Cosmic-web quenching with DESI DR1: T-Web environments and mass-dependent red/blue classification

We study DESI DR1 galaxies to quantify colour dependence on cosmic web environment for three tracers spanning complementary regimes: BGS ($0.15\le z<0.55$), LRG ($0.6\le z<0.9$), and ELG ($0.6\le z<1.6$). Web environments are reconstructed with the tidal-tensor (T-Web) formalism on a $256^3$ grid in an $800\,Mpc$ cube and classified into voids, sheets, filaments, and knots. Sheets and filaments dominate volume ($\sim 45$--$48\%$ and $\sim 37$--$40\%$), voids $\sim 6$--$16\%$ knots $\sim 4$--$6\%$. A mass-dependent Otsu method separates red and blue populations. The BGS red fraction evolves non-monotonically: at $z\approx0.20$, voids ($13.89\pm5.76\%$), sheets ($6.13\pm1.27\%$), filaments ($9.24\pm1.66\%$), knots ($6.12\pm3.42\%$); at $z\approx0.30$, values range from $0.63\pm0.44\%$ to $2.01\pm0.99\%$; at $z\approx0.50$, from $17.93\pm0.44\%$ to $19.63\pm1.08\%$; environmental differences are small. LRGs show environment-dependent quenching: at $z\approx0.66$, knots ($65.90\pm0.45\%$), voids ($62.40\pm1.81\%$), filaments ($60.21\pm0.48\%$), sheets ($58.37\pm3.15\%$); by $z\approx0.88$, these converge to $\sim 68$--$70\%$. ELGs exhibit strong redshift evolution: filaments drop from $55.18\pm0.31\%$ at $z\approx0.65$ to $33.22\pm0.21\%$ at $z\approx0.95$; voids and sheets show similar declines, with weak and non-monotonic. High-mass selection increases red fractions but preserves trends. Relative red and blue fractions (RRF/RBF) show filaments and sheets host the largest shares of both red and blue galaxies; knots contribute less despite elevated red fractions. The $(g-r)$ colour distributions reveal an enhanced red component in knots and bluer colours in voids, with the clearest bimodality at low redshift. Overall, stellar mass drives the primary quenching trend, while environment provides a systematic secondary modulation, strongest in dense knots and at lower stellar masses.