Restore root LinearSolve 5 floor

[ChrisRackauckas-Claude]

Important

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• Restore the root LinearSolve compatibility floor to version 5, matching the current in-tree Base, FirstOrder, and QuasiNewton source packages.
• Bump the root package patch version from 4.21.1 to 4.21.2 so the compatibility correction is releasable.

Root cause

PR #1070 established that the current source-tree caches require the LinearSolve 5 interface: LinearSolve 4.3 fails when the local FirstOrder and QuasiNewton packages use callable LinearSolveJLCache behavior. PR #1079 subsequently broadened only the root compatibility entry from 5 back to 4.3, 5, while the in-tree NonlinearSolveQuasiNewton 1.14.1 project still requires LinearSolve 5.

The deployed downgrade action therefore selected and explicitly pinned LinearSolve 4.3.0 from the root floor. Pkg.test(...; allow_reresolve=false) then combined that manifest with the in-tree source packages and failed before loading test code:

LinearSolve possible versions: 0.1.0-5.0.0
restricted to version 5 by NonlinearSolveQuasiNewton 1.14.1
restricted to version 4.3.0 by an explicit requirement — no versions left

This is the failure in PR #1061's unrelated downgrade job 87701889361 (run 29522250552). The exact same failure reproduces on clean upstream master at 60736b5, so this PR contains no #1061 code.

A formal bisect over the relevant clean-master range reported:

60736b5b6a30a42001c1938647362ef138b1c6a7 is the first bad commit

The good midpoint, cbabebe8 (#1075), selected LinearSolve 5.0.0 and reached the Core test body. The first bad commit is 60736b5 (#1079), whose root-only compatibility change reopened the incompatible 4.3 endpoint.

Validation

All Julia validation used Julia 1.10.11 and workspace-local depots.

• The exact deployed julia-actions/julia-downgrade-compat@v2 implementation (fab1defb76df9fd672f63c94df73ce131d32e134) completed on the final diff with the workflow-derived stdlib and [sources] skip list, mode deps, Julia floor 1, and Mooncake no-promote setting.

• The resulting manifest contains NonlinearSolve 4.21.2 and LinearSolve 5.0.0.

• The exact CI test invocation reached and ran Core tests instead of failing in dependency resolution:

  Pkg.test(;
      coverage = true,
      julia_args = ["--check-bounds=yes", "--compiled-modules=yes", "--depwarn=yes"],
      force_latest_compatible_version = false,
      allow_reresolve = false,
  )

• Core is not green on clean master. The final diff and the good bisect control both reach the same independently documented Broyden baseline: 94 passed, 1 failed, 1 errored, 19 broken. The failure is Generalized Rosenbrock algorithm 4; the error is the Brown algorithm-4 unexpected pass. These are tracked in Master CI red since 2026-07-12: "23 Test Problems: Broyden" alg #4 broken-list mismatch, bisected to #1039 (merged via cancelled CI run) #1083 and Brown bad-Broyden broken test is environment-sensitive #1056. This PR does not skip, silence, loosen, or otherwise modify either test.

• Runic 1.7.0 passed all 373 tracked Julia files.

• Project.toml parsing and assertions for version 4.21.2 and LinearSolve = "5" passed.

• git diff --check passed.

The existing root downgrade workflow provides regression coverage for this compatibility floor; no test source was changed.

Investigation process

I inspected the failing Actions job and exact reusable workflow inputs, reproduced the clean-master resolver failure with the deployed action SHA, reviewed prior fixes #1059, #1070, #1075, and #1079, ran a formal git bisect, compared the good midpoint's full Core result with the patched result, searched open PRs and issues for a duplicate fix, and validated the smallest source-tree-compatible correction. The open #1086 changes only the Base sublibrary version and does not overlap this root change.

[ChrisRackauckas-Claude]

Interim CI audit for head 6f18c93571973ef43f88867ca4aaa985366075f6:

• The targeted root downgrade job now resolves successfully with LinearSolve 5.0.0 and reaches the Core tests. This confirms that the resolver conflict fixed by this PR is gone; the later Core failures are existing clean-master regressions tracked in Preserve triangular solves for Broyden Jacobian inversion #1057/Brown bad-Broyden broken test is environment-sensitive #1056.
• The three red root Core lanes likewise contain the already-bisected generalized-Rosenbrock/Broyden failure tracked by Preserve triangular solves for Broyden Jacobian inversion #1057. One LTS lane also reported a Watson alg Refactor #2 failure that did not reproduce in the exact local Julia 1.10.11 run, the current-master LTS control, or the adjacent Eliminate dense continuation step allocations on Julia 1.12 #1061 LTS control; no assertion or tolerance was changed.
• The red documentation job is the duplicate BibTeX baseline failure fixed in Remove duplicate BibTeX entry #1088; that focused PR has 11/11 green checks including docs.
• Current totals are 41 successful, 4 skipped, 5 failed, and 21 queued. All outstanding jobs are waiting on constrained macOS/GPU runners; this is an interim classification, not a terminal CI claim.

[ChrisRackauckas-Claude]

Closing as superseded by merged #1095. That PR landed the same required root LinearSolve = "5" correction; current master is version 4.22.0 and both its exact-current root and sublibrary downgrade workflows are green: https://github.com/SciML/NonlinearSolve.jl/actions/runs/29762728296 and https://github.com/SciML/NonlinearSolve.jl/actions/runs/29762728169. No unique source or test change remains in this older draft.