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+# ADR-CE-011: Residual = Contradiction Energy
+
+**Status**: Accepted
+**Date**: 2026-01-22
+**Parent**: ADR-014 Coherence Engine Architecture
+
+## Context
+
+The edge residual r_e = ρ_u(x_u) - ρ_v(x_v) measures local mismatch. This mathematical quantity needs a universal interpretation across domains.
+
+## Decision
+
+**Residual = contradiction energy - universal interpretation across domains.**
+
+The residual represents:
+- **AI Agents**: Logical contradiction between belief and evidence
+- **Finance**: Regime mismatch between positions
+- **Medical**: Clinical disagreement between vitals and diagnosis
+- **Robotics**: Physical impossibility between sensor and plan
+- **Security**: Authorization violation between permission and action
+
+The weighted residual norm |r_e|² is always "how much these two things disagree."
+
+## Consequences
+
+### Benefits
+- Universal semantics: "disagreement" makes sense everywhere
+- Quantitative: larger residual = bigger problem
+- Localizable: can identify which edges contribute most
+
+### Risks
+- Restriction map design determines what "disagreement" means
+- Poor maps give meaningless residuals
+
+## References
+
+- ADR-014: Coherence Engine Architecture
+- ADR-CE-009: Single Coherence Object