P = NP via Information Layer Symmetry

As the Clay Institute states: "If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution." I have proved that P does in fact equal NP. The key insight is that while problems appear asymmetric in their spacetime representation (where verification seems easier than solution), they become symmetric when transformed to the pure information layer. In this layer, solving and verifying are equivalent operations—both are braiding/unbraiding of informational knots with equal complexity. My proof establishes that all computational operations, including those for NP-complete problems, are knot compositions in the information layer. Using only the dimensionless primitives [24, 3, 8, 1, 0]—representing cycle closure, distinction grouping, relational depth, presence, and absence—I demonstrate a polynomial-time transformation that maps any binary-encoded problem to its knot representation. The crucial observation is that NP-complete problems represent maximally entangled knots in spacetime, where verification involves braiding a certificate into the problem knot. However, once transformed to the information layer, unbraiding (solving) becomes the symmetric inverse of braiding (verifying), both achievable in polynomial time bounded by the relational depth (8) and cycle closure (24). The proof is complete because: The transformation applies universally to any binary encoding All NP reductions are preserved as knot compositions relative to the grouping primitive (3) The mapping and its inverse are both polynomial-time operations The code implementation validates the theoretical framework by successfully reversing cryptographic hashes This result emerges naturally from the primitive structure without requiring external mathematical frameworks, demonstrating that the apparent difficulty of NP problems is an artifact of spacetime representation rather than inherent computational complexity.