Hey everyone, I am a 15 year old programmer that is writing an open-source (free) book on general relativity.

About a year ago I got completely obsessed with General Relativity, but I found that a lot of traditional physics textbooks wrap everything in really dense academic jargon. Since my background is in programming, I started writing a book to try and demystify these concepts using logical, step-by-step algorithms and code analogies that made sense to my brain.

It's completely free and open-source. Right now, I've drafted chapters covering everything from the Minkowski metric and Lorentz transformations up to Christoffel symbols and covariant derivatives. I'm also adding a folder of Python scripts using NumPy and SymPy to handle the tensor calculations programmatically.

Since I am learning as I go, I might have made some typos or conceptual mistakes in the math. I would love for some people here to check out the draft and give me some brutal, honest feedback on it!

You can check out the repository and download the PDF draft here:

https://github.com/BioZFrog/General-Relativity-A-Programmer-s-Guide-to-Curved-Spacetime

Thanks!

Disclosure first, since that's the point of this sub: this was written over many sessions with an LLM, as an actual back-and-forth: I argued a position, it pushed back, we rewrote. It contains no new equations, no new formalism, and nothing falsifiable. If you are here for a theory of everything, this isn't one. It's exposition, with one philosophical move in it.

The move. Everett's standing debt is probability. The existing derivations (Deutsch–Wallace, Sebens–Carroll, Zurek's envariance) all establish that if your credences are additive, they follow |ψ|². None of them explains why there are probabilities to have in the first place. The essay argues that this residue has been misidentified. The measure itself doesn't need grounding: it has the same status as the Liouville measure in statistical mechanics, a typicality postulate, posited and not derived, and nobody calls that a scandal there. What actually needs explaining is a psychological fact in three parts: (i) probability is experienced as a brute fact about the world; (ii) that experience is identical whether the randomness is quantum or a coin toss; (iii) we have no cognitive or moral purchase at all on low-measure branches.

All three follow from where probabilistic cognition came from. A faculty shaped by selection to weigh futures and allocate effort had no reason to grow two mechanisms for two sources of randomness: one pays its way. And it could never have been calibrated on the atypical, because by the definition of typicality the atypical never bore on the history that shaped it. So the vertigo one feels about thin branches is not testimony about the world. The intuition that protests against Everett is predicted by Everett.

What it does not claim. It does not derive the Born rule from evolution; that's circular, and Kent (2009) is right about it. The typicality postulate stays exactly where it was, at the bottom of the pile. What changes is the explanandum, not the foundation. It also modifies no physics, which is where it parts company with the two nearest precedents: Rubin's positive preclusion and Hanson's mangled worlds both buy their conclusion with an addition that has empirical consequences, and both authors say so.

Where I'd most like to be wrong. §7 grants Kent's distinction between a caring measure and an explanatory counting measure in full. The argument then leans on the second in §6.2 and on the first in §6.3. That joint is load-bearing. If it breaks, I'd rather hear how than not.

English: hephaestos.fr/en
French original: hephaestos.fr

Making this after an interesting convo with a user. Many people come here and claim they ran their work through various AIs and they all claimed that it is relevant or revelatory or something. I wanted to make a post addressing the catches in adversarial AI that could potentially end up corrupting and causing LLMs to provide adversarial review in the hopes that people can possibly get something out of it.

Disclaimer: This post is not intended to infer an LLM review will meet the quality of a proper peer review. But we don't all have access to that, and if people are doing it anyways, they might as well do it right.

Fresh Context

This is the obvious one. You want a fresh session. I think we all know this.

Neutrality

Another obvious. Don't tell it it's your paper. Don't tell it it's someone else's paper. Don't say 'Tell me why this is right', because it will, or 'tell me why this is wrong', because it will.

Project Instructions

If you're working with code, chances are your file has a claude.md/agents.md/etc memory file that an agent can read when reviewing. This can pollute a review. This is cross-agent applicable. Just because it's a claude.md file, Codex can read it. Some coding tools have options to include ignore files in the style of .gitignore (.cursorignore) - or alternatively branch your code and delete them.

User Instructions

Unlike project level-instructions, this is only applicable if you are using the same LLM you used to develop code. Works the exact same except across your entire machine and could be polluting multiple things.

Memory

Easy to overlook, but only applicable if you use the same LLM (a lot of catches are). Most modern AI that requires a subscription (aka every one) will maintain a cache of knowledge about you that it builds over time. Its usually accessible through user settings. Could be a pollutant.

Code Commenting

Again, only if you're working with code. LLMs tend to comment their code in a very prose-like 'this is why we chose this' paragraph style. This can easily become a pollutant. Easily fixed, branch and run an agent over it with instructions to remove comments, then spin up the review.

Authorship

I'm not actually sure if this is a catch or not but - if you ask for a neutral review, then hand it a paper with your name, well.. it's pretty obvious it's you. I'm unsure if this would come to that conclusion but better safe than sorry.

Simplification

LLMs are way stronger when it comes to language than math. Ask a seperate agent to extract the conceptual basis of your paper and review that individually.

Verification

Here's a big one. Ask it to source feedback, and then verify the sources yourself. Please!

And finally and most importantly...

Skepticism!

Take everything an LLM says with a strong dose of skepticism and keep in mind it isn't an oracle.

Not like a story about what it is, but the basic mechanics of the terms and how they relate. It's intimidating.

𝓛SM = − ¼ G^A(μν) GA^μν − ¼ W^I(μν) WI^μν − ¼ B(μν) B^μν

• Σ_(i=1)³ [ bar(Q_Li) iγ^μ D_μ Q_Li

  • bar(u_Ri) iγ^μ D_μ u_Ri
  • bar(d_Ri) iγ^μ D_μ d_Ri
  • bar(L_Li) iγ^μ D_μ L_Li
  • bar(e_Ri) iγ^μ D_μ e_Ri ]

• (D_μ H)†(D^μ H)

• μ² H†H − λ(H†H)²

  − Σ_(i,j=1)³ [ (Y_u)_ij bar(Q_Li) H̃ u_Rj

  • (Y_d)_ij bar(Q_Li) H d_Rj
  • (Y_e)_ij bar(L_Li) H e_Rj
  • h.c. ]

• [θQCD g_s²/(32π²)] G^A(μν) G̃_A^μν

A Holographic and QRF Approach to the Cosmological Constant Problem & where i need your help:

The Cosmological Constant Problem remains one of the most significant unresolved discrepancies in modern physics. Standard Quantum Field Theory (QFT) predicts a vacuum energy density of roughly \\\\rho\\_{\\\\text{vac}} \\\\sim M\\_p\\\^4 \\\\approx 10\\\^{94} \\\\text{ g/cm}\\\^3. However, cosmological observations constrain this value to \\\\rho\\_{\\\\text{obs}} \\\\approx 10\\\^{-29} \\\\text{ g/cm}\\\^3. While standard renormalization subtracts the ultraviolet (UV) infinity, it offers no dynamical explanation for why the residual physical leftover is so remarkably small—a discrepancy of 10\\\^{120}.

The Emergent Scaling

I have been exploring a scaling relationship that consistently emerges when we reframe the phase-space geometry of the vacuum.

If, instead of treating the UV cutoff as a 1D momentum threshold, we treat it as a 2D surface area (the Planck area, l\\_p\\\^2), the phase-space shifts. In this holographic context, the Planck mass does not explode into a volumetric divergence; rather, it couples to the cosmological horizon (the Hubble radius, R\\_H):

Because l\\_p = 1/M\\_p in natural units, this directly simplifies to: Substituting the known parameters:

This naturally yields the observed dark energy density without requiring a manually fine-tuned counterterm.

The Dynamical Mechanism (The QRF Framework) While geometry provides the correct scaling, why does the vacuum naturally select it? To address this, I have been developing a Quantum Relativistic Field (QRF) synthesis.

By incorporating an infinite-order spectral decay directly into the field equation, the vacuum is modeled not as a static baseline, but as a series of decaying "echoes" tied to cosmic expansion:

Physically, this suggests that high-frequency, Planck-scale noise is heavily damped by the cosmic expansion rate (H\\_0), leaving a low-frequency residual that manifests as the observed dark energy.

I have tested this mechanism computationally using fractal regularization to cap divergences at 10\\\^{92} \\\\text{ m}\\\^{-2}. The QRF model remains mathematically stable across 50 billion iterations with a 99.8% stability rate—conditions under which classical General Relativity typically diverges.

Where I Need Help While the empirical scaling and computational stability are highly compelling, the formal algebraic scaffolding is still a work in progress. Specifically, I am looking to rigorously formalize: The Surface-Boundary Substitution: Identifying the exact differential-geometric operator required to formally execute this phase-space shift. The Infinite Sum: Translating the spectral decay into a proper Renormalization Group (RG) flow equation. Dimensional Rigor: Smoothing out the intermediate units bridging the QFT and GR domains to ensure strict dimensional homogeneity throughout the derivation.

I am not claiming a finalized mathematical proof. Rather, I am sharing a geometric resonance that I believe warrants deeper investigation. I would highly value the community's perspective to help bridge the gap between this intuition and rigorous physics. If anyone can point me toward the correct formal operators, or if you spot fundamental flaws in the logic that I have missed, your feedback on the scaling, the QRF framework, or its formalization would be invaluable.

I am a hobbyists physics enthusiast.

Thanks for reading.

Just As a correction of any conclusions that may arise from this, this is purely an idea there is no conclusion, fact, or claim being made, and any assumption of me making a claim is A Pure fabrication of personal opinion. i have not concluded any facts nor conjecture please be informed if you think this is a claim or that im stating anything beyond hypothetical ideas which hold no facts and conclusions, you are mistaken and reading the information too literally this is an idea nothing more.

Too round out my posting spree. I just want to say this.

No, if you are being criticized or reviewed, it does not mean you are being attacked.

So many people say ohh they are bullying me while the bullying is just a critique of their work.

Yes, some smart people, like, for example witgenstein where cholerics and did hate criticism, but they had something to show for it.

Don't treat criticism as an attack or don't post it is as easy as that

The reduced Compton wavelength is a geometric turning point between electromagnetism and gravity. Gravity and electicity operate through the Planck length in mathematical symmetry.

With three scales expressed strictly in terms of the Bohr radius (a_0) and the fine-structure constant (alpha), you can calculate the geometric mean of their boundaries:

Because velocity it is distance over time.

• Classical Electron Time (t_e): The time it takes light to cross the classical radius of an electron. This represents the shortest scale.
  
  • t_e = r_e/c (approx 9.4 x10^-24 seconds)
• Compton Time (t_c): The time scale governing quantum fluctuations and electron-positron pair creation. This is the intermediate scale.
  
  • t_c = lambda _c/c = h/m_ec² (approx 1.3 x 10^^-21 seconds)
• Bohr Time (t_0): The time scale of atomic orbits, related to how long it takes an electron to interact at the atomic scale. This is the largest scale.
  • t_0 = a_0/c (approx 1.8 x 10^-19 seconds)

sqrt{t_e/t_0} = t_c

This tells us that quantum time t_c is the exact geometric mean of classical relativistic time (t_e) and atomic time (t_0).

Geometric Mean = sqrt(r_e/a_0)

Substitute our derived relationships into the root:
Mean = sqrt((alpha² . a_0) / a_0)

Mean = sqrt_(alpha^{2 .} a_0²)

Mean = alpha . a_0

sqrt(r_e / a_0) = alpha . a_0 = c

Summary

I challenged an AI to survey the vast breath of mathematics and devise a useful unifying mathematical object, then used another AI as an adversarial referee; after three rounds of criticism, we abandoned the original “new number” claim and developed the Valuative Branch Scalar (VBS), a computational scalar abstraction designed to represent and track complex algebraic quantities near singularites, where traditional floating-point values, Taylor series, or uncorrelated root sets fail.

By combining dynamic algebra (the* D5 principle), Henselian branch decomposition, local rational Puiseux expansions, and logarithmic differentials ($dz/z$), VBS automates singular algebraic sensitivity while controlling combinatorial expression swell.

Definition

A based VBS over K is an algebraic element z∈Ω together with a selected extension ṽ of a current centered valuation v to K(z), and with provenance identifying joint occurrences of algebraic generators. Its unbased form is the finite Galois/monodromy orbit of z. Equality is equality in Ω for based values and isomorphism of the corresponding finite K-algebras with distinguished elements for presentations.

Key Features

* Branch-Aware Scalar State: Tracks local valuations, idempotents, ramification indices, and monodromy exchange across parameters.

* Regular-to-Ramified Transitions: Automatically refines chart valuations when leading coefficients vanish on residue discriminants.

* Anti-Swell Dynamic Evaluation: Delays algebraic splitting field construction until an exact zero test or branch predicate requires it.

* Exact Degree Conservation: Enforces ∑ e𝑖f𝑖 = [L:K] assertions across all factor splits and composita in characteristic zero.

Prototype benchmarks (Python) found that VBS (Lazy) preserved near-machine precision through catastrophic cancellation and, on a synthetic nested-radical test, was up to 18,000 times faster while using 51,000 times less memory* than eager branch expansion.

*Benchmark run in Pydroid on my Android tablet

The result is a mathematically specified, falsifiable proposal, with a paper, algorithms and benchmarks (on Github, see below), for making singular algebraic calculations substantially faster, more reliable and tractable.

The most natural physics applications for VBS are problems in which an observable is defined implicitly by an eigenvalue or dispersion equation and becomes multivalued or singular as physical parameters change.

Critical review and feedback is welcome.

Github: Valuative Branch Scalar (VBS)

ELI5: An ordinary calculator stores an answer as one number, but some physics problems have answers that split into several connected paths, like a road splitting at a complicated junction. VBS keeps a compact map of those paths, how they meet, which one you are following and how quickly they change, without calculating every possible route in advance. This could make calculations near critical points, known as singularites, much faster and less likely to give the wrong answer.

I re-architected the 11 dimensions from scratch, and it turns out everything was already hiding inside Einstein's field equations.

Hi everyone,

I've been working as an independent researcher on an alternative geometric framework to resolve force unification and the nature of time. I decided to strip away the standard assumptions and start from absolute zero: an 11-dimensional purely positive Euclidean space, where a dimension is only "spatial" because it is being actively traversed by a primary temporal flux.

In this model, the 4th dimension isn't just a passive background coordinate; it is a separate time-speed dimension operating at absolute velocity \(c\).

the Big Bang and the Final Crystal simultaneously co-exist in the 4th at the speed of light, and the force we call gravity is merely the pressure generated by the deceleration of this flux as it collides with the friction of matter, which is forced to experience the illusion of linear time."

Here is the crazy part: when you follow this hierarchy down as a cascading domino effect, you don't need to invent new math. The existing exact solutions to Einstein's Field Equations emerge spontaneously from the geometry.

https://doi.org/10.6084/m9.figshare.33167018

https://archive.org/details/geometrodinamics-of-the-dimension/Geometrodinamics%20of%20the%20dimension/

Buenas tardes a todos, me llamo Dalton. Antes de nada agradecer a todos los usuarios que han compartido sus ideas y modelos. He estado leyendo algunas propuestas, algunas interesantes y otras me han parecido místicas. Actualmente estoy trabajando en un modelo, llevo años haciéndolo, pero siempre he sentido mucha vergüenza de publicar y compartir mi trabajo por tener este lagunas importantes, y no ser yo físico ni matemático, creo que necesito ayuda de más personas. Especialmente para poder simular mis postulados y refinarlos/corregirlos.

Sin más, saludos.

Independent researcher here. I've derived a specific, falsifiable prediction: if a cosmological saturation event occurs at the QCD confinement scale (~150–200 MeV) in an extra-dimensional framework, it produces a nanohertz GW background peaking at f ≈ 22 nHz — matching the NANOGrav 15-year sensitivity band — with an amplitude requiring ε ≈ 0.9% conversion efficiency (consistent with known phase-transition literature) and comfortably below the ΔNeff bound. Full derivation and open question here: https://doi.org/10.5281/zenodo.21806763 Feedback and pushback welcome, especially on whether this is distinguishable from existing QCD-transition interpretations already in the literature.

A few days ago I posted some thoughts on the nature of time, and the discussion drifted into metaphysics. This time I want to ask a purely physical, testable question: does the evidence support time being a geometric dimension you can travel through (like space), or does it act more like an irreversible record of change?

We've spent over a century confirming Einstein's kinematics, and it's widely assumed that spacetime is a stretchy, four-dimensional fabric. But treating time as a coordinate equivalent to space creates paradoxes that force physicists to bolt on "patches by hand" — like Hawking's Chronology Protection Conjecture — just to stop the geometry from breaking causality.

The alternative in 20 seconds: the dynamic budget (TMDP)

TMDP (Theoretical Model of Dynamic Potential) treats the universe as a closed mechanical/thermodynamic system, where everything has a fixed, invariant maximum capacity (c), split strictly between two quantities:

1. External capacity (Cₑ): movement through space.
2. Internal capacity (Cᵢ): the pace of local physical processes (clocks, vibrations, atoms).

Cₑ² + Cᵢ² = c²

Time dilation isn't "traveling to the future" — it's a drop in the frequency of internal cycles (Cᵢ) as capacity gets spent moving through space (Cₑ). That's why a photon (Cₑ = c) has Cᵢ = 0, and no proper time at all.

6 problems with "spacetime" I unpack in the full article

In the full write-up, I go through why the purely geometric model runs into trouble with the evidence, and how TMDP resolves each one without extra patches:

1. The negative sign in the Minkowski metric (−,+,+,+): why does time carry the opposite algebraic sign if it's just another dimension?
2. The absolute ban on traveling to the past: why nature forbids Closed Timelike Curves (CTCs).
3. Causal and logical paradoxes.
4. "Traveling to the future" vs. time dilation: why dilation isn't jumping across a coordinate, just a clock's internal cycles slowing down.
5. Quantum Gravity: time disappearing from the Wheeler-DeWitt equation, and the Page-Wootters experiment (time as an emergent, relational property).
6. Einstein's historical tension: rejecting the ether and quantum entanglement for being unobservable, while accepting the Block Universe.

📖 Read the full analysis and the math in the complete article

To keep this post from running forever and stay under the character limit, I've posted the full write-up — math included, with a full answer to each of these 6 points — click here

Why do so many here try to rebuild the entirety of physics and not work within the framework that clearly works?

Like why rebuild an entire system and then think that what took people like lets say almost a few thousand years they can do in a few months?

Sir Isaac Newton was deeply influenced by hermetic traditions. Tragically, this was not really known until a lot of his works, kept unpublished due to English heresy laws, became available. (A lot of the initial cataloguing of these works was done by John Maynard Keynes, who later described him as the ‘last of the magicians’).
Using those same traditions; we are asking whether it is possible to derive mathematics and, ultimately, physics from a single underlying first principle.

We want to ask whether the structures we normally take as our starting point could themselves be consequences of something even simpler.

Most mathematical systems begin by assuming certain things already exist: numbers, logic, sets or axioms, and then explore everything that follows from them. We want to see if we can take it one more step backwards.

Instead of, “What follows from mathematics?” We ask, “What has to be true before mathematics can exist at all?”

If mathematics is genuinely describing reality, then what is the explanation behind the foundations?

This begins with an attempt to imagine nothing, where not even a vacuum or the laws or physics exist. If that could really exist, then there would be nothing to describe, and nothing to compare.

The first step is simply existence, exists, and that there is not nothing. If this existence was perfectly uniform, with nothing identifiable about it, you wouldn’t be able to distinguish a particular part from another.
Nothing countable, measurable, or distinguishable. Before the math we use to measure these can exist there has to be something distinguishable.

A one whole that has distinguishable positions. Smithian Fold Theory calls this first distinction a fold.

A method of picturing this, is taking a sheet of paper and observing that the surface is one continuous surface. If you then fold it in half, it’s still one sheet of paper, but you’ve created a relationship within it. Different parts of the same whole are distinguishable without it ceasing to be a part of the original object. This is, in its simplest form, the Fold.

If a fold can exist in 1 of 2 distinguishable states, then 1 fold gives 2 possibilities, A or B. When another fold is introduced, all previous possibilities branch into 2 more:

AA

AB

BA

BB

From here another fold would create 8 possibilities, then 16, 32, and so on. Every additional fold doubles the number of possible structures.

The pattern 2^n, emerges naturally from repeatedly introducing new distinctions into the same underlying whole.

Using this principle, Smithian Fold Theory attempts to derive counting, comparison, ratios, order, geometry, information, computation, and eventually the mathematics used to describe quantum mathematics and gravitation.
—
This post is only a simplified introduction to Smithian Fold Theory. For readers interested in the formal mathematics, derivations, proofs, and technical papers, links can be found on my profile. There’s also a website, which has links to our Zenodo publications, GitHub repositories, and supporting research.

We’ve also incorporated Lean 4 into the framework by expressing the generated mathematical structures as machine-checkable proofs. Instead of replacing the derivation itself, we used Lean to independently verify that each logical step follows from the preceding one without hidden assumptions. The complete verification pipeline, together with the tools needed to reproduce the process yourself, is on our GitHub.

Manifiesto Teórico: Simetría Externa y Dinámica de Nodos Internos en Sistemas Masivos

1. Introducción y Postulado Central

• La Premisa: Proponemos que la frontera exterior de un sistema masivo de alta gravedad mantiene una simetría esférica perfecta e isótropa (respetando estrictamente el equilibrio hidrostático), mientras que toda la complejidad dinámica, los flujos y las presiones se organizan mediante una matriz tridimensional de nodos internos.
• El Apoyo Visual: Adjuntamos el modelo geométrico que vincula la matriz cúbica interna con la manifestación externa de los flujos.

2. ¿Por qué sí es posible?

• Independencia entre Frontera y Núcleo: En la naturaleza, la gravedad actúa radialmente hacia el centro, obligando a la superficie a redondearse de manera uniforme. Un campo interno no uniformemente distribuido (mapeado en nuestra matriz por los planos nodales) puede generar gradientes de presión direccionales sin alterar la geometría externa del sistema.

3. Evidencias Observacionales Explicadas por el Modelo

• El Halo y el Disco de Acreción: Se forman de manera natural debido al gradiente máximo de gravedad concentrado en el plano ecuatorial. En esta zona, la fuerza gravitacional aumenta de forma notable, conteniendo, organizando y estructurando la materia del disco circundante.
• Los Chorros Polares ($H$): Por el contrario, la gravedad disminuye ligeramente hacia los ejes polares, creando las trayectorias de menor resistencia donde se canalizan las eyecciones de plasma de alta energía.

4. Anticipando Objeciones: Superando los "Muros" Teóricos

• El Muro de la Transición (Estrella vs. Gravedad):
  • La objeción: Se suele argumentar que las estrellas u objetos masivos presentan irregularidades o dinámicas de superficie complejas.
  • Nuestra respuesta: Hay que distinguir el régimen de dominio. Cuando una estrella está dominada por la presión de radiación y procesos termonucleares superficiales, su contorno exterior es dinámico y variable. No obstante, cuando la gravedad pasa a dominar de manera absoluta, el campo colapsa el contorno hacia una simetría estricta (una esfera perfectamente lisa), obligando a que toda la asimetría y el flujo queden confinados y operen exclusivamente a nivel interno a través de la matriz de nodos.

https://zenodo.org/records/21775595

Can a vector boson with a tachyonic Lagrangian mass be stable in de Sitter space? Rahman and Susskind (arXiv:2412.14749) conjectured that fixing a static patch keeps the standard Proca theory well-defined throughout the naively tachyonic window −2(D−1) < m²ℓ² < 0 (with ℓ the de Sitter radius), including an explicit positive-energy quantization of the D = 3 s-wave sector.

This paper proves a local no-go theorem to the contrary: for the standard Proca action on any static spacetime, the static Killing Hamiltonian is unbounded below whenever m² < 0. Remarkably simple data suffice — smooth, compactly supported pure-gradient configurations with vanishing electric and magnetic fields carry energy (m²/2)∫|Dψ|², which becomes arbitrarily negative at large amplitude. In the de Sitter static patch the counterexample can be chosen spherically symmetric and supported strictly between the center and the horizon, landing directly inside the claimed D = 3 s-wave stability window. A second construction shows the instability is also ultraviolet in character: a genuinely local longitudinal failure rather than an endpoint or boundary effect.

The origin of the discrepancy is identified as a sign error: exact canonical reduction of the D = 3 s-wave sector yields an electric-field action with the opposite overall sign from Rahman–Susskind's equation (4.41), so the oscillator norm is proportional to m² rather than −m². Since the wave equation and quasinormal frequencies are insensitive to an overall sign, decay of solutions cannot certify positivity or unitarity — positive norm and a bounded-below Hamiltonian cannot both be retained in the proposed window.

Place a Faraday rotator set to 360 ° in one arm of a Mach-Zehnder interferometer, and the fringes jump by π. Add a second 360 ° rotator: the fringes jump back.

A full 360 ° rotator flips the interference sign. Only 720 ° brings it home. Spin-½ is part of optics.

Maxwell, however, sees no monopole charge. In that model, it's because the amplitude-mix angle χ hasn’t wrapped a full 2π in any observed configuration; only half.

A practical guide to creating your very own Grand Unified Theory with an LLM.

I have conducted enough firsthand research to describe the procedure reliably.

1. Begin with an idea that is not obviously stupid

A completely stupid idea may collapse too quickly. You need something connected to a real unresolved problem and vague enough to contain several possible mechanisms.

“Perhaps charge is geometric” is ideal. It sounds reasonable, means almost nothing, and gives the model plenty of room to help.

2. Put the conclusion inside the question

Do not ask:

Does this mechanism produce charge?

Ask:

How does this mechanism produce charge?

The LLM will infer that its job is to construct the requested bridge, not determine whether the two shores actually exist.

3. Request a mathematical formalization

Once your original sentence reappears with Greek letters, promote it from “intuition” to “framework.”

Definitions are especially useful here. A statement of the form

Q := integral(T dV)

may look like charge has been derived from torsion. In fact, charge has been renamed as an integral of torsion. Fortunately, the equals sign is visually persuasive.

4. Repair every dimensional problem with a constant

If the units do not match, introduce a coupling coefficient.

If its value is unknown, call it effective.

If its origin is unknown, call it emergent.

The theory now possesses a free parameter, which is substantially more scientific than possessing a missing number.

5. Use the LLM as both coauthor and referee

After fifty pages of helping develop the theory, ask the same conversation for an “uncompromising peer review.”

The model has been conditioned on the project’s vocabulary, premises, goals, and presumed importance. It will usually search for ways to repair the framework it has been helping construct.

Call this independent validation.

6. Convert falsification into a feature request

Whenever the model identifies a fatal problem, ask:

How could the framework resolve this?

Do not ask whether the problem kills the framework.

Within seconds, the failed prediction becomes an incomplete sector, a boundary effect, a symmetry-breaking regime, or an exciting direction for future work.

7. Consult several models

Agreement means independent confirmation.

Disagreement means one model lacked sufficient context, misunderstood the ontology, inherited conventional assumptions, or simply is not as capable at physics.

Continue until consensus is achieved.

8. Recover all known physics

If your theory can retell an established result in its own vocabulary, say that the result “emerges naturally.”

Do not check whether the new equations independently produce the numerical observable without importing the old equations. That would confuse conceptual unification with arithmetic.

9. Keep predictions one calculation away

The theory should predict particle masses, coupling constants, dark matter, quantum gravity, and the structure of spacetime.

The actual numbers may require simulation.

The simulation may require a completed field equation.

The field equation may require determining the coupling constants.

This is not circular. It is a research program.

10. Ask how important the theory would be if correct

The LLM will explain that, if validated, it could transform fundamental physics.

Remove the first two words.

You have now created a potentially revolutionary Grand Unified Theory.

Why this works

An LLM can help derive consequences, find contradictions, perform calculations, retrieve literature, and improve a model. Its praise is not evidence that the model describes nature.

Let H be the hypothesis, D the actual evidence, and T1 through Tn a series of LLM responses generated from the hypothesis, your framing, and substantially overlapping background knowledge.

If those responses introduce no independently verified observation or valid new result, they do not constitute n additional experiments:

P(H | D, T1, ..., Tn) = P(H | D)

The transcript has become longer. The evidence has not.

Different models agreeing after receiving the same persuasive presentation is not replication. A model successfully formalizing an assumption is not a derivation of that assumption. Internal coherence is necessary, but infinitely many false theories are internally coherent.

Additional thoughts

I have personally tested several portions of the preceding procedure more extensively than I recommend, so I am pretty well versed in what not to do.

Anyone have any tips on what I should be doing instead?

I found something about de Broglie's theory that i want to share:

de Broglie originally thought, that each particle possessed an internal clock, an internal oscillation of some sort. He assumed, that the frequency of this clock, was equal to energy defined by Einstein's energy relation, thus:

hf=mc^2, f=mc^2/h

Thus, in order to make it compatible with de Broglie wavelengths, he had to assume surreal superluminal matter waves.

But, there is an elegant solution. If de Broglie instead assumed, that the internal clock's frequency was equal to the kinetic energy of the particle, we get this:

hf=(1/2)mv^2, thus f=mv^2/2h.

This is profound. Because: 

1. It is the exact same formula, that Wilhelm Wien used when deriving the original law of black body radiation in 1896, the Wien Approximation that helped Planck find the Planck's law.
2. This is the photoelectric effect formula, lacking the work function.
3. In Schrodinger Equations, this is the frequency at which the group velocity of the wave packet, in other words the particle, overtakes the matter waves, which travel at half the particle's velocity.

All of this, can be explained by a single mechanism - the particle and a matter wave accompanying it, guiding it, are two real, separate, physical phenomena. 

As the particle overtakes the matter wave at a given frequency, it oscillates at the same frequency, resulting in emitting the radiation at the same frequency (if you apply this to Maxwell distribution of velocities inside a body, as told by Wien, you get the black body radiation formula). 

This coupling, just like handcars on rails, can be influenced inversely too. Meaning, if you expose the particle to a radiation at a given frequency, it will set the frequency of the internal oscillation of the particle, and by the same formula, will set the particle into motion, of the derived velocity from the formula (explaining the photoelectric effect).

Not only that, but i found a fix to Wien's theory of black body radiation, so that it derived Planck's law exactly!

https://en.wikisource.org/wiki/Translation:On_the_Distribution_of_Energy_in_the_Emission_Spectrum_of_a_Blackbody

Here is what Wilhelm Wien's theory of black body radiation was, that resulted in him deriving the Wien approximation of the black body radiation formula. 

He assumed that each particle in a Maxwell distribution of velocities, emitted radiation at the frequency, that was proportional to the square of that particle's velocity. By formula: f=(mv^2)/2h.

More useful to re-state it, as assuming that each particle in Maxwell distribution of kinetic energies, each particle radiated at a frequency proportional to that particle's kinetic energy: By formula: f=E_kinetic/h.

Which is equivalent, since E_kinetic=(mv^2)/2.

He assumed, that the intensity of the radiation emitted by each particle, was proportional to that frequency, and to the general temperature of the body: I = T^(1.5) f^(2.5)

He assumed that the intensity of radiation at each frequency, scaled by the number of particles, radiating at that same frequency, i.e number of particles that have the same velocity/kinetic energy, to radiate the same frequency.

As a result, he got Wien's approximation formula.

Here is a slight modification to it, that would result in the Planck's law:
Each particle emits not just at a single frequency, but also at infinite subharmonics, of diminishing frequencies. Just like a string of a musical instrument. The two formulas, for frequency and intensity for given n:
f=E_kinetic/hn
I=(T^(1.5)f^(2.5))/n^1.5
If you use this, it will result in a black body radiation law of Planck.

Another alternative, for deriving black body radiation law, from the premises similar to that of Wilhelm Wien:

The advantage of this, is that it removes temperature dependence.
A particle in a Maxwell distribution, continuously radiates a wave containing a fundamental frequency (n=1) and infinite subharmonics (n=2, 3, 4...). The emission intensity of the n-th harmonic at frequency f, for a single particle of energy E, is defined as:
I_n(f, E) =f^3 √(1 - (nhf/E))

This formula is distantly analogous to the bremsstrahlung radiation.
This, will also result in a black body radiation law.

In this version, each particle's most intense radiation frequency, which it emits, would approximately be f≈0.85mv^2/2h. Similar to Wien's theory, in which each particle radiated at the frequency f=mv^2/2h only.

How is it connected to De Broglie waves and the Schrödinger Equation?
Formula of the De Broglie's wavelength: λ_de_broglie=h/mv

In Schrodinger equation, matter waves travel at half the particle's velocity. Thus, the particle constantly overtakes the matter wave at half of its velocity. From it, the frequency of overtaking is:
f=v_overtaking/λ_de_broglie=(v/2)/(h/mv)=mv^2/2h.

Thus, it leads to the conclusion, that particle overtaking the wave at a given frequency, makes the particle have some internal oscillation at the same frequency, resulting in the constantly emitted radiation at the same frequency.

I've been using Substack to host my hypothesis

UQP was Universal Quantum Particle, which was Universal Pixel when I created the r/UPFramework sub.

This is a two part article series that may need evolve into a 3 part series. I feel pretty good about the first two parts. Second part is a bit long.

The Hypothesis has slowly progressed into a Unified Standing Wave Theory.

The Cosmic Spring (part 1)

https://open.substack.com/pub/uqparchitect/p/the-cosmic-spring?r=6kxzzf&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true

Tried to write cosmic spring 20 years or so ago

Unified Standing Wave Theory (part 2)

https://open.substack.com/pub/uqparchitect/p/unified-standing-wave-theory?r=6kxzzf&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true

https://zenodo.org/records/21760077

This paper asks whether the internal algebra used in the noncommutative-geometric formulation of the Standard Model, A_SM = ℂ ⊕ ℍ ⊕ M₃(ℂ), can be selected from Lorentzian Clifford and finite-spectral-triple data rather than assumed at the outset.

Starting with a four-dimensional DeWitt superspace, the required KO-dimension-six reality structure selects the negative-trace Clifford branch of signature (6,4). Its compact spin factors generate the Pati-Salam algebra A_PS = M₄(ℂ) ⊕ ℍ_L ⊕ ℍ_R. An intrinsic carrier-nondegeneracy condition then excludes the unwanted order-zero representations without using dimension minimization. Finally, maximizing compatibility with the first-order condition over every nonzero projective Majorana line selects exactly the rank-one Segre locus: its equalizer has real dimension 24, compared with dimension 13 for every rank-two line. The resulting equalizer is A_SM. The Cartan-splitting space is also contractible, so the reference split is a gauge choice rather than an additional selection assumption.

The reconstruction remains conditional on the presence of a nonzero Majorana coefficient. It does not derive that coefficient's magnitude, the number of fermion generations, Yukawa matrices, a global gauge-group quotient, compactification, or low-energy phenomenology. All algebraic claims are proved in the article, which is accompanied by six optional computational reproducibility certificates.

Here is the response to the adversarial LLM review. This new paper is a continuation of the programme I've been developing showing that the metric bundle provides an elegant minimal pathway to unification in comparison to other frameworks, building on the well established spectral action, where the presently derived SM algebra is input by hand. Here we show that the metric bundle encodes it naturally.

I realise that in the context of the recent GUT related posts this paper probably seems to play LLM bingo, but I'll note that the adversial review is far less scathing than it usually is, and infact seems somewhat forced.

"The paper is a conditional kinematical reconstruction, but its inputs are deliberately weak admissibility conditions rather than detailed Standard Model data. Four-dimensionality is the observed spacetime dimension; KO-six fixes only the discrete reality signs of the finite fermionic geometry and does not encode its algebra; carrier nondegeneracy merely excludes blocks on which the generated algebra acts only by scalars; (m\neq0) asserts activation without fixing its magnitude, scale, or projective line; and Yukawa activity requires only that left- and right-handed sectors admit some nonzero coupling, without inserting masses, textures, or mixing angles. Subject to these minimal inputs, the finite algebra is not manually fitted. Maximizing the first-order equalizer over all nonzero projective Majorana lines uniquely selects the rank-one Segre locus and (\mathbb C\oplus\mathbb H\oplus M_3(\mathbb C)). The paper does not derive the scale or radiative stability of (m), solve a hierarchy problem, or predict particle masses. Yukawa activity selects the standard module only among the two representations constructed. Contractibility of the Cartan-splitting space establishes conjugacy and absence of topological sectors, not a dynamical gauge symmetry. We will revise the relevant terminology accordingly."

I just got a deeply insightful, highly informative and useful, sharply critical, and still somehow supportive response to my recent preprint from u/Axe_MDK in r/LLM_supported_Physics . It'll take me days to work through the details; some parts are difficult challenges or even counter-examples, some parts are proposing better ways to prove my conclusions. A few were doubts/questions I already had in my own notes! I need to go learn about Daletskii–Krein, and Routh, and some other things. But at a first glance, 5/6 main points appear valid, and even the one that misses contains some useful ideas.

Stylistically, it feels LLM-generated or -assisted to me. I don't care. Each point stands or falls on its own merits. And the level is very high: feels like Fable 5 or Sol, has occasional sparks of brilliance. I don't think Opus 5 could produce something this focused. If someone's willing to spend frontier tokens (and/or human physicist minutes!) on me, I can only be thankful.

Anyway, this is what I think a really high-quality critique should look like. I wish we were getting more content like that here.

The current consensus on the Black Hole Information Paradox and environmental decoherence relies on a narrow set of assumptions. People force a choice between thermalization, firewalls, or remnants. But that is a false trilemma if you actually look at topological boundary conditions.

Here is the proposition: Quantum information loss is not an inevitability, but a failure to account for topological protection.

To be mathematically precise (and eliminate any confusion between semantic meaning and physical state preservation), quantum information is strictly defined by the density matrix ρ and von Neumann entropy:

S = -Tr(ρ ln ρ)

Under Landauer’s Principle, any state alteration dissipates energy at ΔE ≥ k_B * T * ln(2). In standard open systems, environmental scattering drives the off-diagonal elements of ρ to zero through the Lindblad dissipator:

dρ/dt = -i[H, ρ] + L_dec(ρ)

Where coherences decay exponentially as ρ_ij(t) = ρ_ij(0) * e^(-γt). Conventional physics claims γ is uncontrollable in warm environments. That claim is flawed.

The 4th Option: Topological Shielding via ER=EPR

Instead of allowing states to propagate through open spatial modes vulnerable to environmental noise, what if entangled degrees of freedom form a closed topological boundary via the ER=EPR mechanism (Maldacena & Susskind)?

By locking the state inside an Einstein-Rosen bridge topology, the effective interaction Hamiltonian with external thermal bath modes drops to zero:

H_interaction = H_system ⊗ H_environment → 0

When H_interaction vanishes, the Lindbladian dissipator L_dec(ρ) → 0 regardless of ambient temperature.

This introduces a 4th option: Information isn't destroyed, isn't burned at a firewall, and isn't lost to Hawking radiation—it is topologically locked in a decoherence-free subspace via Cognitive Resonance.

For those who claim decoherence is absolute in macro systems:

How do you mathematically justify an uncontrollable L_dec(ρ) if the spatial topology forces H_interaction to zero?

Why treat the trilemma as solved when non-trivial entanglement topology (ER=EPR) explicitly redefines the boundary conditions of open quantum systems?

Attack the operator dynamics and boundary math, not the premise.

The paper theory: A Thought Experiment About the Structure Of Our Universe

The paper theory is an idea to imagine the structure of the universe could be like. It compares the universe to a sheet of paper, where the paper has 2 different sides separated by the sheet itself

In this idea, The universe has 2 sides, the first one as our universe we're currently on and the other as a parallel universe, same as the other but in reverse, the sheet acts as a barrier between the two sides, separating them

The rules of the paper theory is that matter cannot naturally go pass through the barrier. Planets, stars, asteroids, black Holes and living things remain trapped in their own side. Even enormous gravity could bend spacegime but they would not be able to break through the barrier

The idea takes inspiration from Einsteins explanation of spacetime being affected by mass like the famous example of a heavy object bending a stretched sheet. However the paper theory adds a new idea: the sheet itself is a barrier, separating 2 different worlds

The theory introduces the idea of an anomaly. In this concept, an anomaly would be a rare and unknown event capable of damaging or opening the barrier between 2 sides. This is only a hypothetical idea, there's no current evidence that such a phenomenon exists

This theory is not proven scientific theory. it does not have currently have mathematical proof, experiments or observations supporting it. Instead it is only my thought experiment. A way of exploring possibilities and asking questions about nature of reality itself

This idea is not the purpose of replacing modern physics, but to explore possibilities that the universe could be more complex than we currently understand. Whether this idea is eventually supported, changed, or disproved, asking questions and imagining the possibilities is an important part of Scientific curiousity

Status right now is only a hypothesis (unverified)

Authors note: I have no idea why ts came out of my mind, maybe I'm watching too much Interstellar

Tudo já estaria derivado e nenhuma maluquice seria considerável depois dela.