Limited sensitivity of published InSight RISE rotation products to the seismically proposed Martian inner-core family: a prospectively specified reanalysis

Artus Krohn-Grimberghe 

The InSight Rotation and Interior Structure Experiment (RISE) measured the rotation of Mars by radio tracking; Le Maistre et al. (2023) report the detection of the Free Core Nutation (FCN, period −243 ± 3.3 d) and no detection of the Free Inner Core Nutation (FICN) that a solid inner core would add. Bi et al. (2025) subsequently reported a 613 ± 67 km solid inner core from seismology, without addressing the FICN. We ask whether the published RISE rotation products can test that specific proposed core family — whether the FICN non-detection is evidential or uninformative — using three analyses whose grids, statistics, thresholds and outcome wordings were specified and archived before the outcome-determining computations were run. Analysis A, a forward detectability sweep over a registered 45-cell family grid (three radii × five density contrasts × three coupling treatments), evaluates 27 cells and conservatively withholds 18 under registered validity gates; every evaluated cell returns the registered verdict "below the measurement floor" from a joint consistency statistic against the published Mars-orientation uncertainties (largest per-cell reduced χ² 0.2921; largest single-term diagnostic 2.105 σ). Analysis B projects the same family onto the published fixed-period FICN-strength scan and returns its registered outcome: "No evaluated admitted model has a FICN signature that is both representable in the published F* parameterization and demonstrably recoverable at the registered sensitivity. The published RISE FICN null is therefore uninformative for this test and supports neither the presence nor the absence of a Martian inner core." Analysis C, a joint Bayesian confrontation of inner-core radius and density contrast with the 16 published nutation-term perturbations, finds the family consistent with the published products (minimum joint χ² = 0.021) and the result prior-dominated: the joint core posterior is the published seismic posterior essentially unchanged (90% width ratios 0.884 and 0.926). The inferred FICN period, residue, phase and damping depend on an Earth-anchored first-order gravitational-coupling treatment, zero-defaulted Mars compliances and the explicitly sampled coupling branches. Models outside those branches were not tested and are not excluded. At current sensitivity the published rotation products neither confirm nor refute the proposed inner core; we quantify the sensitivity gap and identify the observation types that could close it.