Conventional protein folding methods rely on computationally intensive molecular dynamics or iterative optimization heuristics. This work introduces the Chimera framework, which employs a fast 6-degree-of-freedom (6DoF) geometric resolver to map the manifold of physically allowed backbone rotations. A specialized Transformer is trained on high-fidelity “Geometric Truth” extracted from 37 high-resolution PDB structures. The resulting model solves protein structures including unknown segments (“Z-gaps”) in amortized constant time (≈2 ms per protein on consumer Apple Silicon hardware) with sub-ångström backbone precision (motive MSE ≈ 0.0197 on benchmark structures). We demonstrate high throughput (∼43 million proteins/day), effective de-novo bridge sequence design via geometric smoothness and clash scoring, and strong generalization on synthetic chimeric sequences. The approach reframes folding as deterministic manifold projection rather than search, offering a scalable path toward real-time structural biology and therapeutic protein design. Source code and the trained UFT-Global-Brain-V2 weights are provided to ensure full reproducibility of the $O(1)$ benchmark.