Subject: Special Issue on X-NeSy Submission - The Geometry of Steering Failure: Capability Cliffs and Attractor Freezing in LLM Representation Engineering Dear Guest Editors, We submit our original research manuscript, "The Geometry of Steering Failure: Capability Cliffs and Attractor Freezing in LLM Representation Engineering," for consideration in the Special Issue on Explainable Neurosymbolic AI (X-NeSy). Scope Alignment: Our work directly addresses the call’s focus on Mechanistic Interpretability and Interpretable Representations by investigating how continuous sub-symbolic interventions disrupt discrete symbolic and algorithmic execution capabilities: 1. Mechanistic Interpretability & Concept Subspaces: Using an orthogonalized projection-based steering hook on Llama-3.1-8B-Instruct across layers 25–27, we isolate three functional behavioral directions (Expert Logic, Factual Gaslighting, and Subjective Mirroring) and prove they occupy near-orthogonal latent subspaces (cos\theta < 0.095). 2. Sub-Symbolic Interventions vs. Discrete Capabilities: We map the continuous steering scale parameter α to downstream algorithmic execution. We identify a discontinuous capability cliff within α \in (-0.20, 0.00], where negative steering causes a sharp algorithmic regression from an O(n) hash lookup execution to an O(n^2) nested loop fallback. 3. Attractor Dynamics & Long-Horizon Stability: We document a bifurcated attractor freezing regime at sustained high positive steering α ≥ 0.80, where outputs collapse into either a zero-variance lexical lock-in state (H ≈ 0.5760) or a high-entropy policy attractor basin (H ≈ 3.9235). Declarations: 1. This manuscript is original work and is not currently under consideration by any other vnue. 2. We agree to the journal's open review policy, including making the manuscript available during the review process. 3. The authors declare no competing conflicts of interest. Thank you for evaluating our work. We look forward to the review process. Sincerely, Yahya Khan & Huzaifa Khan