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Sequence is the critical determinant of macromolecular function, yet current polymer design approaches often optimize monomer composition and ratios while ignoring sequence. This creates poorly defined design spaces for active learning that miss the vast combinatorial landscape of sequence possibilities. We introduce ChainSpace, a computational framework that maps synthetically accessible sequence space through four orthogonal control mechanisms: compositional (random copolymerization), kinetic (relative reactivity differences), temporal (staged monomer injection), and spatial (post-polymerization functionalization). Using three orthogonal descriptors (second eigenvalue λ₂, Shannon entropy, and mean run length), we characterize sequence statistics across experimentally achievable synthesis conditions. Parameter space exploration reveals that accessible sequences form a curved three-dimensional manifold with distinct regions accessed by different synthesis strategies. Kinetic control provides the broadest sequence access, temporal control enables highly blocky architectures, and spatial control favors alternating motifs. We demonstrate this framework using cationic polymers for gene delivery, where sequence statistics correlate with transfection efficiency and salt resistance. A top-performing, multi-component gene delivery polymer achieved 85% transfection efficiency, with sequence analysis revealing optimal blockiness and entropy values. This sequence-centric approach provides a systematic foundation for active learning design spaces, enabling rational navigation of sequence space that is especially useful for the advancement of multimonomeric polymers for industrially relevant end-use technologies.