Allow LinearSolve 5 in root tests

[ChrisRackauckas-Claude]

Please ignore this draft until reviewed by @ChrisRackauckas.

Summary

• Allow LinearSolve 4 and 5 in the root test compatibility range.
• Unblock the BoundaryValueDiffEq downstream lane in Add reusable homotopy solver caches NonlinearSolve.jl#1100.
• Keep the change test-only: LinearSolve is an extra/target here, not a runtime dependency of the root package.

Diagnosis

The failing downstream job developed current NonlinearSolveFirstOrder, which requires LinearSolve 5, while the BoundaryValueDiffEq root test project restricted LinearSolve to major 3. A clean resolver replay reproduced the empty intersection.

A resolver bisect from NonlinearSolve commit c802a160 to current master identified 6a7687f5 (SciML/NonlinearSolve.jl#1039) as the first commit that exposes the stale ceiling. That NonlinearSolve change legitimately needs LinearSolve 4.3 or newer for its linear-solve workspace behavior, so the owner fix is to broaden this test-only BoundaryValueDiffEq range rather than revert NonlinearSolve.

Local validation

• Exact downstream replay with current NonlinearSolve master paths (1d51c8dac), NonlinearSolveFirstOrder 2.2.4, and LinearSolve 5.2.0: GROUP=All Pkg.test() passed; observed root totals were 163 pass and 4 unchanged pre-existing broken cases, with outer Pkg.test reporting tests passed.
• Clean one-line tree with no path dependencies in Project.toml independently resolved LinearSolve 5.2.0, NonlinearSolveFirstOrder 2.2.2, NonlinearSolveBase 2.37.0, and SciMLJacobianOperators 0.1.16; GROUP=All Pkg.test() passed with the same observed root totals and outer success.
• Whole-repository Runic check passed.
• git diff --check passed.

[ChrisRackauckas-Claude]

Diagnostic scratchpad:

1. Reproduced the NonlinearSolve #1100 BoundaryValueDiffEq/All failure on clean BoundaryValueDiffEq master before tests: NonlinearSolveFirstOrder 2.2.4 fixed LinearSolve to major 5 while the root test Project allowed only 3.87.
2. Resolver-bisected NonlinearSolve from c802a160 to current master. First exposing commit: 6a7687f542cde52b4bfeef5b473c6156c8d453a1 (#1039), which intentionally raises the LinearSolve floor for the quasi-Newton linear workspace.
3. Kept the owner patch to the single test-only compat line; no source or runtime dependency changes.
4. Ran both the exact current-master path replay and a second unpolluted registered-dependency GROUP=All run. Both outer Pkg.test processes exited successfully; Runic and diff checks also passed.

[github-actions]

Benchmark Results (Julia v1.11)

Time benchmarks

	master	b49ec00...	master / b49ec00...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.588 ± 0.0028 s	0.582 ± 0.0041 s	1.01 ± 0.0087
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	12.2 ± 0.23 ms	12.2 ± 0.18 ms	1 ± 0.024
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	2.67 ± 0.076 ms	2.66 ± 0.082 ms	1 ± 0.042
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	3.21 ± 0.082 ms	3.19 ± 0.088 ms	1.01 ± 0.038
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.54 ± 0.049 ms	1.54 ± 0.045 ms	0.999 ± 0.043
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.53 ± 0.07 ms	1.51 ± 0.059 ms	1.01 ± 0.062
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.1 ± 0.098 ms	3.14 ± 0.097 ms	0.987 ± 0.044
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0389 ± 0.0026 s	0.0396 ± 0.0027 s	0.982 ± 0.095
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0591 ± 0.0019 s	0.0592 ± 0.002 s	0.999 ± 0.046
Simple Pendulum/IIP/Shooting(Tsit5())	0.18 ± 0.073 ms	0.185 ± 0.072 ms	0.974 ± 0.55
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.721 ± 0.011 s	0.732 ± 0.0039 s	0.985 ± 0.017
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	15.4 ± 4.1 ms	15.7 ± 4.2 ms	0.984 ± 0.37
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	3.19 ± 0.15 ms	3.2 ± 0.14 ms	0.997 ± 0.063
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	3.86 ± 0.23 ms	3.85 ± 0.2 ms	1 ± 0.08
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	1.86 ± 0.11 ms	1.85 ± 0.1 ms	1 ± 0.081
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.25 ± 0.44 ms	3.25 ± 0.42 ms	1 ± 0.19
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	6.33 ± 5.3 ms	6.39 ± 5 ms	0.991 ± 1.1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0812 ± 0.0033 s	0.0854 ± 0.0027 s	0.952 ± 0.048
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.128 ± 0.0037 s	0.126 ± 0.0044 s	1.01 ± 0.046
Simple Pendulum/OOP/Shooting(Tsit5())	0.595 ± 0.041 ms	0.594 ± 0.039 ms	1 ± 0.095
time_to_load	7.43 ± 0.13 s	7.29 ± 0.06 s	1.02 ± 0.02

Memory benchmarks

	master	b49ec00...	master / b49ec00...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.389 M allocs: 0.0443 GB	0.389 M allocs: 0.0443 GB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	0.0436 M allocs: 4.88 MB	0.0436 M allocs: 4.88 MB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	15.7 k allocs: 1.65 MB	15.7 k allocs: 1.65 MB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	22.1 k allocs: 2.04 MB	22.1 k allocs: 2.04 MB	1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	12.8 k allocs: 1.05 MB	12.8 k allocs: 1.05 MB	1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	25.5 k allocs: 1.82 MB	25.5 k allocs: 1.82 MB	1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	0.049 M allocs: 3.39 MB	0.049 M allocs: 3.39 MB	1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.553 M allocs: 0.0535 GB	0.553 M allocs: 0.0535 GB	1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.833 M allocs: 0.0778 GB	0.833 M allocs: 0.0778 GB	1
Simple Pendulum/IIP/Shooting(Tsit5())	4.64 k allocs: 0.224 MB	4.64 k allocs: 0.224 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.89 M allocs: 0.984 GB	0.89 M allocs: 0.984 GB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	0.0932 M allocs: 24.8 MB	0.0932 M allocs: 24.8 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	0.0324 M allocs: 3.96 MB	0.0324 M allocs: 3.96 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	0.045 M allocs: 4.99 MB	0.045 M allocs: 4.99 MB	1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	25.3 k allocs: 2.17 MB	25.3 k allocs: 2.17 MB	1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	0.142 M allocs: 10.2 MB	0.142 M allocs: 10.2 MB	1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	0.266 M allocs: 18.7 MB	0.266 M allocs: 18.7 MB	1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	2.52 M allocs: 0.279 GB	2.52 M allocs: 0.279 GB	1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	3.82 M allocs: 0.404 GB	3.82 M allocs: 0.404 GB	1
Simple Pendulum/OOP/Shooting(Tsit5())	0.0373 M allocs: 1.69 MB	0.0373 M allocs: 1.69 MB	1
time_to_load	0.159 k allocs: 11.2 kB	0.159 k allocs: 11.2 kB	1