Computable Information Density as a Projection Diagnostic: An Information-Dynamics Reading of Entropy Imaging in Quantum Matter

Wu et al. (arXiv:2610.35790) introduced entropy imaging for quantum matter: a microscopy image is serialized along a Hilbert curve, compressed with a lossless algorithm, and the computable information density (CID) is used as a measure of spatial complexity. Applied to microwave impedance microscopy of graphene, CID peaks near quantum Hall transitions, tracks fractional transitions, and resolves fractional puddles in a local map, while a trivial band-edge crossover does not show the same enhancement. This preprint offers an information-dynamics reading of that result. In this reading, a microscopy image is a projection, and CID is treated as an indicator of the arrangement information in the projection. The reading changes no number in Wu et al. No new data are reported. All numbers are Wu et al.'s as reported. Three falsifiable predictions are stated, testing the CID diagnostic.