Information Relational Manifestation Theory (IRMT) (VI): The Measurement Problem as Relational Consistency

The measurement problem—why quantum systems produce definite outcomes upon observation—remains unresolved within standard quantum mechanics. This paper presents a complete resolution within Information Relational Manifestation Theory (IRMT) through five results. First, Lemma A derives the critical coherence threshold κ_c=1/(2√(N_W )), obtained directly from the Marchenko–Pastur spectral edge, without the introduction of free parameters. Second, Lemma B establishes rank(P_"obs" )=d=3, through a two-step argument: finite rank is necessitated by the coherence budget of the Unity Wedge, while the specific value d=3 follows from Poisson causal geometry in 3+1 dimensions. Third, Theorem C proves Projection Necessity and explicitly identifies a breakdown of unitarity. For coherence values exceeding the critical threshold (κ>κ_c), the phase variance undergoes unbounded random-walk growth on the unit circle S^1. This growth violates the unitarity of relational transport, which is a conserved quantity of the substrate. Projection emerges as the unique mechanism that restores unitarity. Fourth, the theory yields a falsifiable prediction distinguishing IRMT from both standard decoherence theory and Everettian interpretations. No quantum system can remain in superposition beyond the timescale τ_"dec" ∼l_* " " N_W^(1/2), without violating normalization. Fifth, the framework extends naturally to continuous-variable systems through coherent-state representations of the Clifford algebra Cl(3). Within this formulation, wavefunction collapse is not a postulate, but a necessary unitarity-restoration event.