Constraining <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="script">R</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi mathvariant="script">L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mi mathvariant="script">T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity with millisecond pulsar observations

Pulsars, with their extreme densities and precise measurements, offer an exceptional probe of matter under intense gravity. We examined compact star structures within the extended f ( R , L m , T ) gravity framework, incorporating the Ricci scalar, matter Lagrangian, and energy-momentum trace. Introducing coupling constants λ 1 and λ 2 enabled a realistic description beyond general relativity. Using the Durgapal-Bannerji-type metric, we derived modified field and TOV equations, obtaining expressions for energy density and anisotropic pressures. With the transformation e B ( r ) = Φ 2 ( r ) and a chosen anisotropy function Δ( r ), regular stellar models were integrated and matched smoothly to the exterior Schwarzschild-de Sitter spacetime. All physical conditions are satisfied: density and pressures are positive and finite; Δ( r ) > 0 implies an outward-directed force; sound speeds remain subluminal; and the adiabatic index Γ > 4/3 ensures dynamical stability. The generalized TOV equation confirms equilibrium among gravitational, hydrostatic, anisotropic, and curvature-matter coupling forces. The M − R relations exhibit clear trends. For λ 1 = − 4 , λ 2 = 0.4 : PSR J2215+5135 (2.28, M ⊙ ) has R = 13 . 05 − 0.20 + 0.13 km (GR: 12.33 km); PSR J0740+6620 (2.08, M ⊙ ): 12.68 → 13.32 km; PSR J0348+0432 (2.01, M ⊙ ): 12.76 → 13.39 km; PSR J0030+0451 (1.44, M ⊙ ): 13.19 → 13.77 km. Positive λ 1 compresses stars ( R = 11 . 26 + 0.33 km for λ 1 = 5 ) , while λ 1 = − 5 expands to 13 . 07 − 0.20 + 0.14 km. At λ 1 = 3 , varying λ 2 shifts R from 12 . 32 − 0.29 + 0.18 km ( λ 2 = − 5 ) to 11 . 23 + 0.35 km ( λ 2 = 5 ) . Overall, including L m or T slightly enlarges radii, showing that tuning λ 1 , λ 2 precisely controls compactness and maximum mass—consistent with observations and testable by future data.

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