Randomness is often treated as either ontic indeterminacy or epistemic ignorance. We develop a third, operational account within Six Birds: layer-relative randomness is the predictive residue of non-closure under a chosen packaging and budget. For a micro process Xₜ and a packaging Π: X → Y, we define the micro-closure deficit at scale τ by CD_τ (Π) = I (Xₜ; Yₓ+⏣ | Yₜ), the information about the next packaged state that remains hidden inside the current macro-object. This yields the exact decomposition H (Yₓ+⏣ | Yₜ) = H (Yₓ+⏣ | Xₜ) + CD_τ (Π), separating intrinsic substrate uncertainty from randomness introduced by discarded distinctions. We connect this exact quantity to computable diagnostics native to earlier Six Birds work, including route mismatch for coarse-grained Markov dynamics and predictive log-loss gaps under limited-memory models. In controlled Markov benchmarks, closure deficit vanishes on exactly lumpable partitions and rises with within-fiber heterogeneity, while route mismatch tracks it closely. In budgeted prediction, increasing memory order buys back hidden distinctions and lowers held-out log loss. In toy hashing, one-wayness and random-lookingness emerge as the same packaging-and-budget phenomenon: high-entropy inputs obey q/2ⁿ inversion scaling, while low-entropy inputs collapse the effect. The result is a measurable account of randomness that unifies coarse-graining, limited prediction, and feasible one-wayness without treating randomness as primitive.
Ioannis Tsiokos (Mon,) studied this question.