diff --git a/src/CoolPDLP.jl b/src/CoolPDLP.jl
index 84da9be..3336822 100644
--- a/src/CoolPDLP.jl
+++ b/src/CoolPDLP.jl
@@ -65,6 +65,7 @@ export preprocess, initialize, solve, solve!
 export PDHG, PDLP
 @public Algorithm
 @public KKTErrors, relative
+@public termination_status
 export is_feasible, objective_value
 
 @public Optimizer
diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index 32a3dc1..2fa0b9f 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -254,7 +254,7 @@ function MOI.optimize!(dest::Optimizer{T}, fcache::MOI.Utilities.UniversalFallba
     dest.dual_obj_value = (max_sense ? -raw_dual_obj : raw_dual_obj) + obj_constant
     dest.solve_time = stats.time_elapsed
 
-    cts = stats.termination_status
+    cts = termination_status(stats)
     @assert cts != MOI.OPTIMIZE_NOT_CALLED "solve did not reach a terminal status"
     dest.termination_status = cts
     dest.primal_status, dest.dual_status = if cts == MOI.OPTIMAL
diff --git a/src/algorithms/common.jl b/src/algorithms/common.jl
index d749542..5647f7c 100644
--- a/src/algorithms/common.jl
+++ b/src/algorithms/common.jl
@@ -255,7 +255,7 @@ function try_solve_noconstraints!(state::AbstractState, milp::MILP)
         @. sol.x = ifelse(c > 0, lv, ifelse(c < 0, uv, clamp(zero(eltype(lv)), lv, uv)))
         kkt_errors!(state.stats.err, state.scratch, sol, milp)
         state.stats.time_elapsed = current_time() - state.stats.starting_time
-        state.stats.termination_status = MOI.OPTIMAL
+        state.stats.termination_status_code = status_code(MOI.OPTIMAL)
         return true
     else
         return false
diff --git a/src/components/termination.jl b/src/components/termination.jl
index a85b5f5..24a382c 100644
--- a/src/components/termination.jl
+++ b/src/components/termination.jl
@@ -40,7 +40,7 @@ end
 
 $(TYPEDFIELDS)
 """
-mutable struct ConvergenceStats{T <: BatchedNumber, F <: Number, I <: Number}
+mutable struct ConvergenceStats{T <: BatchedNumber, F <: Number, I <: Number, S <: Number}
     "current KKT error"
     err::KKTErrors{T}
     "time at which the algorithm started, in seconds"
@@ -49,8 +49,8 @@ mutable struct ConvergenceStats{T <: BatchedNumber, F <: Number, I <: Number}
     time_elapsed::F
     "number of multiplications by both the KKT matrix and its transpose"
     kkt_passes::I
-    "termination status (should be `MOI.OPTIMIZE_NOT_CALLED` until the algorithm actually terminates)"
-    termination_status::MOI.TerminationStatusCode
+    "integer code of the termination status (should be that of `MOI.OPTIMIZE_NOT_CALLED` until the algorithm actually terminates), read with [`termination_status`](@ref)"
+    termination_status_code::S
     "history of KKT errors, indexed by number of KKT passes"
     error_history::Vector{Tuple{I, KKTErrors{T}}}
 end
@@ -60,36 +60,60 @@ function ConvergenceStats(
         starting_time = current_time(),
         time_elapsed = 0.0,
         kkt_passes::I = 0,
-        termination_status = MOI.OPTIMIZE_NOT_CALLED,
+        termination_status_code::S = status_code(MOI.OPTIMIZE_NOT_CALLED),
         error_history = [(kkt_passes, copy(err))]
-    ) where {T, I}
+    ) where {T, I, S}
     F = Base.promote_type(typeof(starting_time), typeof(time_elapsed))
-    return ConvergenceStats{T, F, I}(
+    return ConvergenceStats{T, F, I, S}(
         err,
         starting_time,
         time_elapsed,
         kkt_passes,
-        termination_status,
+        termination_status_code,
         error_history
     )
 end
 
+"""
+    status_code(status)
+
+Return the integer code of a `MOI.TerminationStatusCode`, as stored in the
+`termination_status_code` field of [`ConvergenceStats`](@ref).
+
+Unlike the enum itself, this code is an ordinary number, so Reactant can trace it: a compiled
+solve can write its own status instead of freezing the trace-time one.
+"""
+status_code(status::MOI.TerminationStatusCode) = Int32(status)
+
+"""
+    termination_status(stats)
+
+Return the termination status of `stats` as a `MOI.TerminationStatusCode`.
+
+Decodes the `termination_status_code` field, which is stored as a plain number so that it
+survives a Reactant-compiled solve. Only call this outside a compilation context: mid-trace the
+code is a traced number with no value yet.
+"""
+function termination_status(stats::ConvergenceStats)
+    return MOI.TerminationStatusCode(Int32(stats.termination_status_code))
+end
+
 function instance(stats::ConvergenceStats, i::Int)
     return ConvergenceStats(
         instance(stats.err, i);
         starting_time = stats.starting_time,
         time_elapsed = stats.time_elapsed,
         kkt_passes = stats.kkt_passes,
-        termination_status = stats.termination_status,
+        termination_status_code = stats.termination_status_code,
         error_history = [(passes, instance(err, i)) for (passes, err) in stats.error_history],
     )
 end
 
 function Base.show(io::IO, stats::ConvergenceStats)
-    (; err, time_elapsed, kkt_passes, termination_status) = stats
+    (; err, time_elapsed, kkt_passes) = stats
     return print(
         io,
-        """Convergence stats with termination status $termination_status:
+        """Convergence stats with termination status $(termination_status(stats)):
         - $err
         - time elapsed: $time_elapsed seconds
         - KKT passes: $kkt_passes""",
@@ -101,9 +125,13 @@ end
 
 Decide how the algorithm terminates, using `dest` as scratch space for the relative errors.
 
-Set `stats.termination_status` and return whether the algorithm should stop. The returned
-boolean is traced under Reactant, unlike the `MOI.TerminationStatusCode` enum, so it is what
-the solve loops branch on.
+Set `stats.termination_status_code` and return whether the algorithm should stop.
+
+The status is selected with nested `ifelse` calls rather than with branches, so that it survives
+a Reactant-compiled solve: an assignment inside a `@trace if` only ever contributes its
+trace-time value, whereas an `ifelse` over traced conditions is part of the compiled program.
+The returned boolean is what the solve loops branch on, since a status code cannot drive traced
+control flow.
 """
 function set_termination_status!!(
         stats::ConvergenceStats,
@@ -115,18 +143,20 @@ function set_termination_status!!(
     is_optimal = batched_all(<=(termination_reltol), relative!!(dest, err))
     is_time_limit = time_elapsed >= time_limit
     is_iteration_limit = kkt_passes >= max_kkt_passes
-    # Reactant doesn't like `elseif`, see https://github.com/EnzymeAD/Reactant.jl/issues/2563#issuecomment-5584197336
-    # The branches are ordered by increasing priority, so that the last write wins.
-    @trace if is_iteration_limit
-        stats.termination_status = MOI.ITERATION_LIMIT
-    end
-    @trace if is_time_limit
-        stats.termination_status = MOI.TIME_LIMIT
-    end
-    @trace if is_optimal
-        stats.termination_status = MOI.OPTIMAL
-    end
-    # `stats.termination_status` is a plain enum, so it cannot drive traced control flow.
-    # Return the decision as a (possibly traced) boolean instead.
+    # nested `ifelse` instead of `if`/`elseif`: it is a plain (traceable) computation, and it
+    # states the priority between simultaneous criteria in one place
+    stats.termination_status_code = ifelse(
+        is_optimal,
+        status_code(MOI.OPTIMAL),
+        ifelse(
+            is_time_limit,
+            status_code(MOI.TIME_LIMIT),
+            ifelse(
+                is_iteration_limit,
+                status_code(MOI.ITERATION_LIMIT),
+                status_code(MOI.OPTIMIZE_NOT_CALLED),
+            ),
+        ),
+    )
     return is_optimal | is_time_limit | is_iteration_limit
 end
diff --git a/test/algorithms/all.jl b/test/algorithms/all.jl
index 9a49447..95c59bb 100644
--- a/test/algorithms/all.jl
+++ b/test/algorithms/all.jl
@@ -1,5 +1,6 @@
 using Adapt
 using CoolPDLP
+using CoolPDLP: termination_status
 using HiGHS: HiGHS
 using JLArrays
 using KernelAbstractions
@@ -33,7 +34,7 @@ function test_optimizer(
     sol, stats = solve(milp, algo)
     x = sol.x
 
-    @test stats.termination_status == MOI.OPTIMAL
+    @test termination_status(stats) == MOI.OPTIMAL
     @test is_feasible(Array(x), milp; cons_tol, int_tol)
     @test isapprox(objective_value(jump_x, milp), objective_value(Array(x), milp); rtol = obj_rtol)
     return nothing
diff --git a/test/algorithms/batching.jl b/test/algorithms/batching.jl
index 1b05e71..5a4f185 100644
--- a/test/algorithms/batching.jl
+++ b/test/algorithms/batching.jl
@@ -1,6 +1,7 @@
 using CoolPDLP
 using CoolPDLP: KKTErrors, Scratch, initialize, instance, kkt_errors!,
-    nbinstances, prog_showvalues, relative, restart!, restart_check!, step!
+    nbinstances, prog_showvalues, relative, restart!, restart_check!, step!,
+    termination_status
 using Random
 using Test
 
@@ -138,7 +139,7 @@ end
             sol, stats = solve(milp_id, sol_id, algo)
             sol_single, stats_single = solve(milps[1], sols[1], algo)
             @test stats.kkt_passes == stats_single.kkt_passes
-            @test stats.termination_status == stats_single.termination_status
+            @test termination_status(stats) == termination_status(stats_single)
             for i in 1:NBATCH
                 @test sol.x[:, i] ≈ sol_single.x
                 @test stats.err.primal[i] ≈ stats_single.err.primal
diff --git a/test/components/show.jl b/test/components/show.jl
index cbe448e..f14417c 100644
--- a/test/components/show.jl
+++ b/test/components/show.jl
@@ -1,5 +1,5 @@
 using CoolPDLP
-using CoolPDLP: KKTErrors, Scratch, kkt_errors!
+using CoolPDLP: KKTErrors, Scratch, kkt_errors!, termination_status
 using Random
 using SparseArrays
 using Test
@@ -37,7 +37,7 @@ end
     _, stats = solve(milp, PDLP(; max_kkt_passes = 200))
     str = sprint(show, stats)
     @test occursin("Convergence stats", str)
-    @test occursin(string(stats.termination_status), str)
+    @test occursin(string(termination_status(stats)), str)
     @test occursin("KKT passes: $(stats.kkt_passes)", str)
     @test occursin("KKT relative errors", str)
 end
diff --git a/test/components/termination.jl b/test/components/termination.jl
index 7466798..0118f0e 100644
--- a/test/components/termination.jl
+++ b/test/components/termination.jl
@@ -1,4 +1,5 @@
 using CoolPDLP
+using CoolPDLP: termination_status
 import MathOptInterface as MOI
 using Random
 using SparseArrays
@@ -12,7 +13,7 @@ using Test
     milp = CoolPDLP.MILP(; c, lv, uv, A, lc, uc)
     algo = CoolPDLP.PDLP()
     sol, stats = CoolPDLP.solve(milp, algo)
-    @test stats.termination_status == MOI.OPTIMAL
+    @test termination_status(stats) == MOI.OPTIMAL
 end
 
 @testset "Termination statuses" begin
@@ -21,11 +22,11 @@ end
 
     @testset "$alg" for alg in (PDHG, PDLP)
         _, stats = solve(milp, alg(; termination_reltol = 0.0, max_kkt_passes = 200))
-        @test stats.termination_status == MOI.ITERATION_LIMIT
+        @test termination_status(stats) == MOI.ITERATION_LIMIT
         @test stats.kkt_passes >= 200
 
         _, stats = solve(milp, alg(; termination_reltol = 0.0, time_limit = 0.0))
-        @test stats.termination_status == MOI.TIME_LIMIT
+        @test termination_status(stats) == MOI.TIME_LIMIT
         @test stats.time_elapsed >= 0
     end
 end
@@ -41,7 +42,7 @@ end
 
     @testset "$alg" for alg in (PDHG, PDLP)
         sol, stats = solve(milp, alg())
-        @test stats.termination_status == MOI.OPTIMAL
+        @test termination_status(stats) == MOI.OPTIMAL
         @test sol.x == clamp.(0.0, lv, uv)
         @test is_feasible(sol.x, milp)
         @test objective_value(sol.x, milp) == 0
@@ -59,7 +60,7 @@ end
 
     @testset "$alg" for alg in (PDHG, PDLP)
         sol, stats = solve(milp, alg())
-        @test stats.termination_status == MOI.OPTIMAL
+        @test termination_status(stats) == MOI.OPTIMAL
         @test !any(isnan, sol.x)
         @test sol.x == [0.0, 5.0, 0.0]
         @test objective_value(sol.x, milp) == -5.0
@@ -82,7 +83,7 @@ end
         )
         sol, stats = solve(milp, algo)
         @test !any(isnan, sol.x) && !any(isinf, sol.x)
-        @test stats.termination_status != MOI.OPTIMAL
+        @test termination_status(stats) != MOI.OPTIMAL
     end
 
     @testset "unbounded direction (c[1] > 0, lv[1] == -Inf)" begin
@@ -91,7 +92,7 @@ end
         )
         sol, stats = solve(milp, algo)
         @test !any(isnan, sol.x) && !any(isinf, sol.x)
-        @test stats.termination_status != MOI.OPTIMAL
+        @test termination_status(stats) != MOI.OPTIMAL
     end
 
     @testset "unbounded direction (c[1] < 0, uv[1] == Inf)" begin
@@ -100,7 +101,7 @@ end
         )
         sol, stats = solve(milp, algo)
         @test !any(isnan, sol.x) && !any(isinf, sol.x)
-        @test stats.termination_status != MOI.OPTIMAL
+        @test termination_status(stats) != MOI.OPTIMAL
     end
 end
 
diff --git a/test/gpu/batching.jl b/test/gpu/batching.jl
index c34ae86..4af8f2c 100644
--- a/test/gpu/batching.jl
+++ b/test/gpu/batching.jl
@@ -1,6 +1,6 @@
 using CoolPDLP
 using CoolPDLP: KKTErrors, Scratch, initialize, instance, kkt_errors!,
-    nbinstances, preprocess, relative, step!
+    nbinstances, preprocess, relative, step!, termination_status
 using GPUArraysCore: @allowscalar
 using Random
 using Test
@@ -91,7 +91,7 @@ function test_batching(
             algo_solve = alg(T, Int, matrix_type; backend, max_kkt_passes = 200)
             sol, stats = solve(milp_id, algo_solve)
             sol_single, stats_single = solve(milps[1], algo_solve)
-            @test stats.termination_status == stats_single.termination_status
+            @test termination_status(stats) == termination_status(stats_single)
             x, x_single = Array(sol.x), Array(sol_single.x)
             obj_single = objective_value(x_single, milps[1])
             for i in 1:nbatch
diff --git a/test/gpu/reactant/runtests.jl b/test/gpu/reactant/runtests.jl
index 2c5940b..827fb81 100644
--- a/test/gpu/reactant/runtests.jl
+++ b/test/gpu/reactant/runtests.jl
@@ -1,5 +1,6 @@
 using CoolPDLP
-using CoolPDLP: KKTErrors
+using CoolPDLP: KKTErrors, termination_status
+import MathOptInterface as MOI
 using MathOptBenchmarkInstances
 using Reactant
 using Reactant: to_rarray
@@ -113,6 +114,13 @@ configs = [
             @test isapprox(err_r, err; rtol)
         end
     end
+
+    @testset "Same termination status" begin
+        # the status is stored as a traced integer code, so the compiled run reports the
+        # criterion it actually stopped on instead of the trace-time `OPTIMIZE_NOT_CALLED`
+        @test termination_status(state_r.stats) != MOI.OPTIMIZE_NOT_CALLED
+        @test termination_status(state_r.stats) == termination_status(state.stats)
+    end
 end
 
 # Reading the host clock inside a compiled program needs a Reactant callback, which not every
@@ -174,6 +182,7 @@ else
         @testset "The solve stops on the time limit" begin
             @test elapsed >= time_limit
             @test passes < max_kkt_passes
+            @test termination_status(state_r.stats) == MOI.TIME_LIMIT
         end
     end
 end