A Calibrated Radial–angular Fourier Framework for Detecting Annular Structure in Microtubule Reconstructions: Synthetic Recovery, Adversarial Controls, Artifact Taxonomy, and Controlled Null Results

This paper documents the development and adversarial validation of a radial–angular Fourier detector intended to identify annular structure in cryo-EM and cryo-ET microtubule datasets. Synthetic signal injection demonstrated successful detector recovery of isotropic annular structure, while increasingly strict adversarial controls revealed that apparent biological positives were dominated by reconstruction geometry, missing-wedge anisotropy, grid-locking, helical reconstruction leakage, and reconstruction-box interference. Clean single-particle reconstructions produced controlled null results while still permitting successful synthetic recovery. The study ultimately establishes a controlled null result for biological annular structure near the tested wavelength while providing a reproducible computational framework, artifact taxonomy, and reconstruction-aware validation methodology for future imaging studies.