Aggregation-Concealment Independence Theorem

Canonical definition

The signal-to-noise ratio for the M-component at any aggregation rung r (SNRr) is a function of aggregation scale and structural loop parameters and is not a function of the concealment level Cr operating at that rung. Formally: for each rung r ∈ {1, …, 6} of the Aggregation Gradient, SNRr = f(r, κS, β, γ, σ'(V)) where κS, β, γ, σ'(V) are the fast-layer loop parameters of Appendix A and Cr is the concealment density at rung r facing the observer who reads the rung-r aggregate without being among the Individuals whose valuations compose it. The theorem establishes independence: ∂SNRr/∂Cr = 0. Where the concealment faces the participants themselves it raises their slow-layer gain through the restricted Hypothesis Space, and the independence becomes the one-sided statement ∂SNRr/∂Cr ≥ 0: concealment cannot lower SNRr. Concealment operates on Hypothesis-space access (reducing the set of admissible source-attributions at any rung), not on the aggregation-induced signal separation between bounded and unbounded sources. The unbounded compounding of M and the bounded satiation of A and I are structural properties of the sources, not properties of the Hypothesis Space available to the observer. Raising Cr cannot alter the fact that A and I average out across large samples while M compounds; it can only prevent the observer from correctly labelling what they have observed. Corollary (Gradient Survives Camouflage Architecture). At rungs 5 and 6, aggregation has suppressed the bounded-source contributions to a negligible fraction of the signal and the M-component dominates. Full concealment (Cr = 1) does not lower SNR5 or SNR_6: the M-dominated signal persists in population-scale outcome distributions regardless of whether the observer has the vocabulary to attribute it correctly. The Camouflage Architecture's eight concealment layers do not undo the gradient because they evolved against the threat of individual recognition and academic naming, not against population-scale statistical analysis of outcome distributions.