RMB Status Note v2: Notation Separation, Dimensional Analysis, and Structural No-Go Results of the Minimal Tensor Formulation

This status note continues the scientific consolidation of the RMB (Space–Matter–Motion) framework initiated by the July 2026 Corrections Note (DOI: 10.5281/zenodo.21219761). It documents three results.

First, the previously ambiguous coupling notation is formally separated: the dimensionless microscopic quantity α_QFT, the dimensionful tensor coupling κ_T ([κ_T] = m), and the phenomenological SPARC fit parameters (λ_gal, r₀, r_c) are distinct objects whose identification has not been derived.

Second, the minimal RMB tensor M^μν = ρ₀c²v^μv^ν + κ_T F^μν can be written in a dimensionally homogeneous form but exhibits two structural no-go results in the weak-field, stationary, axisymmetric limit: (a) the temporal component of the balance law ∇_μM^μν = 0 modifies the standard matter continuity equation by a diffusion term and excludes stationary rotating discs with realistic density profiles for κ_T ≠ 0; and (b) the antisymmetric correction produces no radial force for a purely azimuthal flow and therefore cannot modify rotation curves in this limit.

Third, a conservative stability estimate gives |κ_T| ≲ 3×10⁻¹⁷ m, whereas galactic relevance would require κ_T ∼ 10¹⁷ m — a discrepancy of ~34 orders of magnitude.

Consequently, the empirically successful SPARC parametrisation is not a limiting solution of the minimal tensor equation and remains phenomenological. RMB currently has no coupling value transferable to laboratory, plasma, or accelerator systems; corresponding extrapolations (collider signatures, X17, plasma, solar-wind momentum balance) are classified as not yet calculationally well-defined. The note is Finding 6 of the July 2026 corrections series and remains a status clarification, not an invalidation of the empirical fits.