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Charged-Lepton Masses from Relational Rank Collapse and Determinant-Line Holonomy (IRMT XV): Koide Stabilization, Absolute Scale, Flavor Phase, and the Remaining Microscopic Closure Problem in IRMT
Papers VIII through XIII of the IRMT program established that the Koide value K=2/3 arises from the Z_3-Frobenius geometry of the Cl(3)boundary algebra, that it corresponds to a distinguished configuration in the rank collapse of the projected relational operator M_ab=⟨ψ_a∣Φ∣ψ_b⟩, and that this configuration can be stabilized through a deficit-gated support mechanism with equilibrium response h_*=1. The present paper addresses the two remaining components of the charged-lepton mass problem: the absolute packet scale and the flavor azimuth. A continuum analysis of weighted minimal causal diamonds fixes the proper-time weight k=2 and renormalization power r=1/2 from asymptotic scaling, yielding the exact six-bivector coefficient ξ_6=51/(1400√π) and the protected triplet susceptibility ξ_3=ξ_6/2. The three protected rank-two Clifford sectors determine a canonical three-component flavor bundle through an exterior-square, or determinant-line, construction. This removes the arbitrary internal SU(2)frame and resolves the obstruction that singular values alone do not determine a physical flavor frame or holonomy. The central U(1) component of U(2) transport acts nontrivially on the determinant lines. Its exact fundamental Wilson trace supplies the finite-holonomy correction to the packet scale, while its determinant supplies the phase required for flavor transport. The lowest oriented D_3-invariant coupling then selects the flavor azimuth ϕ=2/9. Together, these mechanisms produce a unified effective mass formula containing no charged-lepton masses or flavor-specific fitted parameters. Using the electroweak scale as an external Standard Model input, the construction gives m_e=0.510861 MeV, m_μ=105.631 MeV, and m_τ=1776.507 MeV, with a maximum relative discrepancy of approximately 3×10^(-4). The residuals separate naturally into a common packet-scale discrepancy of approximately 0.02% and a ratio-only discrepancy below 0.007%, indicating that the predicted flavor phase is more accurate than the raw individual mass errors alone suggest. One constitutive bridge remains open: the identification of the stabilized packet responses with additive Lie-algebra coordinates on their associated determinant lines. The paper shows that this identification does not follow from singular-value data, gauge invariance, unsourced Wilson dynamics, weak-response normalization, or imaginary-time continuation of the scalar stabilization flow. The remaining microscopic problem is thereby isolated as a directly testable matrix-valued closed-packet holonomy condition.
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