Quintessence Dynamics of Generalized Holographic Ricci Dark Energy in $f(\mathcal{T})$ Gravity: Stability, Phase-Space Attractor, and Statefinder Analysis
The cosmological dynamics of generalized holographic Ricci dark energy (GHRDE) of Xu type, embedded within power-law $f(\mathcal{T})=α\mathcal{T}+β\mathcal{T}^{m}$ teleparallel gravity and driven by the Hubble-parameter-dependent deceleration law $q=b-ν/H$, are investigated. The deceleration law yields an exact closed-form Hubble function $H(z)$ that interpolates between an early decelerating phase and an asymptotic de~Sitter regime, enabling all cosmological diagnostics to be expressed as explicit analytical functions of redshift. The present-day deceleration parameter $q_{0}=-0.60$ and transition redshift $z_{t}=1.0$ are consistent with current observational estimates. The GHRDE equation-of-state parameter $ω_{G,0}=-0.81$ lies within the quintessence band, and the effective equation of state evolves monotonically toward $-1$ without phantom crossing. The geometrical statefinder pair locates the model in the quintessence region of the $r$--$s$ plane, clearly displaced from the $Λ$CDM fixed point. A phase-space analysis reveals a stable-node de~Sitter attractor with strictly negative eigenvalues, guaranteeing robust late-time acceleration for generic initial conditions. The null, weak, and dominant energy conditions are satisfied throughout the redshift range considered, while the strong energy condition is violated at low redshift, as expected for an accelerating Universe. An observational constraint methodology combining cosmic chronometer data, Pantheon$+$ supernovae, and baryon acoustic oscillation measurements is outlined as the natural continuation of this work.