Make linear_compartment_model ODE print order deterministic

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Summary

linear_compartment_model was building an ODE via the 3-arg constructor, which sets x_vars/y_vars from Dict key order. show(::ODE) already iterates x_vars, so the printed (and doctest-pinned) equation order reshuffled across Julia versions. This passes the already-built ordered x_vars/y_vars into the 5-arg constructor and re-pins the lincomp doctest to compartment index order (x1…x4).

Fail before / pass after

Negative control (src reverted to master, same order assertions):

 [4] macro expansion
   @ ~/.julia/juliaup/julia-1.12.7+0.x64.linux.gnu/share/julia/stdlib/v1.12/Test/src/Test.jl:680 [inlined]
linear_compartment_model variable order is deterministic: Test Failed at /home/crackauc/sandbox/goals/issue-backlog/ibd/StructuralIdentifiability.jl/jobs/559-cursor/scratch/check_order.jl:20
  Expression: occursin(r"^x1'.*\nx2'.*\nx3'.*\nx4'.*\ny1 ="s, printed)
   Evaluated: occursin(r"^x1'.*\nx2'.*\nx3'.*\nx4'.*\ny1 ="s, "x1' = -x1*a_2_1 - x1*a_4_1 + x2*a_1_2 + x4*a_1_4\nx3' = x2*a_3_2 - x3*a_2_3 - x3*a_4_3 - x3*a_0_3 + x4*a_3_4\nx2' = x1*a_2_1 - x2*a_1_2 - x2*a_3_2 - x2*a_0_2 + x3*a_2_3 + u2\nx4' = x1*a_4_1 + x3*a_4_3 - x4*a_1_4 - x4*a_3_4\ny1 = x1\n")

Stacktrace:
 [1] top-level scope
   @ ~/sandbox/goals/issue-backlog/ibd/StructuralIdentifiability.jl/jobs/559-cursor/scratch/check_order.jl:17
 [2] macro expansion
   @ ~/.julia/juliaup/julia-1.12.7+0.x64.linux.gnu/share/julia/stdlib/v1.12/Test/src/Test.jl:1777 [inlined]
 [3] macro expansion
   @ ~/sandbox/goals/issue-backlog/ibd/StructuralIdentifiability.jl/jobs/559-cursor/scratch/check_order.jl:20 [inlined]
 [4] macro expansion
   @ ~/.julia/juliaup/julia-1.12.7+0.x64.linux.gnu/share/julia/stdlib/v1.12/Test/src/Test.jl:680 [inlined]
Test Summary:                                            | Pass  Fail  Total  Time
linear_compartment_model variable order is deterministic |    2     2      4  5.6s
RNG of the outermost testset: Random.Xoshiro(0xe07a0862f74f428a, 0x6f30d612ccbb3381, 0x61dd84f68d83e949, 0x1ef8782cffaa70ca, 0xf02b6ca71ebd8100)
ERROR: LoadError: Some tests did not pass: 2 passed, 2 failed, 0 errored, 0 broken.
in expression starting at /home/crackauc/sandbox/goals/issue-backlog/ibd/StructuralIdentifiability.jl/jobs/559-cursor/scratch/check_order.jl:16

After the fix (3 fresh Julia processes):

x1' = -x1*a_2_1 - x1*a_4_1 + x2*a_1_2 + x4*a_1_4
x2' = x1*a_2_1 - x2*a_1_2 - x2*a_3_2 - x2*a_0_2 + x3*a_2_3 + u2
x3' = x2*a_3_2 - x3*a_2_3 - x3*a_4_3 - x3*a_0_3 + x4*a_3_4
x4' = x1*a_4_1 + x3*a_4_3 - x4*a_1_4 - x4*a_3_4
y1 = x1
--- assertions ---
Test Summary:                                            | Pass  Total  Time
linear_compartment_model variable order is deterministic |    4      4  1.7s
===== PASS RUN 2 =====
x_vars = ["x1", "x2", "x3", "x4"]
--- printed ---
x1' = -x1*a_2_1 - x1*a_4_1 + x2*a_1_2 + x4*a_1_4
x2' = x1*a_2_1 - x2*a_1_2 - x2*a_3_2 - x2*a_0_2 + x3*a_2_3 + u2
x3' = x2*a_3_2 - x3*a_2_3 - x3*a_4_3 - x3*a_0_3 + x4*a_3_4
x4' = x1*a_4_1 + x3*a_4_3 - x4*a_1_4 - x4*a_3_4
y1 = x1
--- assertions ---
Test Summary:                                            | Pass  Total  Time
linear_compartment_model variable order is deterministic |    4      4  1.8s
===== PASS RUN 3 =====
x_vars = ["x1", "x2", "x3", "x4"]
--- printed ---
x1' = -x1*a_2_1 - x1*a_4_1 + x2*a_1_2 + x4*a_1_4
x2' = x1*a_2_1 - x2*a_1_2 - x2*a_3_2 - x2*a_0_2 + x3*a_2_3 + u2
x3' = x2*a_3_2 - x3*a_2_3 - x3*a_4_3 - x3*a_0_3 + x4*a_3_4
x4' = x1*a_4_1 + x3*a_4_3 - x4*a_1_4 - x4*a_3_4
y1 = x1
--- assertions ---
Test Summary:                                            | Pass  Total  Time
linear_compartment_model variable order is deterministic |    4      4  2.1s

test/bodies/linear_compartment.jl with fix: 12/12 (master baseline was 8/8; +4 order assertions):

Test Summary:                                | Pass  Total     Time
Identifiability of linear compartment models |   12     12  2m13.2s

Doctest expected text matches sprint(show, ode) (DOCTEST_MATCH on Julia 1.12.7).

Commands run

• julia +1.12 --project=. scratch/check_order.jl (before, negative control, 3× after)
• julia +1.12 --project=. -e '… include(\"test/bodies/linear_compartment.jl\")' (master baseline 8/8; with fix 12/12)
• Runic --check src/lincomp.jl test/bodies/linear_compartment.jl (exit 0)
• typos src/lincomp.jl test/bodies/linear_compartment.jl (exit 0)

Not verified

• Full Pkg.test() / docs Documenter doctest CI job on Julia 1.13
• Other call sites that still use the 3-arg ODE constructor (still Dict-order for x_vars)

Reviewer pushback

• Prefer sorting in the 3-arg ODE constructor instead of only fixing linear_compartment_model
• Prefer collect(x_vars) vs Array{…}(x_vars) style

Fixes #559

Please ignore this draft until reviewed by @ChrisRackauckas.

Risk assessment

Risk: low
Blast radius: linear_compartment_model return value's x_vars/y_vars order and printed equation order only; identifiability results unchanged (existing 8 cases still pass).
Evidence: fail-before / pass-after order assertions; linear_compartment body 8→12; doctest text match; Runic/typos clean.
Independent review: Claude Code (Opus 5.5) rated it low, high confidence: order assertions fail on master in 6/6 fresh processes (session-dependent order, e.g. x1,x3,x2,x4) and pass on the PR in 4/4; doctest equals sprint(show) byte-for-byte; assess_identifiability identical on master and PR for a 2-compartment model and the test file's 10 result assertions pass on both; the 5-arg ODE constructor receives exactly the dict keys. Follow-up (not in this PR): other 3-arg ODE{P}(x_eqs, y_eqs, inputs) call sites inherit Dict order the same way (src/ODE.jl:53-54 root cause; src/ODE.jl:114, src/parametrizations.jl:246).
Merge: needs human review (StructuralIdentifiability is excluded from auto-merge).

Harness: Cursor Agent CLI 2026.09.28-64d2043; model: auto; transcript: /home/crackauc/sandbox/goals/issue-backlog/ibd/StructuralIdentifiability.jl/jobs/559-cursor/log.txt on amdci2.julia.csail.mit.edu

[pogudingleb]

Thanks!