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LRG HOD analyses infer satellite fraction and velocity bias using high-fidelity mocks, but simplified public-box analyses can reveal which observables drive these parameters. Using the public AbacusSummit base simulation at z = 0.8 , a compact halo/subhalo-like candidate catalogue, and a DESI DR1 LRG clustering vector over 0.6 < z < 0.8 , we fit exact-number-density SHAM-like and minimal-HOD samples to w p + ξ 0 + ξ 2 . The baseline minimal-HOD grid favours a low satellite fraction, f s a t = 0.04 , with α s = 1.1 , while observable splits show that this preference is driven mainly by small-scale w p , not by the full vector uniformly. A phenomenological radial-dilution stress test improves the diagnostic score from χ h e u r 2 = 282.6 to 222.3 , but direct radial diagnostics show that q = 4.0 moves 0.723 of satellites beyond an estimated R 200 m , so it is not a physical profile model. An occupation-control test varying the satellite host-mass power shifts the selected host masses but leaves the median satellite radius nearly unchanged, and an NFW remapping gives only modest improvement. The low- f s a t preference should therefore not be interpreted as a physical low satellite fraction without matched occupation freedom, profile freedom, selection and covariance. This is not a replacement for full DESI AbacusHOD inference, but a diagnostic study of satellite-profile systematics. [ABSTRACT FROM AUTHOR] |