Kun Framework Extension: Theorems T87 through T91, the Lepton Spectrum and Gauge Staircase

This paper extends the Kun Framework and its unification principle, published separately because the original framework paper covers 88 theorems across 61 orders of magnitude and the lepton and gauge sector results warranted standalone treatment. Five new theorems are derived from the Young-Laplace pressure equation and the Lid winding number operator. T87 (The Muon) and T88 (The Tau) give the muon and tau masses at 0.0012% and 0.0072% error respectively, with zero free parameters, from the electron mass anchor (T80) and the Koide phase delta = 2/9 (T84). The Koide phase itself is identified geometrically as N_spin divided by W squared, where W = 3 is the Y-junction winding number measured by the Lid operator (T84 update). T89 derives why the strong force has exactly 3 colors: the 3-junction is the unique stable elementary vertex of a YL foam network by Plateau’s theorem; all N greater than 3 decompose into 3-junctions. T90 maps the full gauge group stability staircase: N=1 loop (U(1), EM unbroken), N=2 segment (SU(2), neutral equilibrium, spontaneously broken), N=3 junction (SU(3), Plateau-stable, confining). T91 derives the spontaneous symmetry breaking mechanism numerically: the neutral N=2 junction drifts freely under ambient foam noise, collapses to the N=1 remnant, and sheds exactly 3 drift modes mapping to W+, W-, Z, with the massless photon as the N=1 loop mode. The breaking scale (v = 246 GeV) and SU(2) chirality remain open. For more information, please visit: Our website - ofmagnitude.com Our Github - https://github.com/OrdersOfMagnitudeLLC/type1-toolkit Kun Framework - https://doi.org/10.5281/zenodo.22896946