arXiv 2607.17146 proposes a continuous geometric framework that compresses the discrete operations of the Transformer into integral-differential equations on a semantic fiber bundle. Attention is no longer a "weighted sum", but a Schrödinger Bridge under the entropic optimal-transport view; SGD and AdamW are also translated into Itô diffusions that violate detailed balance, where weight updates equate to parameter turbulence in a non-equilibrium steady state. The authors start from a geometric axiom (the token sequence is a discrete 1-manifold with a regular measure grid), and translate RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, and Weight Decay all into a unified vocabulary of differential geometry, measure theory, and stochastic calculus. In six experiments across five architectures (Qwen3, LLaMA-3.1, Gemma-3, GPT-2, Mistral) at 124M to 8B parameter scales, the geometric predictions align tightly with empirical observations: ε^(-1/2) Lipschitz calibration reaches R² = 1.000 at machine precision; Lie-Trotter operator-splitting torque, the dual-law topological instability under symmetric ablation, O(1/√k) thermodynamic suppression of Poincaré recurrence, and the RoPE-torus context-limit phase transition are all reproduced. The two most engineering-valuable conclusions are: the physical upper limit of the context window is a thermodynamic phase-transition point, predictable by the O(1/√k) law; and the stability boundary of the Transformer is set by "dual-law topological stability", which means ablation must be done pairwise or it triggers symmetry breaking. This isn't another "philosophical framework" paper — it advances the Transformer from an engineering black box to a differentiable, predictable, tunable geometric object, and the next step may be to write a unified scaling law for "context length" and "training steps" into the pre-training recipe. Original paper: https://arxiv.org/abs/2607.17146