Independent Reproduction of Chameleon Fifth-Force Stiffness in MICROSCOPE-Like Nested Cylinders: Geometry-Sensitive Benchmarks and Source-Consistency Checks

Version:1.1.0 Resource type:Publication / Preprint Creator:Darren Dominic Fabri Description: This work independently reproduces and reconstructs theoretical chameleon-force benchmarks for the idealized infinite nested-cylinder geometry studied by Pernot-Borràs et al. in Phys. Rev. D 101, 124056 (2020), DOI 10.1103/PhysRevD.101.124056. A one-outer-cylinder radial boundary-value solve and direct force quadrature reproduce the four source Table-I exact-force values with a maximum relative difference of 0.346%. For the two-cylinder problem, the displaced inner annulus is treated through the first-order shape expansion phi_delta(r,theta)=phi_0(r)+delta q(r) cos(theta)+O(delta^2), including interface derivative jumps derived directly from the translated piecewise density. The cancellation-stable separated-solution implementation exhibits second-order grid refinement, with observed orders p=2.00074 and 2.00168, and yields k_h=-3.526268533e-5 N m^-2 in the convention F/h=-k_h delta+O(delta^2). A separate sparse nodal finite-difference implementation extrapolates to |k_h|=3.526278363e-5 N m^-2, agreeing with the first continuum estimate to approximately 2.8e-6 relative. The reconstructed continuum stiffness is 6.71% below the source Table-IV magnitude 3.78e-5 N m^-2. This difference remains unresolved. The source's own small-displacement multipole data make omitted higher multipoles quantitatively implausible as a percent-level explanation; at delta=1e-6 m the quoted l=2 force contribution is only about 3.0e-6 of the net force implied by the Table-IV stiffness. The source decomposition is strongly cancellation-sensitive between much larger radial/monopole and dipole contributions, identifying source implementation and force-assembly details as high-leverage future audit targets without establishing causation. Two source-consistency checks are also reported. Under the 2020 equations as printed, direct differentiation of the unnormalized angular force integral in source Eq. (50) gives a coefficient differing by a factor 2pi from printed Eq. (51). The printed Table-I linear stiffness and angular frequency also fail omega^2=|k_h|/(m/h) under the stated density and geometry. These are localized as-printed consistency observations, not an official erratum or an experimental anomaly. A source check of the 2021 MICROSCOPE chameleon companion paper finds no demonstrated direct propagation of the printed Eq. (51) or Table-I omega into its exclusion contours: that work recomputes chameleon stiffness with multi-cylinder and one-dimensional methods. Because its screened-regime calculation extends the same semianalytic cylindrical lineage, a dedicated model-to-data replay remains a justified future reproducibility target. No change to the published 2021 constraints is inferred here. The present paper closes only the idealized theoretical chain: chameleon PDE -> nested-cylinder geometry -> fifth-force stiffness. It does not reproduce MICROSCOPE flight-data stiffness residuals, a detector likelihood, or an exclusion contour. It makes no fifth-force detection, new experimental bound, or new-physics claim. The release includes native REVTeX source and a reproducibility toolkit containing numerical checkers, machine-readable results, a claim matrix, source-version notes, Red Team adjudication, and SHA-256 integrity records. Files included: 1. Fabri_2026_MICROSCOPE_Chameleon_Stiffness_v1.1.0.pdf2. Fabri_2026_MICROSCOPE_Chameleon_Stiffness_v1.1.0.tex3. MICROSCOPE_Chameleon_Stiffness_APS_Source_v1.1.0.zip4. MICROSCOPE_Chameleon_Stiffness_Reproducibility_v1.1.0.zip5. FINAL_RELEASE_AUDIT_v1.1.0.md6. README_RELEASE_v1.1.0.md7. Fabri_2026_MICROSCOPE_Chameleon_Stiffness_v1.1.0.sha256