Correlation-Order Compression in Closed Quantum-Waveguide Spectroscopy

A closed curved quantum waveguide is used as a controlled inverse-spectral system whose geometry encodes a binary chirality word. A fixed-reference Boolean/Walsh filtration identifies which multi-cell correlations can enter finite-width effective matrices, while exhaustive enumeration of the anti-periodic 24-cell class isolates six nontrivial pair-homometric collision pairs. Controlled nearest-neighbour support overlap generates bond variables b_j = epsilon_j epsilonⱼ₊₁ through local torsion-squared finite-width terms and promotes a quartic chirality discriminator to O(ell^4). The mechanism is realized by an exactly closed, embedded, constant-curvature, zero-torsion-holonomy centreline constructed from an anti-periodic spherical tangent indicatrix. An unreduced finite-width weak-form calculation on an amplitude-enhanced closed witness gives Delta E proportional to ell^3.99957646 and an extrapolated coefficient -0.01646850, within 0.916% of the retained-theory prediction -0.01662079. An independent public solver replay regenerates every archived Delta E/ell^4 row within 0.52%. The result is a correlation-order compression principle: geometric support structure can change the perturbative width order at which hidden multi-cell information becomes spectrally observable.