How Many Layers, and How Concentrated Within Each What would falsify "the more complex, the more centralisation is needed": one decomposition and a test design for three propositions

Abstract That rising complexity requires more centralisation is used repeatedly in cybernetics, organisation theory and complexity science, yet it has never been taken apart, and so can neither be falsified nor turned into an executable prescription. This paper does not argue that the claim is true; it asks what would count as falsifying it. The argument has two steps. The first shows that "centralisation" is not one dial but at least four separately adjustable quantities: the number of layers, the concentration of coordination load within a layer, the strength of authorisation, and enforceability. None of the four determines the others, and compressing them into a single word is the principal source of the claim's unfalsifiability. This yields a two-dimensional reading that replaces the single axis: read layers vertically, within-layer concentration horizontally. The second step splits the claim into three separately testable propositions. Proposition 1: the number of layers a system requires is no fewer than the number of separable characteristic scales in its environment’s screening-length spectrum. This is composed from the law of requisite variety and the fact that one layer screens only one scale band; it is tier B, because the judgement of "separable" itself carries a threshold that has no independent calibration. Proposition 2: when a function is conjunctive, that is, the thinnest of its several components determines the whole and its aggregation operator is the minimum, that function's coordination load must be concentrated, while additive functions are not so constrained. This is tier A, and it supplies an item-by-item answerable list of *what to centralize*, not a global answer to *how centralised to be*. Proposition 3: the concentration of coordination load within a layer has an interior optimum, fixed by the lower envelope of three mutually independent constraints: identification delay, maintenance power, and conjunctive collapse. This is tier B, and this paper takes no position on which side the optimum lies. Each of the three carries independent falsification conditions and non-overlapping data sources; this is set out separately in Section 7, because if the three shared one body of evidence they would collapse back into one claim. Section 6 walks a concrete system through all four quantities and all three propositions; Section 7 explains why the three must be falsified separately; Section 8 treats four classes of case unfavourable to this paper; Section 9 gives the domain gate; Section 10 lists what is not claimed.