Four Objects Called Scale A machine-checked anchor, a unique orbit section, an adopted selection law, and a measured display

The word scale in a mass program names four different objects with incompatible formal types. This paper separates them and grades each one. First, a number: the gap-one topology anchor of the Recognition Science mass law has the fixed RS-native value 2φ42, and its positive factor amplitude is m/16. That is a theorem. The source audit finds no measured quantity in its dependency closure. Second, a section: for every nontrivially loaded pattern there is exactly one positive real scale on its orbit at which the realized window load equals the topology-predicted mass. That is a theorem, and it is a statement about cardinality, not about physics. Third, a law: the recognition ground-state law R4 asserts that creation deposits at that point. R4 is an adopted foundational model, asserted of the very proposition whose solution set the section counts; the two share a type and differ in force. No theorem derives it; the full sourced-channel emission envelope refutes it, and it is independent of the permitted premises in the library’s explicit witness-pair sense. It is adopted on a restricted realized class whose membership rule is the open problem. Fourth, a display: converting the RS-native number to MeV uses the measured electron mass, and nothing in this paper is compared to measurement beyond that one display input. We give the classification of the registered internal selector routes. Eight named theorem groups classify those registered routes, each with its declared scope. On the creation side, four boundary groups classify the coupling corner, and the organ-arrow reduction sharpens the residual to one real number: an organ must return the factor amplitude at the octave of use and avoid three decoy scales at every octave. The registered settlement derivation cone cannot supply that number: its pure fragment is exactly Q(√2), the factor amplitude lies outside it, and the J-cost fragment is excluded because e is transcendental while the amplitude is algebraic, so no element of the cone at either marking names it, and the registration is guarded by a frozen replayable census instrument. The relative-modular rung probe determines the deposit rung while remaining exactly amplitude-blind, which sharpens the boundary without closing it. T10 is not unconditionally closed. The remaining work is one creation-side, scale-bearing parent, and this paper gives it a type signature.