Persistent Chiral Hodge Responses: Molecular Topology, Constrained Geometry and Stereoselectivity

Distance-based molecular topology is reflection-even and cannot alone encode handedness. We construct reflection-odd cochains propagated through a real persistent Hodge Laplacian and paired with even probes. Proofs establish inherited-metric and spectral-detection statements, topological obstructions to complete odd readouts, and intrinsic shape derivatives. One connected extension develops conformer-law geometry and realizable constrained motion: odd Gaussian embeddings expose a molecular rank bottleneck, while stress compatibility distinguishes infinitesimal flexes from finite motions. A frozen analysis has full numerical torsional response rank in 204 of 206 isomers. Mechanical connections supply horizontal molecular vector fields, noncommuting lifts and rotational holonomy. Closed-form analysis defines an effective nuclear torsional Hamiltonian, proves mirror isospectrality and nested Fourier convergence, and separates those guarantees from unresolved nu-merical convergence. Exact Temperley–Lieb calculations distinguish mirror knot sectors; 192 closures of three experimental protein backbones retain open-chain closure uncertainty. Biological evaluation remains limiting: in 512 external constitutional parents and 5,514 conformers, the primary persistent-minus-source separation difference is −0.0425, with bootstrap 95% interval [−0.0523, −0.0326]. An exploratory analysis of 143 same-assay stereoisomer comparisons across 103 parents and 65 human targets gives association ρ = 0.0499 [−0.1537, 0.2463] with absolute binding selectivity, establishing no advantage. High-energy persistence and effective-rotor basis sensitivity remain unconverged. The framework connects algebraic topology, linear algebra, geometry and computational biology through explicit information limits, without claiming receptor mechanisms or a universal stereoselectivity predictor.