Why P ≠ NP: A Look Through Geometry, Physics, and Lattices

This preprint presents a new approach to the separation of complexity classes P and NP. Using geometric, algebraic, and spectral methods, the author constructs a framework that suggests the impossibility of solving NP-complete problems by polynomial-time algorithms. The result includes a proof sketch and several theorems leading to the main claim.

This English version is an automatic translation of the original Russian manuscript. I am not a native English speaker, and some parts may contain linguistic inaccuracies or formatting issues. The Russian version is the primary and more accurate version.

Feedback and corrections are welcome.

This version contains a contradiction between the "complex" function (ε=2^(—n)) and the statement of Algphys ⊆ P. The approach is currently being revised, but the concept will be retained.