Spectral-Timing Evolution of a Black hole X-ray binary Swift J1727.8-1613: Linking Disk Reflection and Type-C QPO Frequency During the 2023 Outburst

We present a comprehensive spectral-timing analysis of a BHXB Swift J1727.8$-$1613 during its 2023 outburst, using five pointed $\mathit{\text{NuSTAR}}$ observations sampling the luminous hard-intermediate state. Broadband 3-79 keV spectroscopy employs a physically motivated model combining a cool truncated disk ($\mathtt{\text{diskbb}}$), relativistic reflection ($\mathtt{\text{relxill}}$ in reflection-only mode), and Comptonized continuum ($\mathtt{\text{nthComp}}$) to probe the inner accretion geometry around a rapidly spinning black hole ($a_{\ast }\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0.98$) at moderate inclination. Simultaneous timing analysis reveals type-C quasi-periodic oscillations (QPOs) with novel coherence evolution: the quality factor ($Q$) exhibits a striking non-monotonic dependence on both QPO frequency and luminosity, peaking near ${\nu }_{\mathrm{Q}\mathrm{P}\mathrm{O}}\text{\hspace{0.17em}⁣}\sim \text{\hspace{0.17em}⁣}1.2$~Hz and declining at both lower and higher frequencies. This turnover directly constrains Lense-Thirring precession geometry, implying optimal coherence at intermediate truncation radius. A tight photon-index-QPO-frequency correlation demonstrates that spectral softening and frequency rise are concurrent signatures of inward truncation-radius motion. The triadic luminosity evolution-rising disk and Compton, declining reflection-traces precession-driven geometry changes and corona beaming effects. Interpreting disk-normalization variability as apparent-area changes rather than physical radius swings provides new insight into disk-corona boundary layers. These quantitative results provide strong evidence for global Lense-Thirring precession regulation of both timing and spectral properties, establishing Swift J1727.8$-$1613 as a benchmark source for understanding accretion-geometry physics during black hole state transitions.