[math-06] Verify equilibrium and plasma-background formulas

[krystophny]

Summary

• derive multispecies equilibrium, collision, thermodynamic-force, and geometry formulas
• correct shared constants and background formula inconsistencies across KIM and KiLCA
• add deterministic KIM and KiLCA oracle consumers

Why

Both solvers use source-checked equilibrium quantities with consistent units and species sums.

Validation

Validated cumulatively at the stack head:

• cmake --build build -j2
• ctest --test-dir build -E 'test_rhs_balance|test_periodic_convergence|test_periodic_vs_global' --output-on-failure — 35/35 passed

Known red gates are intentionally excluded from that command: the pre-existing test_rhs_balance baseline failure, the periodization-deformation acceptance gate, and the unresolved periodic-vs-global 5% agreement gate.

Stack

Base: fix/kim-fp-188-matched-bvp
Head: fix/kim-fp-198-equilibrium-oracle

Closes #198

[marjohma]

Closing this draft because GitHub cannot change a pull request author in place. It will be recreated unchanged using Markus Markl's marjohma credentials.

[marjohma]

Replacement authored by Markus Markl (@marjohma): #218