Migrate AD backends to a group env (test/AD/Project.toml)

[ChrisRackauckas-Claude]

Note

Please ignore this PR until it has been reviewed by @ChrisRackauckas. Draft — opened by an automated agent.

What

Move the heavy optional AD backends Mooncake and Zygote (plus the AD-only quadrature helpers FiniteDiff, ForwardDiff) out of the root package's old-style [extras] + [targets].test and into a group-specific test/AD/Project.toml.

Why

Integrals.jl is a hybrid: it uses SciMLTesting folder-model test groups (test/test_groups.toml declares Core/AD/QA; test/runtests.jl is just run_tests()), but the root Project.toml still carries the old-style [extras] + [targets].test listing all test deps, including Mooncake/Zygote.

Because the root has [extras], the Downgrade CI lane resolves the root/test dependencies through the merged [extras] joint graph. Mooncake/Zygote are [weakdeps] that are also test-[extras], so the downgrade harness floor-checks each backend against that root graph. Min-version resolving the optional AD backend trees against the root is the fragile part of the downgrade lane (Resolver.jl --min on the joint optional-backend graph).

Moving the AD backends into their own group env means:

• The root/Core downgrade no longer floor-resolves the Mooncake/Zygote/ForwardDiff backend graph at all — those names leave [extras], so intersect([weakdeps], [extras]) (the harness's per-backend floor-check set) drops from 13 entries to 10 (Mooncake, Zygote, ForwardDiff gone).
• The AD backends' downgrade floors are still exercised — now inside test/AD/Project.toml, whose [compat] mirrors the root floors.
• SciMLTesting folder-discovery auto-activates test/AD/Project.toml for the AD group (_run_group_folder → activate_group_env), developing the root package by path. No runtests.jl change needed.

Changes

• New test/AD/Project.toml — group env with exactly the deps test/AD/*.jl uses (Integrals, Mooncake, Zygote, FiniteDiff, ForwardDiff, Cuba, Cubature, FastGaussQuadrature, Test, SafeTestsets, SciMLTesting), [sources] Integrals = {path = "../.."}, and [compat] mirroring the root floors (modeled on test/qa/Project.toml).
• Root Project.toml — drop Mooncake, Zygote, FiniteDiff, ForwardDiff from [extras] and [targets].test. Mooncake/Zygote/ForwardDiff stay [weakdeps] (their [compat] entries stay, since they still gate extensions). FiniteDiff was a pure test dep (never a weakdep), so its now-dangling [compat] entry is removed too.

The cross-backend AD tests (test/AD/derivative_tests.jl, test/AD/nested_ad_tests.jl) are unchanged — they still cross-compare ForwardDiff / FiniteDiff / Zygote / Mooncake in a single environment. test/quadrule_tests.jl's only using Zygote is inside a #= ... =# block comment (a commented-out derivative example), so Core never actually needed Zygote.

Local validation

• Downgrade (jdc-52 harness, mode=deps, julia=1): master floor-checks 13 weakdep extensions incl. Mooncake/Zygote/ForwardDiff (writes Manifest-Mooncake.toml/-Zygote.toml/-ForwardDiff.toml); this branch floor-checks 10 and produces no Mooncake/Zygote/ForwardDiff manifests. Base Manifest.toml contains none of them. Root downgrade Successfully resolved on both, but the AD joint graph is no longer in the root.
• AD group env (Julia 1.12): activate test/AD + develop root + instantiate resolves Mooncake 0.5.36, Zygote 0.7.11, ForwardDiff 1.4.1, FiniteDiff 2.31.1; IntegralsMooncakeExt/IntegralsZygoteExt/IntegralsForwardDiffExt precompile.
• Core group (GROUP=Core, Julia 1.12): all 8 top-level test files pass (1740 assertions), Testing Integrals tests passed, with no Mooncake/Zygote in the env.
• AD group folder-discovery (Julia 1.10 lts): GROUP=AD auto-activates test/AD/Project.toml, develops Integrals by path, instantiates the AD backends.

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