Alignment Is Coherence: A Unified Failure Metric for AI Systems, the F-First Warning Theorem, and Three Testable Predictions

AI alignment lacks a unified failure metric. Current approaches treat alignment faking, reward hacking, goal misgeneralization, deceptive alignment, and sycophancy as separate failure modes. This paper shows they are one failure mode: coherence collapse. The coherence metric K(t) = ρ(t)·I_Φ(t)·F(t) — validated against 52 institutional collapses with zero false negatives — applies directly to AI systems. ρ measures behavioral consistency, I_Φ measures objective stability, F measures corrective openness. Every known alignment failure is K < K_crit in at least one component. The F-First Warning Theorem predicts alignment failure always begins with F↓ before I_Φ↓ before ρ↓, empirically validated with 52/52 ordering and zero exceptions. The multiplicative structure means high behavioral scores cannot compensate for closed feedback channels — this is why alignment faking (high ρ, near-zero F) is detectable when behavioral evals alone are not. Three testable predictions: F-first ordering in AI failures, alignment faking detection via K, and K_crit ≈ 0.127 as universal threshold. References Anthropic (Constitutional AI, Alignment Faking, Red Teaming), OpenAI (RLHF, Concrete Problems), and DeepMind (Specification Gaming). Part of the Spektre research corpus.