This paper introduces a configuration reading into the reciprocal dual model (Papers 1–6): the fragments after splitting are occupied cells of a shared parent lattice, and a state is the set of occupied cells. From this minimal embedding hypothesis, the following are derived. First, exclusion statistics: since a state is a set, no label of "which fragment is which" exists, and double occupancy of the same cell is impossible by the non-overlap = orthogonality theorem (Paper 5). Indistinguishability and the exclusion principle become theorem-like consequences, not assumptions. Second, the stable-species spectrum: from exclusion follows the shell capacity law nm ≤ c(m), and an exhaustive scan (s ≤ 25) of the allowed decay channels under odd partitions and the capacity law establishes that s = 1, 3, 5 are absolutely stable (no channel exists) and that the decay threshold is s = 7. For the first time the model possesses a spectrum of stable states. Third, timeless branching ratios: the question "when, and triggered by what, does decay occur" is ill-posed in this model, where time = a sequence of events; the absence of a trigger (spontaneity) is a constitutive principle of time. What can be predicted are the relative weights among channels (branching ratios), and at s = 9 the configuration counting of the two allowed channels yields the unique ratio (5,3,1):(3,3,3) = 192:56 (77.4% : 22.6%). Fourth, the birth and readout of relational geometry: the configuration of a single fragment is a non-observable under the B4 gauge, but with two or more fragments, for the first time, the inner products = angles between occupied cells become gauge invariants. We show that this relational data can be read out completely from the λ-side record (the intensity of the interference pattern) alone: the five relation classes of the s = 9 final decay configurations are completely separated by the multiplicity-weighted power spectrum alone (a theorem over all 248 configurations), and the entirety of the data required for identification is obtained exactly from a single unit record (the unit-record sufficiency theorem). The amplitudes lie on a discrete alphabet of powers of √2, and the readout is digital decoding. Channels containing the minimal fragment (the zero mode) are of holographic type, permitting complete reconstruction of the configuration; channels without it are of interferometric type, yielding relations only. Finally, as consequences of the exclusion rule, we show that within a shared lattice the existing occupancy blocks the decay channels of other fragments — a blocking effect (environment dependence of decay channels) — and that the timeless state space of small systems can be enumerated completely as a finite closed set.
Noriaki Kihara (Thu,) studied this question.