The nonlinear PMF program is motivated by Jedamzik, Abel, and Ali-Haïmoud (2025). The independent linear, photon, and recombination tools follow Schiff and Venumadhav (2025), including the corrected equations and implementation choices recorded in their source provenance. These references specify related model systems; matching a shared limit does not establish equivalence of the complete nonlinear calculations.
GLM divergence cleaning follows Dedner et al. (2002) and the HLLD flux follows Miyoshi and Kusano (2005). Kernel-level modifications for cosmological clocks, stiff drag, photon coupling, and conservation are documented in the implementation pages.
All four citation records were checked against NASA ADS when this standalone distribution was prepared. ADS links are retained in references.bib. For a result, cite the physical model, exact software revision, numerical controls, and any supplied response table or recombination history.
Dedner, A., F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, et al. 2002.
“Hyperbolic Divergence Cleaning for the MHD Equations.”
Journal of Computational Physics 175: 645–73.
https://doi.org/10.1006/jcph.2001.6961.
Gardiner, Thomas A., and James M. Stone. 2005.
“An Unsplit Godunov
Method for Ideal MHD via Constrained Transport.” Journal of
Computational Physics 205: 509–39.
https://doi.org/10.1016/j.jcp.2004.11.016.
Jedamzik, Karsten, Tom Abel, and Yacine Ali-Haïmoud. 2025.
“Cosmic
Recombination in the Presence of Primordial Magnetic Fields.”
Journal of Cosmology and Astroparticle Physics 2025 (03): 012.
https://arxiv.org/abs/2312.11448.
Miyoshi, Takahiro, and Kanya Kusano. 2005.
“A Multi-State HLL
Approximate Riemann Solver for Ideal Magnetohydrodynamics.”
Journal of Computational Physics 208: 315–44.
https://doi.org/10.1016/j.jcp.2005.02.017.
Schiff, Jonathan, and Tejaswi Venumadhav. 2025.
“Primordial
Magnetic Fields and Modified Recombination Histories.” arXiv
e-Prints.
https://doi.org/10.48550/arXiv.2506.16517.