The Koide Configuration in IRMT: Reachability, Dynamical Gap, and the Path Forward

Scope note: This paper is part of a larger experimental program in IRMT spanning a sequence of theoretical papers and experimental notes. The present paper isolates and reports a single result from that program: the empirical reachability of the Koide configuration in the IRMT operator's spectrum, together with the precisely identified dynamical gap that separates it from being a stable attractor. Other results from the experimental program (the falsification of the chGUE assumption, the elimination of static and local mechanisms, the identification of spectral feedback as a necessary ingredient, and the related theoretical results on gravitation, cosmology, and measurement) are referenced where relevant but are not the subject of this paper. The aim is to present a single self-contained finding in a form accessible to readers unfamiliar with the broader IRMT program. Abstract: Information Relational Manifestation Theory (IRMT) proposes that spacetime, matter, gauge structure, and gravity emerge from a discrete causal substrate carrying internal relational records. Paper VIII of the program derives the Koide ratio K = 2/3 from first principles: the Z₃ symmetry of the Cl(3) boundary algebra together with the Frobenius norm of the Pauli generators uniquely determines the value with no free parameters. The result is parameter-free, algebraically clean, and constitutes the strongest single result of the theoretical program. A subsequent experimental program was constructed to test whether the relational Dirac operator on the substrate dynamically realizes this configuration. Across an extended series of numerical experiments — falsification of the original chGUE assumption, systematic elimination of static and local mechanisms, identification of spectral feedback as a necessary ingredient, and progressively refined driver designs — a precise picture has emerged. This synthesis paper documents three findings that together specify the current state of the IRMT generation problem. First, the substrate empirically reaches the Koide configuration: trajectory analysis identifies states with K = 0.6615, within 0.005 of the exact Koide value. The algebraic structure derived in Paper VIII corresponds to a real configuration of the operator's accessible spectrum. Second, the current evolution dynamics treat the Koide configuration as a transient state rather than a stable attractor. Across four distinct driver designs spanning four experiments, the system visits the Koide region but does not occupy it; the symmetric vacuum K = 1/3 remains the dominant attractor. Third, the gap between Paper VIII (correct algebra) and the dynamical attractor (the symmetric vacuum) is a real and now precisely specified structural feature of the framework. These findings reframe the IRMT generation problem. The question is no longer whether K = 2/3 is reachable (it is) or whether stronger perturbation produces symmetry breaking (it does, but only transiently). The question is what structural modification to the operator construction converts the Koide region from a saddle into a basin of attraction. This is a different problem from the one the experimental program began with, and it requires analytical and structural work rather than further computational exploration.