Speech anti-spoofing countermeasures degrade when the generator, codec or channel changes, and a common remedy is an auxiliary objective that shapes the embedding space; whether it does is invisible to EER, a pure ranking metric. We compare seven such objectives with cross-entropy over 113 runs on five corpora, AASIST3 at three seeds plus four pre-trained detectors, and measure the embedding space of the 24 AASIST3 runs directly. Raw augmentation displacement makes cosine consistency look effective, but the gain is a smaller space, not a more stable one: normalised by the spread, no configuration consistently improves on cross-entropy. Every trained space is dominated by the single decision axis expected for two classes, whose training-set structure does not transfer, and four runs collapse to a near-constant output that displacement rewards and EER reports as poor accuracy. No auxiliary objective keeps an advantage over cross-entropy across architectures, corpora and seeds.

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