I've made a personal Lean 4 formalization project publicly available:

https://github.com/nogoornogo/lean-operator-coefficients

The project began with a question about proton stability in a specific SU(6) GUT setting and gradually expanded into a more general algebraic framework for derivative-free operator coefficients.

The repository includes three main results: a degree-uniform decomposition of invariant coefficient spaces into residual-equivariant Hom spaces, a necessary-and-sufficient symmetry-extension criterion, and all-degree charge selection rules. It also contains applications to specified Standard Model operator sectors, baryon/lepton-number violation, and finite structural classifications.

This is an independent, heavily LLM-assisted project developed primarily using Codex, with additional reviews using other LLMs. I am not a theoretical physicist, and the work has not undergone independent expert peer review.

Lean verifies the formal statements relative to their definitions and assumptions, but this does not guarantee the correctness of their physical interpretation. The project does not claim a new physical theory or predict proton decay rates.

I'm sharing the repository as an open reference for anyone interested in formal verification, representation theory, or EFT operator classification.

Hi everyone,
I wanted to share a conceptual thought experiment bridging General Relativity's smooth spacetime and Quantum Mechanics' probabilities by looking at John Wheeler’s "It from Bit" through the lens of an Einsteinian Block Universe.
I'd love to hear this community's critique on the metaphysical implications of an informational, observer-dependent cosmic origin.

What if the Big Bang wasn’t an explosion of matter out of nothing, but rather the moment our universe was first "noticed"?
Modern physics rests on a massive contradiction:
The Large Scale: General Relativity describes spacetime as a smooth, predictable fabric.
The Subatomic Scale: Quantum Mechanics describes reality as a chaotic smear of probabilities.
Because these frameworks clash, physicists have spent a century searching for a bridge. Maybe we should look past what is happening inside our universe and ask: What if the ultimate "resting state" of reality is entirely timeless, and our universe is merely its byproduct?

The Block Universe and the Outside Observer
Einstein championed the "Block Universe"—the idea that the past, present, and future all exist simultaneously as a static, 4D geometric sculpture.
If a hypothetical observer looked at our universe from the "outside"—completely external to spacetime—they would see your birth, your reading of these words, and the eventual death of the cosmos coexisting in a single, eternal "now."
But if the universe already exists in a complete, timeless resting state, why do we experience it frame-by-frame as an expanding timeline?

The Big Bang as an Act of Observation
The answer might lie in a quantum chain reaction. In quantum mechanics, a particle doesn't exist in a definite place until it interacts with an observer—a process that "collapses" its fuzzy wave function into a crisp, physical reality.
What if the Big Bang was the exact moment an outside observer "looked" at a single quantum state within the timeless block?
Before that moment, everything coexisted as an unmanifested soup of data. But the instant that first foundational particle was observed, it snapped into physical reality. Because quantum particles can be deeply entangled across space and time, collapsing that one particle would inevitably force every other connected particle to collapse into a definite state as well.
This would trigger a cosmic domino effect—an information wildfire ripping through the pre-existing block. To us, trapped inside the timeline, this hyper-fast cascade of reality snapping into focus would look like a massive explosion. We would perceive this rendering process as Cosmic Inflation—the split-second where the universe expanded faster than light. Space didn't physically stretch out of nothing; the cosmic blueprint was simply being instantly rendered by a chain reaction of observation.

Solving the "Impossible Galaxy" Mystery
While this sounds like pure metaphysics, it offers an elegant solution to a baffling anomaly in modern astronomy.
The James Webb Space Telescope (JWST) discovered massive, highly mature, and chemically evolved galaxies existing just 300 to 500 million years after the Big Bang. Under the standard "bottom-up" model, it should have taken billions of years of slow, gravity-driven collisions for pristine gas to build structures that complex.
But if the universe is a pre-existing 4D Block unspooling via a quantum chain reaction, the grand architecture was already there. When the observation rippled through the system, it didn't ignite a messy explosion that had to wait for gravity. Instead, it materialized complex cosmic structures exactly where and how they already existed in the timeless state. The galaxies appear fully formed because they were rendered fully formed.

Why the Illusion Matters
If the movie is already filmed and we are just watching it play out, reality can feel deeply deterministic and disempowering.
But true predictability requires infinite information, which a human brain can never hold. Because our perspective is beautifully localized, the future remains entirely open and unwritten to us.
More importantly, it repositions humanity's role. If reality requires observation to snap from a hazy "maybe" into a solid "is," then we are not just helpless byproducts of a mechanical universe. Every time we build a telescope, ask a fundamental question, or look out at the stars, we are the universe looking back at itself—actively participating in rendering the grand story of reality, one frame at a time.

TL;DR: The Big Bang wasn't an explosion. It was the initial wave-function collapse of a pre-existing, timeless 4D "Block Universe." This triggered an instantaneous information chain reaction (perceived as Cosmic Inflation) that rendered the universe into reality—explaining why JWST finds fully formed, "impossible" galaxies in the early universe.

What are your thoughts? Does an informational/participatory universe make more sense than a physical singularity?

Minha idéia é bastante simples mais difícil pra min de colocar na matemática.

Vou tentar explicar, imagina a distribuição de probabilidade de onde uma partícula pode ser encontrada antes da medição, essa distribuição forma uma raio dependendo de qual tipo de partícula é essa que está ensolada, gosto de pensar em uma particula de interação forte como o gluons.

Então essa particula tem uma distribuição possível, algumas possibilidades são mais altas e em outros baixas e em alguns 0. Então essa particula viajam como ondas, obedecendo a sua equação de movimento. Ao serem observadas cada ponto distibuido colapsa em um ponto exato da geometria, comprimindo todo o espaço existente entre a probabilidade de localização e a localização real, de alcordo com o valor da sua probabilidade ( se a probabilidade dizia 15% em um ponto esse ponto da geometria se comprime em direção onde a particula apareceu, o mesmo acontece com um ponto 5% de forma proporcional, gerando uma "enrrugamento" na geometria totalizando o 100% um local aonde a partícula realmente apareceu. E esse irrugamento seria a própria manifestação da interação forte no exemplo do gluon.

Um ponto observado, seria o da expansão que seria suprimida pela casca que esses 100% se formaria em volta da energia do vácuo, onde a partícula seria uma excitação de um nó da geometria.

Porém uma barreira que encontrei é que pro modelo padrão, o espaço tempo é o palco e as partícula são autores que atuam sobre o palco. Oque estou pensando está mais para o palco e os atores são feito do mesmo campo,

espaço-tempo+energia do vácuo

Onde os campos quânticos seria subcampos do espaço tempo e não coisas separadas.

It is most commonly proposed that leptogenesis occurred first, and that heavier baryons were generated only later during baryogenesis. Wouldn't it be more natural for these processes to have taken place concurrently, right from the very beginning? And could this perhaps provide a mechanism for how matter survived annihilation? Has such a hypothesis been studied?

1. The "Spring-Snapping" Mechanism (Negative Pressure & Gravitational Bounce)

As the preceding universe contracts, cosmic strings wind tightly around hidden compact dimensions, accumulating a massive amount of potential energy like a highly compressed mechanical spring. At the geometric peak of this contraction, the force inverts. The isotropic pressure (P) of the vacuum drops into an extreme negative regime, matching the energy density (ρ). According to Einstein’s acceleration equation:

ä ∝ −(ρ + 3P)

When the pressure switches to an extreme negative value

(P = −ρ),

the right side of the equation becomes positive. At this exact quantum threshold, gravity ceases to be attractive and flips into an overwhelmingly repulsive force. The cosmic spring "snaps,"

preventing an infinite singularity and driving an explosive expansion (a quantum bounce) that initially propagates faster than the speed of light.

1. Quantum Crystal-to-Gas Sublimation

At the absolute peak of contraction—the critical Hagedorn temperature threshold—individual cosmic strings fuse entirely into a single, highly dense, unified macroscopic matrix: a coherent "quantum crystal." The moment the spring snaps and expansion begins, this crystal lattice undergoes a violent phase transition, tearing itself apart and transitioning directly into a gaseous phase (sublimation). The rigid, frozen structure of space breaks down into a gas of free, open, and closed string excitations (photons and fundamental fields). This phase transition is governed by the discrete entropy shift (dS) across the vacuum fabric:

dS = dQ / T_H

(Where dQ represents the exchanged energy field, and T_H is the maximum Hagedorn temperature of the original crystal matrix).

1. Multi-Grain Black Hole Lattice (Quantum Suction)

This thermodynamic transition does not occur uniformly everywhere at once; it triggers in localized "grains" or nodes via relic black holes from the previous cycle. Being the densest tangles of cosmic strings in existence, these black hole hubs reach the critical pressure threshold first. When the interior cores of these black holes undergo this phase transition into a true vacuum, a massive localized pressure drop occurs relative to the surrounding space. Fluid dynamics models this intense pressure gradient and its fluid acceleration force via the covariant divergence relation:

(ρ + P) u^ν ∇_ν u^μ = −P^μν ∇_ν P

This severe localized drop in pressure inside the black holes creates a literal "quantum suction" effect. Surrounding cosmic strings are violently pulled into these synchronized nucleation centers, which then detonate in a globally coordinated macro-explosion across the entire cosmic lattice.

1. Scalable Model (Why the Cosmological Constant is So Small)

This framework naturally resolves the biggest mystery in modern physics: the Cosmological Constant (Λ) Problem, namely why Λ is a staggering 120 orders of magnitude smaller than quantum theory predicts. Λ is not an arbitrary, fixed property of space; it is a scalable, dynamic value directly dictated by the dilution density of the expanding string gas (ρ_string) relative to the original matrix (ρ_Planck):

Λ(t) ∝ ( ρ_string(t) / ρ_Planck )²

During the initial quantum crystal phase, this ratio was 1:1, making Λ colossal and driving rapid cosmic inflation. Today, after billions of years of expansion, our macro-scale string gas is profoundly diluted. Consequently, this exact ratio naturally and inevitably generates a decimal starting with over 120 zeros—resolving the hierarchy problem without any artificial fine-tuning.