Make simplification deterministic w.r.t. hash/objectid ordering

[baggepinnen]

Problem

mtkcompile can produce different results run-to-run, even within a single Julia session (observed ~9/100 on metadata/array/connector-heavy models). The structural symbol hash is actually stable (SymbolicUtils deliberately avoids objectid), so the leak is elsewhere:

Several pipeline stages order observable output by iterating Dict/Set collections keyed by types. Type iteration order follows objectid/hash(::DataType), which is not stable for types freshly created per compile (e.g. FunctionWrapper{R,Tuple{…}} / closure parameter types that multibody-style models route into nonnumeric parameter buffers). This permutes the parameter buffer layout and generated-function argument order — invisible in the equation list, which is why it's easy to miss. Builtin-typed parameters hash stably, which is why the symptom is intermittent.

Reproduced deterministically with parameters carrying fresh struct symtypes: 176/200 distinct buffer layouts over 200 in-session compiles (with GC.gc(true) between runs); 1/200 after this PR.

A second, independent source: IfLifting stored its condition→variable map in a plain Dict and named the generated condition variables with gensym (global counter) — both non-deterministic. That reproducer went 300/300 distinct → 1/300.

Changes

• lib/ModelingToolkitBase/src/canonical_ordering.jl (new): a shared, hash/objectid-independent canonical_sort_key / canonical_name / canonical_sort, keyed on variable names (mirrors the approach already used in ModelingToolkitTearing).
• index_cache.jl: order the nonnumeric/constant/discrete parameter buffers (and the symbols within each) by canonical_sort_key of the parameters, not by Dict{TypeT,Set} / Set{TypeT} iteration. This is the primary fix.
• if_lifting.jl: conditions is now an OrderedDict, and condition variables get deterministic ifelse_cond_N names instead of gensym.
• sccnonlinearproblem.jl: order SCC cache buffers/types canonically in build_caches!.
• test/nondeterminism_simplification.jl (new, registered in group_interfaceii.jl): compiles representative models 150× with GC.gc(true) between runs and asserts identical compiled structure.

Verification

• index_cache & if-lifting reproducers: distinct=1 (were 176/200 and 300/300).
• Functional solve + symbolic parameter access correct after the buffer relayout.
• Existing if_lifting.jl passes; scc_nonlinear_problem.jl core testsets pass.

Not included (follow-up)

• ModelingToolkitTearing: the lexicographic equation sort (bounded_string in tearingstate.jl) keys on the printed form, whose Add/Mul operand order is in principle hash-dependent. It is currently stable (operand iteration verified stable), so this is latent and lives in a separate repo; suggested patch is to sort by canonical incidence instead:

  sortidxs = sortperm(
      [sort!([canonical_sort_key(v) for v in symbolic_incidence[i]]) for i in eachindex(eqs)];
      alg = Base.Sort.DEFAULT_STABLE)

  (may change which valid tearing arrangement is chosen — re-check test/structural_transformation/tearing.jl).
• HashedRandom initial-guess seeding (seeded by hash(var)) left as-is.

Draft pending a full Pkg.test run; please watch parameter-layout- and tearing-sensitive tests.

🤖 Generated with Claude Code

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change

	Moshi.Match.@match x begin
	return Moshi.Match.@match x begin

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change

	BSImpl.Div(;) => :/
	BSImpl.ArrayOp(;) => Symbol("#arrayop")
	BSImpl.Const(;) => Symbol("#const")
	BSImpl.Div() => :/
	BSImpl.ArrayOp() => Symbol("#arrayop")
	BSImpl.Const() => Symbol("#const")

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change

	sort!(sorted_buffers; by = b -> canonical_sort_key(first(b[2])),
	alg = Base.Sort.DEFAULT_STABLE)
	sort!(
	sorted_buffers; by = b -> canonical_sort_key(first(b[2])),
	alg = Base.Sort.DEFAULT_STABLE
	)

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change

	vcat, (cacheexprs[T] for T in sorted_cache_types); init = SymbolicT[])
	vcat, (cacheexprs[T] for T in sorted_cache_types); init = SymbolicT[]
	)

[github-actions]

[Runic] _{reported by reviewdog 🐶}

Suggested change

	@variables x1(t)=0.1 x2(t)=0.2 x3(t)=0.3 x4(t)=0.4
	@parameters a=1.0 b=2.0 c=3.0
	@variables x1(t) = 0.1 x2(t) = 0.2 x3(t) = 0.3 x4(t) = 0.4
	@parameters a = 1.0 b = 2.0 c = 3.0