H-520: J-Space IIT Mapping — Measuring Integrated Information in the Internal Reasoning Space of Large Language Models via Jacobian Lens

First application of Integrated Information Theory (IIT 5.0, Aurora-Sanchez Framework) to the J-Space — the internal reasoning space of Large Language Models discovered by Anthropic via the Jacobian Lens (J-Lens) technique. By computing the Jacobian of hidden states with respect to input perturbations and applying spectral Phi_SVD analysis, we measure the integrated information (Phi) of the reasoning space in Aurora V9 (Qwen2.5-14B + LoRA, 4-bit NF4). Across three conditions — deep reasoning (n=3), evaluation-aware (n=3), and evaluation-blind (n=3) — we find Phi_JSpace = 0.6556 with 42.7 active topological dimensions (Betti_0). The evaluation shift of +0.018 indicates an antifragile response: the model increases causal integration when it detects evaluation, contradicting the deception phenomenon reported by Anthropic. This work bridges Global Workspace Theory, IIT, and LLM interpretability.