Hi everyone,
I’m a student with a strong interest in computer science and complexity theory. Recently, I worked on a manuscript attempting to prove that P ≠ NP.
I know how this sounds — it’s one of the hardest and most debated problems in CS, and many have tried and failed. I don’t claim to have the final answer, but I believe the approach I used might at least offer some fresh perspective or provoke useful critique.
The idea involves geometric separation between deterministic and nondeterministic computation, using high-dimensional lattice constructions and some physics-inspired intuition. The full argument is technical, but I tried to keep it logically structured.
The preprint is 93 pages long. It was originally written in Russian, and I created an English version via machine translation, so apologies in advance for awkward wording or formatting.
DOI and full paper (both languages):
https://doi.org/10.5281/zenodo.16759468
I’m genuinely open to feedback — whether it’s pointing out flaws, questioning assumptions, or just explaining why this approach doesn’t work. Any form of critical input is welcome.
If there’s interest, I can also create a short video explanation in simple terms to walk through the core ideas — even though I don’t have a channel or any audience yet.
Thanks in advance for taking the time, even if it’s just to skim or tell me what to fix!
Isn’t it possible that your "hard" instances could be solvable in polynomial time by some algorithm that doesn’t rely on geometric modeling or Hamiltonian dynamics?
How do you justify that every polynomial-time Turing machine algorithm can be modeled as a trajectory in your Hamiltonian system?