Wrong With Conviction: Why Confident Errors Evade Detection in Language Models

A language model can be wrong and confident at the same time, and the confident case is the one that matters most for deployment. It is fluent, assertive, and invisible to the signals that screen low-confidence output. We ask why, and answer with a theorem and its empirical validation. For an idealized random-matrix model of a transformer block, the per-layer transition-Jacobian participation ratio is input-invariant. Under an input-dependent gating term that is both rank-o(d) and bounded in operator norm, the normalized participation ratio converges to a constant that depends on the layer's weight ensemble and not on the input. The immediate corollary is an endpoint-blindness bound. Any unsupervised geometric or spectral detector that reads the macroscopic endpoint geometry assigns a confident error and a correct answer the same value, so its AUROC tends to 0.5. We validate the prediction on a real, nonlinear network to within one percent, and we corroborate the blindness behaviorally three independent ways: (a) a hidden-state dispersion that fails to separate the two classes; (b) semantic entropy that is blind on adversarial confident error (AUROC 0.476-0.563 across twelve models and four families while scoring 0.774 on a genuine-uncertainty control, a double dissociation); and (c) a cross-task inversion in which confident errors carry lower semantic entropy than correct answers. Crucially, the bound constrains only unsupervised readers. A supervised probe can still recover a truth direction that the invariant macroscopic geometry hides, and this is the opening we exploit. We construct a Governor that reads the error regime from frozen internal state, routes a regime-matched correction, and refuses when residual risk is high. Routing is a requirement, not an optimization. Applying the wrong regime's fix actively harms. The underlying mechanism is an asymmetric subspace in which corruption rides a specific direction and survives orthogonalization while rescue collapses. The router beats the best single fix by +4.7 to +10.5 points across five models and three families (every confidence interval above zero), and the end-to-end Governor lifts accuracy by +13 to +20.5 points over base. We bound the system candidly. The steering actuator is non-monotone in scale, and cross-benchmark transfer is moderate rather than task-general. The naive claim that the two error regimes are cleanly separable is dataset-confounded at small scale; that confound shrinks with size, and a genuine, capacity-emergent regime representation takes its place as models grow.