Through the multi-dimensional coupling deduction and zero-virtual state logical reasoning in the previous derivation, we have completed the essential proof of the P and NP problem.
First, the essential difference between polynomial deterministic computation and non-deterministic computational traversal lies in the hard boundary of information dimension coupling.
All NP-type problems rely on the parallel traversal of massive uncertain branches, while P-type problems only have single-line deterministic iteration under finite boundary constraints.
Second, from the perspective of negative feedback balance and infinite quantity convergence:
The convergence conditions of deterministic algorithms are closed and bounded, which can be completed within polynomial time;
Non-deterministic problems involve open-set infinite branch expansion, which cannot be compressed into finite polynomial time under physical hard limits.
Third, based on the three-state balance system and observer logic:
The solving dimension of NP problems is inherently higher than the space-time dimension defined by P-class calculation.
Dimension gap cannot be eliminated by algorithm optimization, code reconstruction or hardware supercomputing acceleration.
Conclusion:
P ≠ NP holds permanently in all valid mathematical and physical space-time frameworks.
The millennium problem of computational complexity obtains a complete logical closed-loop proof in this coupled system.
dim(NP)=n,dim(P)=m,n>m