Thoughtweave Geometry develops the formal structure by which multi-strand cognitive, computational, or generative processes interleave while remaining spectrally admissible. The paper shows that thoughtweaves—parallel control trajectories sharing operator substrates—must satisfy strict geometric constraints to avoid drift, interference amplification, or cross-basin semantic collapse. Admissible thoughtweaves require direction continuity, basin alignment, and gate isolation across strands, ensuring that interwoven processes remain stable within thin margins. The theory provides a complete geometric model for coherent, multi-threaded reasoning inside the Einsteinian Stack.