We study rigidity of near-optimal crossing walls in a two-dimensional interacting block-spin strip. A previous static wall theorem established that the minimal strip-crossing energy is of order Lᵧ*K*sqrt (J) and that every minimizer contains a mesoscopic wall of total central-band volume of order Lᵧ*sqrt (J). The present paper addresses the next question: whether such walls must be approximately planar. We prove coarse normalization for good rows and a rigidity theorem in the normalized translated-wall model, and we reduce the full wall-rigidity statement to a spectral closure after translation fixing. The paper should be read as a two-dimensional wall-rigidity preprint whose main geometric mechanism is established explicitly, while the final finite-J spectral closure is formulated and pushed to a discrete-to-continuum contradiction scheme in the technical sections and appendices. Related earlier works by S. Pan are available at DOI: 10. 5281/zenodo. 19673404, DOI: 10. 5281/zenodo. 19689210, DOI: 10. 5281/zenodo. 19690441, and DOI: 10. 5281/zenodo. 19693231.
S. Pan (Wed,) studied this question.