A Structural RTLI Constraint on the Higgs Quartic Coupling: √λH ≈1/e as a Universal Inner-Coherence Boundary

his technical note applies the Relational Threshold and Latent Interaction (RTLI) framework to the Standard Model Higgs sector and demonstrates that a single structural constraint, \sqrt{\lambda_H} \approx 1/e, naturally reproduces the observed Higgs boson mass with remarkable accuracy. Using the structural coherence boundary 1/e, previously identified across gravitational, cosmological, and dynamical RTLI systems, the Higgs quartic coupling is predicted to be \lambda_H^{\rm RTLI} = 1/e^2 \approx 0.1353. Inserted into the Standard Model tree-level relation m_H = \sqrt{2\lambda_H}\, v, this yields a Higgs mass of \sim 128.0\ \mathrm{GeV}, a 2.4% deviation from the measured value m_H \approx 125.1\ \mathrm{GeV}. The analysis shows that the RTLI constraint holds near an electroweak matching scale \mu^\ast \sim 10^2\, \mathrm{GeV}, and the small residual difference arises from known Standard Model threshold and renormalization effects. This identifies the Higgs mass as a structurally determined quantity, set by the same universal coherence boundary (1/e) that governs RTLI behavior across multiple physical domains. The result suggests that electroweak vacuum rigidity is not arbitrary, but part of a deeper geometric structure linking particle physics, cosmology, and coherence formation. The paper outlines this structural interpretation and motivates a full RGE analysis as future work.