Test Brown bad-Broyden convergence on Linux x86_64

[ChrisRackauckas-Claude]

Important

Please ignore this draft until it has been reviewed by @ChrisRackauckas.

Summary

• Require Brown almost-linear problem 8 to converge for true-Jacobian bad Broyden only on the supported Linux x86_64 lanes.
• Retain the existing broken expectation on macOS arm64 and every unverified platform.
• Leave the unrelated generalized Rosenbrock expectation unchanged.

Root cause

The exact-base failure is an unexpected pass, not a new loss of convergence. A frozen-dependency bisect identified 6a7687f (#1039) as the first commit where this unglobalized solve enters the convergent basin. The inverse-workspace change is at roundoff scale, but the Brown start is ULP-sensitive: adjacent floating-point starts switch between a residual of about 7.31e-13 and an Unstable return with residual 5.5.

The supported CI matrix consistently splits by platform across Julia 1.10.11, 1.12.6, and 1.13.0-rc1: Ubuntu 24.04 x86_64 converges, while macOS 26 arm64 remains above the 1e-3 tolerance. Current and downgrade-floor dependency graphs both converge locally on Linux x86_64. Detailed reproduction, dependency, CI, bisect, and perturbation evidence is recorded in #1056.

Li–Fukushima globalization makes representative adjacent-float starts converge, but changing Broyden's default globalization would be a broad algorithm behavior change. This PR therefore scopes the stronger test expectation only to the platform proven by the supported matrix. Unlike #1069, it does not alter the unrelated Rosenbrock expectation or require Brown to converge on macOS arm64.

Validation

• Julia 1.12.6, current graph: Brown problem 8 passed 20/20 times; residual 7.314149286230531e-13 every run.
• Julia 1.12.6, downgrade-floor graph: Brown problem 8 passed 20/20 times; same residual every run.
• Full Broyden robustness file, current graph: 95 passed, 1 failed, 19 broken; Brown alg Make iip a compile-time constant #4 passed normally. The sole failure is the pre-existing generalized Rosenbrock alg Make iip a compile-time constant #4 result (4.4 > 1e-3), which is being investigated separately.
• Full Broyden robustness file, downgrade-floor graph: identical 95 passed, 1 failed, 19 broken result and the same sole pre-existing Rosenbrock failure.
• Runic 1.7.0: --check . passed.
• git diff --check passed.

The official downgrade workflow at the investigated base stopped during package resolution before Core tests ran; the floor graph above was therefore reproduced in a pinned local environment.

[ChrisRackauckas-Claude]

Withdrawing this draft: downgrade CI disproved the proposed Linux x86_64 expectation.

Official downgrade job 87345863358 used Julia 1.10.11 and the action-generated graph (LinearSolve 5.0.0, NonlinearProblemLibrary 0.1.7, SciMLBase 3.34.0, SciMLOperators 1.24.0, SciMLJacobianOperators 0.1.15) on Linux x86_64/EPYC 9354. Brown alg #4 produced residual 5.5; the Broyden summary was 94 passed, 2 failed, 19 broken.

An exact clean-depot reproduction of the action SHA/mode, merge commit, Pkg.test flags, and package versions on Linux x86_64/EPYC 7502 instead made Brown pass; the summary was 95 passed, 1 failed, 19 broken, with only the independently tracked Rosenbrock residual 4.4.

Changing only SciMLJacobianOperators to the in-tree 0.1.16 source did not change the local result. Its runtime source is byte-identical to registered 0.1.15; only version/compat metadata differs, and the tested SciMLOperators 1.24.0 already satisfies that metadata.

Therefore there is no stable OS/architecture/package condition for this expectation. The solve is ULP/hardware-sensitive. Robustness requires a broader globalization behavior change, not test bookkeeping.

Commit 66bc20484 reverts the proposed condition, so this branch now has no source diff from master. Detailed corrected evidence is in #1056 (comment).