We present a method for injecting a frozen continuous-time Kuramoto phase manifold (System Omega) into discrete autoregressive language models via a dynamically trained BridgeMLP. The approach requires zero gradient flow through the frozen manifold and uses pure residual addition at the logit level. The phase manifold adds O(1) memory overhead beyond the base model: no KV-cache, no additional attention heads, no position embeddings. We validate the method on two architecturally distinct 3B-parameter models: Qwen2.5-3B-Instruct (Qwen2, 2048D hidden) and Llama-3.2-3B-Instruct (Llama-3, 3072D hidden). At alpha = 10.0, the phase manifold corrects an incomplete bubble sort implementation in Qwen2.5-3B, adding both the missing return statement and a swapped early-exit optimization, while preserving correctness in Llama-3.2-3B. Semantic coherence on open-ended prompts is maintained at both alpha levels across both architectures. Companion to Bajddi (2026), "Emergence Over Attention: Continuous-Time Phase Synchronization as a Computational Primitive", Zenodo, doi:10.5281/zenodo.20741536. This record contains the publication-ready whitepaper (PDF + LaTeX source) and raw empirical validation metrics. Core model weights and architecture source code are proprietary.
Nossair Bajddi (Tue,) studied this question.