Lingtai: What Concept Geometry Reveals—and Does Not Reveal—About LLM Inference

Observing what a large language model computes during autoregressive inference—online and without training probes—remains difficult. We introduce Lingtai, a training-free **concept telemetry** layer: at each generation step, residual states are projected onto a domain-specific bank of named concept anchors, constructed without labeled concept examples, outcome labels, gradient fitting, or activation-space optimization, producing a structured per-step concept-coordinate signal. Across code generation and grade-school mathematical reasoning, this signal exhibits a robust association with predictive uncertainty: the association survives problem-identity and token-position controls and is not attributable to a single token type, is not explained by a simple correct/incorrect mixture on GSM8K, and is not reproduced by matched random anchors; it is markedly weaker or direction-inconsistent in K-means and PCA projections. Two structures emerge: a recurring **uncertainty-linked activity** signal whose functional geometry is task-conditioned (distinct activity–entropy shapes on HumanEval, MBPP, and GSM8K), and an **execution-specific** trajectory identity with strong local inertia but weak re-instantiation invariance—under completion-only elastic alignment, corruption at $k=32$ (approximately a median quarter of the completion) on the matched re-execution subset still retrieves the archived episode at 62.0%, while a fresh execution retrieves it only 11.7–16.0% of the time. Finally, a matched audit finds **no evidence** that the scalar concept-activity signal used here supplies a stable correctness coordinate under the tested protocol; we therefore treat correctness as externally supplied. Telemetry adds 0.7–1.6% per-token decode overhead for the 161-anchor code implementation, with unchanged generated tokens.