Solve the composite electrode SOH by bracketed rootfind

[MarcBerliner]

Stacked on #5729, which adds pybamm.Brent. Review that first; this diff is against it.

What changes

Each stoichiometry was a variable in one nine-variable algebraic system handed to a Newton solver, which makes reaching a state a basin-of-attraction problem — worn and lithium-poor cells sat outside it.

Now each stoichiometry is an expression, found by inverting the open-circuit potential it sits on with a pybamm.Brent. LithiumIonParameters.U clips its stoichiometry and adds an asymptote, so every OCP diverges outside [0, 1]; every inversion therefore brackets a root and converges from any target — including targets outside the physical range, whose answer is non-physical but exact.

Nothing is left for a solver to iterate, so the stoichiometries are read back through one CasADi function rather than per-variable post-processing. The capacities reach that function as inputs, so only the parameters its graph substitutes can invalidate it: a caller ageing a cell reuses it, a caller swapping an OCP does not.

Measured against main

8000 targets — 1000 states of charge on [0, 1], 1000 voltages on [2.5, 4.2] V, three hysteresis directions, four wear states, through the public API:

	main	this branch
failures	147 / 8000	0 / 8000
build	12.2 ms	18.5 ms
first solve	58.9 ms	14.8 ms

main's failures are silent — every one returns a state violating lithium conservation rather than raising, concentrated at low SOC.

Repeat calls through a reused simulation, reading the stoichiometries back:

	main	this branch
new target	18.8 ms	7.2 ms
aged capacities	15.3 ms	15.6 ms
no reuse (cold)	75.3 ms	91.2 ms

Known limitations

• Reading variables through ProcessedVariable is slower than main (roughly 4×). It converts and evaluates the whole nested rootfind once per variable; the evaluator bypasses that, but only for get_initial_stoichiometries_composite, which is the path Simulation uses. A caller driving ElectrodeSOHComposite directly pays it.
• The build is ~1.5× slower: the Brent graph is larger symbolically than the algebraic system it replaces. Paid once per model.
• solve_split is kept as the fallback and is now actually reachable — the native rootfinder reports failure as RuntimeError, which the old ladder did not catch, and the retry re-ran an identical solve. It now returns the split result instead.
• Bracketing guarantees convergence, not uniqueness. A user OCP that is non-monotone within [0, 1] would still bracket, and Brent would return one of its roots.
• Composite-positive coverage in the sweeps uses parameters aliased from their single-phase equivalents, since Chen2020_composite describes a composite negative. That is a degenerate composite, not a real parameter set.

Tests: 4221 unit, 32 sweep tests in test_electrode_soh_composite_sweeps.py.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 97.46835% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.96%. Comparing base (fa12f8d) to head (3a8b1da).

Files with missing lines	Patch %	Lines
...tery_models/lithium_ion/electrode_soh_composite.py	97.41%	4 Missing ⚠️

Additional details and impacted files

@@                  Coverage Diff                  @@
##           claude/brent-node    #5730      +/-   ##
=====================================================
- Coverage              98.08%   97.96%   -0.13%     
=====================================================
  Files                    341      341              
  Lines                  32916    32993      +77     
=====================================================
+ Hits                   32285    32320      +35     
- Misses                   631      673      +42     

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[aabills]

real review pending #5729

[aabills]

is this logic necessary? Kinda strange that we change the value of temperature based on initialization method