Floorplans are compact, appearance-invariant maps ideal for indoor localization, yet existing methods rely on depth networks that are brittle in cluttered scenes. We propose GALoc, a geometry-first framework that replaces depth prediction with gravity-aligned wireframes that satisfy verticality and coplanarity by construction. Given monocular RGB, camera intrinsics, relative poses, and IMU orientation, GALoc constructs a linear constraint matrix encoding verticality and coplanarity, and finds the camera gauge minimizing its smallest singular value via global search. The rectified wireframes are projected into bird's-eye-view layouts through a closed-form, FOV-consistent transformation and matched against the floorplan via metric-free SE(2) search. We evaluate end-to-end on Structured3D, with calibrated noise on Gibson, and on real-world author-collected sequences. When sufficient wall geometry is visible, GALoc matches or outperforms depth-based baselines -- achieving 88% sequential localization success at 0.1m over 100-step sequences on Gibson vs the baseline's 68% -- while abstaining in structure-blind scenes.

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