The Conditional CRO Trilemma: Impossibility Bounds on Confidentiality, Reliability, and Opposability Under Institutional Extraction Limits

Cryptographic evidence systems face fundamental trade-offs between confidentiality (Conf), reliability (Rel), and opposability (Opp), with Conf ·Rel·Opp products ranging from 0.27 to 0.57 in deployed systems. Although documented empirically in recent work, these limits lack a theoretical explanation. We present theConditional CRO Trilemma, establishing that institutional capacity fundamentally constrains achievable trade-offs. Under explicit assumptions about cognitive limits, we prove Conf ·Rel·Opp ≤ Δ/λ+ ϵ(λ) where Δ quantifies the institutional extraction capacity and λ is the security parameter. Our main contributions are as follows: (1) a formal model with parameters Δ (extraction capacity) and α (verdict granularity); (2) an information-theoretic proof using Pinsker’s and Fano’s inequalities; (3) an analysis showing deployed systems implies Δ = 35–73 bits, consistent with bounded rationality; and (4) a framework for matching protocols to institutional capacity. Overall, this trilemma shifts the protocol design from mathematical optimization to constraint-aware engineering.We provide validation pathways and discuss their applications to legal evidence and regulatory compliance systems.