Open-vocabulary keyword spotting (KWS) must detect arbitrary keywords without retraining. Cross-attention-based models achieve state-of-the-art performance but require pairwise interaction between the audio and each keyword, recomputing the fused representation for every audio--keyword pair. Embedding-based models avoid this computational cost through independent encoding and similarity scoring, yet remain inferior on challenging benchmarks such as LibriPhrase-hard. We show that this gap is primarily a training issue rather than a limitation of model capacity. While contrastive learning encourages correct keywords to rank above negatives, it does not explicitly calibrate absolute similarity scores, which are critical for applying a fixed threshold across keyword detection. We propose Calibrated, Order-aware Detection KWS (CORD-KWS), a training framework that introduces two complementary objectives while retaining the same encoders, cosine scoring, and O(1) keyword enrollment: a calibrated detection head that supervises absolute scores, and a frame-level CTC objective that preserves phonetic order information. CORD-KWS achieves EERs of 0.43% and 9.64% on LibriPhrase-easy and LibriPhrase-hard, respectively, outperforming existing embedding- and cross-attention-based models.

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