Extending discrete tokenization and autoregressive modeling to signals whose latent states follow continuous trajectories introduces phase–morphology ambiguity. Similar local shapes can occur at distinct trajectory positions, while the same position can vary across instances. Standard vector quantization (VQ) may therefore merge contextually different patches and split corresponding ones. We trace this behavior to radial-to-tangential gradient leakage under the straight-through estimator and propose **Geometry Alignment Quantization (GAQ)**. GAQ combines a learned Mahalanobis reshaping of the codebook with a Householder backward map. The map exactly cancels the leakage in the idealized setting, while the numerical stabilization used in practice introduces a bounded deviation. We instantiate GAQ on ECG as **AtomECG**, a tokenizer of sub-waveform atoms composed by a GPT grammar. Atom sequences show long-context scaling from perplexity 488 to 24, split-replicated motif enrichment yields auditable clinical hypotheses, and AtomECG outperforms eight eSSL baselines on more than ten diagnostic tasks. A known-phase limit cycle and PPG results further support GAQ on phase-like signals beyond ECG.