Mixture Probing in Frozen Audio Encoders: Shortcut Bounds and a Suppression Law

Linearly mixed audio is an attractive testbed for representation analysis because the ground-truth sources are known exactly. The standard instrument is a probe: train a classifier on a frozen encoder's embedding of a mixture to name a source inside it, and read its accuracy as evidence about what the encoder retains. We show that this instrument is biased in two ways that have not been reported, quantify what survives once both are removed, and identify the mechanism of what survives. First, if mixtures are built by drawing $k$ *distinct* classes, which is the obvious construction, the masker labels alone determine an AUC of $0.5+(k-1)/(2(n-1))$ with no audio at all. On a ten-class corpus at $k=5$ this reaches $0.722$, exceeding the value our own probe measured there; drawing classes i.i.d. drives the bound to exactly $0.5$. Second, when sources are paired by natural co-occurrence, a predictor given only the masker's class reaches AUC $0.968$ against the audio probe's $0.913$, so the probe is reading the loud source and inferring. Third, with both shortcuts closed, weak-source decodability still falls with the number of sources at a matched conditional ceiling, $\beta =-0.098$ AUC per $\log k$ (95% CI $[-0.133,-0.062]$; 63 cells, three encoders, three corpora). Fourth, corrupting an oracle time-frequency mask at a controlled rate shows this capacity law is entirely a suppression effect: a reader that can remove $5$ dB of masker energy pays only $0.015$ of the $0.201$ AUC that $k$ costs at $0$ dB, and at $19$ dB it pays $0.001$. Naming one class among many is not intrinsically harder; separating it is. Part of the remaining loss is architectural rather than informational: pooling over the encoder's own frame tokens recovers up to $+0.077$ AUC at $k=5$ from the same frozen features, and this margin widens with training budget while the clip vector saturates. We release the diagnostic suite with a full account of the hypotheses we falsified and of the controls we withdrew, so that the retractions can be audited beside the results.