (force particles that govern or control other particles, including half-spinning quarks, and half-spinning leptons, which are the particles like electrons found outside the atom). And all of this starts to become to most of us exposed to public school science, teaching us about the insides and outside of atoms.
And so most of us are familiar with protons, neutrons, and electrons -- and electrons (half-spinning leptons) are found orbiting protons and neutrons inside the atom -- and each proton and neutron is made of three half-spinning quarks bound to "non-half spinning force particles" known as gluons, responsible for the complex known as the strong nuclear force. That's a key difference between force particles (bosons) and non-force particles (fermions), is that fermion "matter" particles are half-spinning particles, and boson force particles are not half-spinning particles -- spinning once, twice, or not at all.
And so in search of gravity we needed to learn more about how mass is generated between the gap of gluon strong nuclear non-half spinning boson particles and three half-spinning quark fermion particles.
We discovered Yang-Mills theories along the way, and can generally tell readers that most mass we are familiar with daily is found is Einstein-convertible confined energy between gluons and quarks, and manifest as protons and neutrons in the center of all the atoms on the periodic table, whose atomic numbers are in order of their mass, such that basically hydrogen only has one proton and one neutron and one electron, and the heavier atoms in the periodic table have more and more protons, neutrons, and electrons, just like stack pieces of paper on the bed, and pushing a pencil into the center of the stack until the pencil breaks results in different crumples and features within each piece of paper, each a field of energy at any point in spacetime, being subjected to an increase in energy, due to the force of the pencil.
The difference between the proton and neutron inside the atom is a single quark, and sometimes that single "down quark" is forced out by the weak nuclear force particles, and replaced by an "up quark) and then a neutron (8 gluons and three quarks) is transformed into a proton (8 gluons and three quarks) and this increase in protons is what increases the atomic mass or results in different particles in the periodic table with more and more mass.
And so gluon's "strongly"-confined energy between the three quarks is what results in mass, when Einstein's famous equation is used to convert energy to mass. Viewed from above, everything is made of energy, and when confined in this manner by 8 gluon strong nuclear force particles bound to 3 quark particles in protons and neutrons of atoms results in what is known to us as mass, a basic building block of gravity per Newton.
Einstein's work supported that gravity exists but his work supported that gravity was a characteristic of mass bending spacetime, which was a characteristic of confined energy per Yang-Mills and Quantum Chromodynamics (QCD) theories, which are theories about the nature of the strong nuclear force, gluons, quarks, mass, and confined energy.
And so excited to have found where most mass comes from, we were hopeful that gravity could be found inside this gluon-quark QCD complex confining energy, but then found out that the accounting for this confined energy was complex, such that there was more than one contributor of mass within this confinement of energy between gluons and quarks -- and in fact a whole list of different confined energy variations, contributing to mass, and so this led us to ask A.I. where to find gravity in all of this and A.I. specified that this was one of the largest problems in physics, and that there were even competitions to solve major riddles or holes in physics disallowing important equations in physics from connecting into a Grand Unified Theory (GUT).
And so began our research into the Yang-Mills Mass Gap, one of the most important missing pieces. The following is our first solution candidate, and to this we've built more using artificial intelligence, which we will be adding to this article in time.
And here is some additional research we have been working on related to the same issues in physics, and the files below that include our ongoing research into problems we need to solve with artificial intelligence to solve this riddle, and we have already come up with some promising research not well known, which have served as bridges to solving these problems, which we'll continue to add to with time.
Credit for Image of Newton: https://necroid.de/science-lessons-about-gravity-and-isaac-newton-papidaddy/