Circulatory Fidelity measures the cost of factorization: the information lost when a system is decomposed into independent parts. When the connections carry more than the components, factorized analysis silently discards what matters. Validated across 41 scientific domains with 50,000+ empirical data points.
Modern science decomposes systems into independent parts — q(x, z) becomes q(x) · q(z). This is factorization: the mathematical operation that discards relational structure. It works spectacularly, and organisms evolved to do it cheaply. But when the connections between parts carry more information than the parts themselves, factorization silently discards what matters most.
Mean-field variational inference, the workhorse of modern Bayesian computation, approximates joint distributions as products of independent factors: q(z) = ∏i qi(zi). This explicitly discards all relational structure between variables.
When does this approximation fail?There is no free lunch in factorization. Every time we treat coupled variables as independent, we pay an information-theoretic cost, a cost that is invisible to the factorized analysis itself. The error grows silently and can be catastrophic.
How do we measure what we've lost?Even when we check for correlations, standard pairwise analysis misses coplexity. XOR-like dependencies, where three variables are tightly coupled but any two appear independent, are invisible to marginal observation.
IC₂ = 0 does not mean independenceBiological observers evolved under severe energy budgets. Pairwise observation is metabolically cheap; higher-order observation is expensive. The apparent rarity of coplex structure is a selection effect of methodology, not a fact about the world.
Coplexity is ubiquitous but invisible to cheap observation