Faithfulness, Gaps, and Lies: A Unified Theory of Neural Model Honesty

We prove that neural model honesty decomposes into exactly two components  an information component (H-axis), detectable without labels from the model's internal geometry, and a magnitude component (G-axis), requiring external grounding and that no single-model reference-free signal can supply both.

Four results:
(1) Conservation Law: L(f) = E[|log|det J(x)||] = 0 iff faithful, verified to <7×10⁻¹¹ nats across six contraction rates. Two-directional extension catches fabrication lies (1.0986 nats measured = predicted). Quantum no-hiding gap = 1.01×10⁻¹³.
(2) Gauge Correction: |det J|=1 is necessary but not sufficient gauge-twin achieves 16.89× attribution swing while passing every determinant test.
(3) NTK Identity: training-support concentration = NTK-GP posterior variance, verified to 3.27×10⁻¹³ over n=300 networks, AUC 0.859±0.084.
(4) Detection Ceiling: ∂v/∂A = 0 — flag-rate locked constant while precision spans 0.000→0.928, confirmed across four architectures including GPT-2.

All results are one-command reproducible from open-source code at
github.com/pulkit6732/rfn-paper