https://github.com/SciML/ModelingToolkit.jl/actions/runs/29237200273/job/86774923389?pr=4742#step:12:1390 maybe a tolerance tweak is necessary.

Addressed the tolerance feedback in commit 69e3e98.

The Julia 1.13.0-rc1 ModelingToolkitBase job produced an absolute error of 1.001607e-6, only 1.607e-9 beyond the existing 1e-6 assertion threshold. The same CI-equivalent command and dependency versions passed locally, and the root nightly job also passed, which points to platform-level numerical variation at the requested 1e-6 solver tolerance.

Change:

• Increased only this assertion tolerance from 1e-6 to 2e-6.
• Added an adjacent comment documenting why the tolerance is wider.

Local verification on Julia 1.13.0-rc1 with GROUP=Initialization and the CI test options:

• Guess Propagation: 11/11
• InitializationSystem Test: 638 passed, 12 pre-existing broken
• Initial Values Test: 63/63
• ModelingToolkitBase tests passed

Runic 1.7.0 --check . also passed.

Rebased the PR onto current upstream master (fd8305b) after the intervening initialization and CI fixes merged.

Rewritten PR commits:

• 3c5e0a0: broaden LinearSolve compatibility
• 47f46d7: relax the initialization assertion tolerance

Both commits retain the required co-author trailer. After the rebase I reran the Julia 1.13.0-rc1 CI-equivalent Initialization group:

• Guess Propagation: 11/11
• InitializationSystem Test: 638 passed, 12 pre-existing broken
• Initial Values Test: 63/63
• ModelingToolkitBase tests passed

Runic 1.7.0 --check . also passed. The branch update used an explicit SHA lease after confirming the remote had no additional commits.

The red Downgrade / Downgrade Tests - InterfaceI check is an exact clean-master failure, not introduced by this PR. Clean master at fd8305b225 failed in run 29244934982: the downgrade action explicitly selected SymbolicUtils = 4.35.2, while the in-tree ModelingToolkitBase 1.51.1 now requires SymbolicUtils = 4.35.3, leaving no resolvable version. The PR job fails for the same resolver conflict before tests run. I am keeping that clean-base dependency-floor repair separate from this focused LinearSolve PR.

CI audit update for the red Benchmarks (lts) check:

• The benchmark suite itself completed and produced both time and memory tables for 47f46d714e.
• The reported ratios are near parity; for example, ODEProblem time is 4.42 ± 0.2 ms on master vs 4.62 ± 0.53 ms on this branch, and the memory table reports identical allocations for every measured case.
• The job is marked failed only in the final comment-publication step: peter-evans/create-or-update-comment@v5 received HTTP 403 Resource not accessible by integration while posting to PR Allow current LinearSolve for downstream ControlSystemsMTK tests #4742. The workflow token has pull-request metadata read permission, not comment write permission.

This is a workflow-permission failure after successful benchmark execution, not a benchmark regression. Failing job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29249396441/job/86813968486

CI audit update for the red ModelingToolkitStandardLibrary/Core downstream check:

This is an exact clean-master failure, independent of #4742. PR job 86813978519 errors in downstream/test/motor.jl because the independent variable is ModelingToolkitBase.PleaseImportDynamicQuantities, leading to _check_if_dde(..., ::PleaseImportDynamicQuantities, ...) with no method. Clean master fd8305b225, run 29244934396, job 86819996357 fails with the same PleaseImportDynamicQuantities / _check_if_dde error, one file earlier in downstream/test/piston.jl.

The recently merged ModelingToolkitStandardLibrary #483 fixed this owner import in that repository own test/motor.jl, but ModelingToolkit downstream test harness still lacks the owner-module import needed by its piston/motor fixtures. Per the clean-main audit rule, this is being assigned to a separate reproduce/bisect/fix investigation rather than folded into #4742 without analysis.

PR job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29249396526/job/86813978519
Clean-master job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29244934396/job/86819996357

The red QA / Julia 1 / Ubuntu check is a self-hosted runner/reporting failure, not a reported test assertion. Job metadata marks the job completed/failure at 13:25:16 UTC, but its Run tests step remains in_progress and every later step remains pending. GitHub has no uploaded log blob for the completed job; the logs endpoint returns BlobNotFound / HTTP 404. There is therefore no package failure output to act on. Job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29249397246/job/86816532314

CI audit update for the red ModelingToolkitBase QA check: this is also exact clean master. PR job 86820621953 and clean-master job 86820576774 both pass JET 54/54, then Aqua reports the same three classes: 45 method ambiguities, five unbound-type-parameter methods, and the same SymbolicUtils/JumpProcesses piracy list. Both finish Aqua at 8 pass / 3 fail.

None of these methods or QA settings is changed by #4742. This cluster requires its own reproduce/bisect/fix audit; I will not silence Aqua or add broad ignores. PR job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29249397225/job/86820621953 ; clean-master job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29244935232/job/86820576774

Existing clean-main audit linkage for the ModelingToolkitBase QA cluster: issue #4670 already contains the exact local reproduction, commit boundaries, and ownership analysis for all three remaining Aqua classes. Focused draft #4738 fixes the five unbound-method reports without ignores and passes Aqua.test_unbound_args(ModelingToolkitBase) locally; #4737 already merged the independent metadata fixes. The 45 ambiguities and 14 piracy-reported methods remain documented in #4670, including the owning-package moves/API redesign needed for the piracy set. No duplicate issue or QA suppression is needed here.

Rebased the PR again onto current upstream/master (aa4afff870) after master advanced during CI. The updated tolerance commit is 8e6fc7f52b; the remote branch was verified unchanged before the SHA-specific lease update.

Post-rebase local validation used the direct sublibrary pre-release CI command on Julia 1.13.0-rc1:

GROUP=Initialization JULIA_NUM_THREADS=1 julia --project=lib/ModelingToolkitBase \
  -e 'import Pkg; Pkg.test(; coverage=true, julia_args=["--check-bounds=auto", "--compiled-modules=yes", "--depwarn=yes"], force_latest_compatible_version=false, allow_reresolve=true)'

Guess Propagation         11 / 11
InitializationSystem    638 passed, 12 broken
Initial Values            63 / 63
Testing ModelingToolkitBase tests passed
exit 0 (940.8 s)

Runic 1.7.0 also passed across all 219 tracked Julia files. Before this final rebase, all six root/direct ModelingToolkitBase Initialization CI variants were green across Julia LTS, stable, and pre-release; the new push has started a fresh CI run.

Fresh rebased CI classification: Downgrade/InterfaceI fails on the independently reproduced clean-main Symbolics API floor (CodegenFunctionOptions unavailable under the selected floor), not this PR’s LinearSolve compat or initialization tolerance changes. The prerequisite Symbolics public+documented API and stacked MTK floor audit is active. Job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29255839047/job/86835800984.

Fresh-run follow-up, all remaining completed reds match existing audits:

• ModelingToolkitStandardLibrary downstream is the exact piston PleaseImportDynamicQuantities sentinel under the active focused MTKSL fix: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29255838769/job/86835837329.
• MTKB QA reports the same ambiguity/unbound/piracy classes from QA: track pre-existing Aqua/JET/ExplicitImports findings (root + ModelingToolkitBase) #4670; focused Fix ModelingToolkitBase Aqua unbound arguments #4738 makes the unbound class pass in its full QA lane without ignores: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29255839356/job/86842071987.
• Benchmark/current was cancelled during the benchmark action with no package assertion: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29255838482/job/86835798619.
• Benchmark/LTS completed its computation and again failed only at the known comment-publication permission step: https://github.com/SciML/ModelingToolkit.jl/actions/runs/29255838482/job/86835798601.

Together with the separately linked Symbolics downgrade floor, these remain independent of #4742.

Fresh CI verification after the final rebase:

• Root Initialization: Julia lts, 1, and pre all pass.
• Direct ModelingToolkitBase Initialization: Julia lts, 1, and pre all pass.

This includes the root Julia pre job that originally failed by 1.607e-9 beyond the old 1e-6 threshold.

The remaining red checks are independent base/workflow issues: the downgrade codegen regression and ModelingToolkitStandardLibrary fixture failures reproduce on clean base branches and are being handled separately; the benchmark computation completed, but its fork-token PR comment POST was rejected with HTTP 403.

The fresh build failure in job 86835798225 is the known post-resolver documentation baseline cluster, not an Initialization regression. The same examples were reproduced after a successful docs install on then-current master and recorded in #4729: undefined incidence_matrix, PeriodicOrbitOCollProblem, FunctionMap, and Rodas4, followed by Documenter reporting [:example_block]. No test or example is being disabled or downgraded. A dedicated clean-main repair audit is queued; the currently active audit slots are occupied by other baseline failures.