Late-Transition Interacting Thawer Dark Energy: Physics and Validation

We formulate the late-transition interacting thawer (LTIT) as a late-activating, variable-coupling realization of coupled quintessence in which a canonical scalar field couples conformally only to cold dark matter. The construction is designed to separate two issues that are often mixed in late-time dark-energy analyses: a genuine low-redshift deformation of the expansion history and a shift of the pre-recombination calibration sector. We derive the exact background equations, the exact CDM scaling identity $\rhoc(a)=\rho_{c0}a^{-3}C[\phi(a)]/C(\phi_0)$, and the linear scalar perturbation equations in synchronous gauge in a form suitable for Einstein--Boltzmann solvers. For representative benchmarks we find $\Omega_\phi(z_*)\sim10^{-9}$ and $|\Delta r_d/r_d|<4\times10^{-3}$, while the low-redshift background shift remains sub-percent and the approximate growth response ranges from sub-percent to several percent, depending on the asymptotic coupling amplitude. LTIT is therefore not a flexible $w(z)$ ansatz but a constrained interacting-dark-energy framework in which any apparent background success must survive perturbation-level closure tests.