Quantum computes are believed to have higher capabilities than Turing machine, bringing question if our physics could allow for even better ways, like the main concern: does our physics allow practical NP-solvers?
I think about it for ~20 years and just worked with topLLMs on big review: https://zenodo.org/records/23125606 - would gladly discuss
Proposed e.g. in https://www.nature.com/articles/s41567-025-03107-0 , worked with Astra-Fable getting they claim good agreements - diagram from https://zenodo.org/records/22942341
Do they seem reasonable?
Halo ( https://en.wikipedia.org/wiki/Halo_nucleus ), borromean nuclei ( https://en.wikipedia.org/wiki/Borromean_nucleus ) hold 1-2 neutrons/protons in large distance for milliseconds, in "borromean" way like knots - could there be 1D structures physically connecting such halos, e.g. quark strings, gluon flux tubes, topological vortices like in https://www.nature.com/articles/s41567-025-03107-0 or shown https://zenodo.org/records/22886273 diagram?
Worked with Astra on symmetric Cyclic Universe hypothesis, repairing hidden asymmetries - leading to conclusion that black holes from second boundary fit well mysterious Little Red Dots: https://zenodo.org/records/22666157
Here is continuation on consequences, e.g. leading to this nice Astra's summary: https://zenodo.org/records/22702753
Do you agree/disagree with this summary?
In liquid crystal they experimentally get point-like quantized topological charges with Coulomb-like interactions ( https://www.nature.com/articles/s41598-017-16200-z ), or topological vortices and their various size knots resembling nuclei ( https://www.nature.com/articles/s41567-025-03107-0 ). Here are Fable-based tests of various models of particles, and liquid crystal-based wins.
So I wanted to propose a discussion if particles around could be of topological nature?
Standard Model is extremely well tested, but e.g. is incompatible with general relativity, is rather for effective perturbative approximations, also uses this gigantic Lagrangian found in epicycle-style: by guess&fit terms.
So maybe like in Copernican Revolution, we should search for compact deeper nonperturbative Lagrangian (e.g. Skyrme-like), effectively described close to Standard Model + gravity?
Nonperturbative Lagrangians look simple, but have extremely complex consequences - maybe AI could search through them, automatically performing simulations testing various agreements?
This kind of approaches have already started, e.g.:
Towards AI-assisted neutrino flavor theory design": https://www.nature.com/articles/s42005-026-02627-2
"Agentic Exploration of Physics Models" https://journals.aps.org/prx/abstract/10.1103/xnqc-q6nt
https://github.com/openwave-labs/openwave/blob/main/MODELS.md actually testing such deeper Lagrangian candidates - currently winning is liquid-crystal-like: just assumption that field has preferred anisotropy.
What do you think about such approaches?
Where to search for such deeper Lagrangian?
The goal here is searching for deeper non-perturbative Lagrangian e.g. Skyrme-like, which effective behavior agrees with Standard Model Lagrangian.
This environment uses AI-agents to write simulations for given Lagrangian, testing agreement of various properties. Current summary:
| Status | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M4) |
|---|---|---|---|
| ✅ validated in-platform | 8 | 4 | 0 |
| ⚠️partial / with caveats | 8 | 5 | 8 |
| ❌ honest negative | 0 | 0 | 3 |
| 🔶 in progress | 0 | 0 | 0 |
| 🚧 planned / not yet | 5 | 12 | 10 |
| Total criteria | 21 | 21 | 21 |
https://github.com/openwave-labs/openwave/blob/main/MODELS.md
OpenWave's mission is to build a platform where multiple candidate field-theoretic models are evaluated numerically, side by side, in the same computational environment. No single alternative framework can map the space of possibilities on its own: when several independent models are run against the same observables with the same pass/fail criteria, the comparison triangulates what is actually out there.
There is this basic similarity test Tr(A^k) = Tr(B^k) for k=1..d for symmetric matrices allowing to conclude existence of orthogonal O such that AO = OB.
The question is how (if possible?) to generalize it (finally to tensors, but at least) to non-symmetric matrices e.g. including transpositions.
Checking Jacobian criterion ( https://arxiv.org/pdf/2601.03326 ) for Tr(A^k (A^T)^j) = Tr(B^k (B^T)^j) for k=1..d, j=0..k-1 at least for up to d=5 has sufficient number of independent invariants (d(d+1)/2) - is it sufficient condition in general dimension?
Maybe such generalized similarity test is considered in literature?
There is this basic similarity test Tr(A^k) = Tr(B^k) for k=1..d for symmetric matrices allowing to conclude existence of orthogonal O such that AO = OB.
The question is how (if possible?) to generalize it (finally to tensors, but at least) to non-symmetric matrices e.g. including transpositions.
Checking Jacobian criterion ( https://arxiv.org/pdf/2601.03326 ) for Tr(A^k (A^T)^j) = Tr(B^k (B^T)^j) for k=1..d, j=0..k-1 at least for up to d=5 has sufficient number of independent invariants (d(d+1)/2) - is it sufficient condition in general dimension?
Maybe such generalized similarity test is considered in literature?
There is this basic similarity test Tr(A^k) = Tr(B^k) for k=1..d for symmetric matrices allowing to conclude existence of orthogonal O such that AO = OB.
The question is how (if possible?) to generalize it (finally to tensors, but at least) to non-symmetric matrices e.g. including transpositions.
Checking Jacobian criterion ( https://arxiv.org/pdf/2601.03326 ) for Tr(A^k (A^T)^j) = Tr(B^k (B^T)^j) for k=1..d, j=0..k-1 at least for up to d=5 has sufficient number of independent invariants (d(d+1)/2) - is it sufficient condition in general dimension?
Maybe such generalized similarity test is considered in literature?
ps. cross from https://mathoverflow.net/questions/512227/how-to-extend-operatornametrak-operatornametrbk-similarity-test-to