u/ConsciousnessNCosmos

Weekend TOE: I would really love to engage on this idea, but it would be a wall of text to present it all here so I'll link to the three foundational papers and full manuscript for reference:

The idea: A fibration of cohesive infinity slice toposes generates physics from the 2-cells between the different nodes in the tower. Typically, the cohesive topos is selected by the gauge groups being studied and serves as a static taxonomy for the theory, but I am working on an algorithmic/constructive Spectral Realization process that generates physical dynamics with the construction of the spectra as witness terms to the identity type associated with that node in the tower. This proves the DCCT applies to the tower, and gives Scholze's Gestalten sequence.

In this theory the gauge groups correspond to their own slice toposes, and the theory derives the standard model by adding the Lorentz group to the standard gauge groups, as the whole theory is background independent.

The papers attempt to formalize the theory's foundations, while the manuscript (7471) outlines my complete vision for the theory *be warned, it's heavy with metaphorical terms and might extend beyond the bounds of the sub.

As just stated, I'm not sure about the limits of discussions here, but hope this can be a good one. I am most interested in getting my foundations (the 3 papers) correct, but also have physical predictions and much more detail I can share. I don't want to overwhelm this first post, so I'll just share 2 highlights:

I have a map of this year's arXiv papers that relate to this theory hosted on my personal website, so I'm not sure if I can link that per the sub rules; if someone let's me know I will edit this to provide the link. Here's an example:

My framework predicts these results correspond to the same phenomenon (dark matter mass generation (Chapter 6 of 7471): https://doi.org/10.1142/S0217751X26460139, https://doi.org/10.48550/arXiv.2606.23418

My theory indicates an extension of Smith's dictionary from the logical side to the physical side:

https://preview.redd.it/uccu0339rs9h1.png?width=783&format=png&auto=webp&s=26c2cf1b1e9772a276f7d065317932fdb49666f8

Let me know what you think!

Here is a hypothesis: Instead of just serving as a static map, the differential cohomology diagram can be used to model a constructive approach to topological quantum field theories.