An Exact Reduction of the Measure Problem: Finite Decomposition into Interference Granularity, Event Structure, and Conditioning (Dual Geometry of Wavelength and Frequency Spaces, Paper 16)

Paper 16 of the series Dual Geometry of Wavelength Space and Frequency Space. The system supplies path amplitudes with no free parameters; what is not fixed is the aggregation rule that bundles them into probabilities — what standard theory installs as the Born rule, by axiom. This paper does not select the rule; it gives an exact reduction of the selection problem. The historical proximity 0.0007 between the derived and counting measures is shown to be an artifact of two-outcome compression (a one-line lemma; the divergence jumps to 0.24 at s=11). Derived measures do not classicalize to counting measures (exhaustive at s=9/11/13), yet the two share their support exactly. Interference granularity is not reducible to convention: the mirror parent has W=0 exactly under channel-consistent aggregation while decaying perfectly normally at configuration granularity (W'=768=W'(A)); at m=4 the unit of cancellation refines to single channels; the occurrence condition is reduced to the four-value lock — algebra that is the object of proof. Conditioning requires the branch-channel stratum of the readout hierarchy (pairs indistinguishable by intensity fringes have different P(X)). Event structure is exactly one bit (one-shot vs sequential), completing a 2x2 table. Main theorem: the inventory-defined candidates organize without duplication into the product granularity x event bit x conditioning, each axis independent — with a decision table of experiments computable inside the model (two executed before publication). Under the reduction, the Born rule has the status of an effective law to be merged with in a suitable limit (convergence / suppression below statistical censorship ~1/sqrt(N) / prediction). Reviewed in two rounds under a two-party independent verification protocol. Japanese and English full texts. No physical identification is made.