Entanglement Without Spookiness: Shared Origin, Product Structure, and Correlation Without a Travelling Signal

Entanglement is derived as one composite state with two local readings, not communication between independent objects. From one machine-checked self-proven theorem, zero axioms and zero fitted parameters, the coprime periods 2 and 3 generate one joint period 6. The shared dimension 15 supplies one origin 1/15, and the fold advances the same connected orbit to 2/15. The complete composite walk sends 8/15 to 1/15 while its local shadows move from (2,3) to (1,1) together, with both local laws agreeing. The no-signalling route derives channels 2/3 and 1/3, proves that they partition the One, cycle into each other and remain closed under their difference. No third signal carrier is generated. The result is deterministic, nonlocal, no-signalling and fully inspectable. It connects the formal derivation, exact implementation, independent certificates and empirical Bell programme without treating opaque statistical prediction as the authority over structural proof. Scientific author and publication authority: Maria Smith, Ernos Labs. Open source: Smithian Fold Theory of Everything.