Naturalness Predicts but Does Not Cause Transferability in Image Encodings of Real-World Streams

A common practice converts a one-dimensional signal into an image so that a vision backbone pretrained on natural photographs can be reused for recognition, yet the encoded image is rarely examined. We ask how the visual naturalness of an encoded image relates to its transfer accuracy under a frozen backbone. We build WorldStream, a corpus of 299 heterogeneous current-value series from key-free public APIs (weather, air quality, earthquakes, gold and oil, equities, crypto, foreign exchange, web activity and space weather), with a nine-way source-recognition task over 3143 temporally split windows. Across seven encodings and six frozen backbones, the Frechet distance of an encoding to natural images (FID) predicts its accuracy: Spearman ρ=-0.72. Two controlled interventions show this is not causal in the spectrum. Our invertible encoder has a single adjustable part, a spectral exponent β (power propto |f|-β); varying β moves the image toward or away from the natural-image manifold at fixed content. FID is lowest near the natural value β ≈ 2, but frozen accuracy stays flat and far below the structured baselines (19.2% vs. 73.0%), and FID and accuracy are only weakly related over the sweep (Pearson -0.32). A second intervention, phase scrambling, holds the power spectrum exactly fixed while removing local structure; now FID and accuracy fall together (Pearson -0.89). The cross-encoding correlation is thus mediated by local structure, not spectral naturalness: FID predicts accuracy because Inception reads the same structure the backbones do. Full fine-tuning does not close the gap (27% vs. 67%), so the deficit is structural. The encoder is exactly invertible, recovering the signal from the 8-bit image at 72.9 dB, so the image doubles as a lossless record of the data.