The P vs NP Problem is a cornerstone of theoretical computer science and asks whether every problem whose solution can be quickly verified can also be quickly solved.
Formally, it questions whether the complexity classes P (problems solvable in polynomial time) and NP (problems verifiable in polynomial time) are equal. A proof either way would have profound implications for cryptography, optimization, algorithms, and beyond.
This problem is deeply connected to what we can feasibly compute — and what remains forever beyond reach.
The resolution of P ≠ NP presented here does not arise from brute diagonalization or oracle relativization, but from the internal logic of structure itself.
Through the lens of constructive resonance, satisfiability is reframed: solutions are not isolated endpoints but encoded rhythms — dispersed globally, impervious to local decoding.
Where the world of NP sees verification, structure sees reflection. But construction demands more: coherence that cannot be mimicked, only revealed.
This is not an attack on NP. It is a realization that computation has a limit — not of time, but of symmetry. In this limit, structure triumphs where algorithms fail.
If you are an arXiv member and believe this contribution deserves broader visibility, you may use the following endorsement code when supporting its publication:
Code: D9JE3Z
This is a one-time option to help open academic channels for independent, non-affiliated solutions.