diff --git a/README.md b/README.md
index b089bb6..ee55a32 100644
--- a/README.md
+++ b/README.md
@@ -7,6 +7,7 @@
 [![Build Status](https://github.com/TensorBFS/TensorInference.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/TensorBFS/TensorInference.jl/actions/workflows/CI.yml?query=branch%3Amain)
 [![Coverage](https://codecov.io/gh/TensorBFS/TensorInference.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/TensorBFS/TensorInference.jl)
 [![status](https://joss.theoj.org/papers/a6792845b2522b07898cd35e246ec4d2/status.svg)](https://joss.theoj.org/papers/a6792845b2522b07898cd35e246ec4d2)
+![Agent maintained](https://img.shields.io/badge/maintenance-agent%20maintained-blue)
 
 <p>
 TensorInference is an open source &nbsp;
diff --git a/test/mmap.jl b/test/mmap.jl
index 89d7fee..6b478de 100644
--- a/test/mmap.jl
+++ b/test/mmap.jl
@@ -1,6 +1,8 @@
 using Test
+using Random
 using OMEinsum
 using TensorInference
+using TensorInference: Factor, UAIModel, get_vars
 
 @testset "clustering" begin
     ixs = [[1, 2, 3], [2, 3, 4], [4, 5, 6]]
@@ -31,20 +33,52 @@ end
     @test log_probability(mmap3, config) ≈ logp
 end
 
-@testset "UAI Reference Solution Comparison" begin
+@testset "MMAP exhaustive small independent oracle" begin
+    rng = MersenneTwister(4279)
+    for trial in 1:12
+        f = trial == 1 ? [1.0 0.0; 0.0 1.0] : rand(rng, 2, 2)
+        g = trial == 1 ? [0.0 1.0; 1.0 0.0] : rand(rng, 2, 2)
+        model = UAIModel(3, [2, 2, 2], [Factor((1, 2), f), Factor((2, 3), g)])
+        for queryvars in ([1], [1, 3]), evidence in (Dict{Int,Int}(), Dict(3 => 1))
+            mmap = MMAPModel(model; queryvars, evidence)
+            scores = Dict{Tuple,Float64}()
+            expected_outputvars = sort!(union(queryvars, collect(keys(evidence))))
+            @test get_vars(mmap) == expected_outputvars
+            for x in 0:1, y in 0:1, z in 0:1
+                assignment = [x, y, z]
+                all(assignment[k] == value for (k, value) in evidence) || continue
+                key = Tuple(assignment[k] for k in expected_outputvars)
+                scores[key] = get(scores, key, 0.0) + f[x + 1, y + 1] * g[y + 1, z + 1]
+            end
+            logp, config = most_probable_config(mmap)
+            @test exp(logp) ≈ maximum(values(scores))
+            @test scores[Tuple(config)] ≈ maximum(values(scores))
+            @test log_probability(mmap, config) ≈ logp
+        end
+    end
+end
+
+@testset "UAI feasible reference lower bounds" begin
     problem_sets = dataset_from_artifact("uai2014")["MMAP"]
     problems = [
         ("Segmentation", 12, TreeSA(ntrials = 1, niters = 2, βs = 1:0.1:40)),
-        # ("Segmentation", 13, TreeSA(ntrials = 1, niters = 2, βs = 1:0.1:40)), # fails!
-        # ("Segmentation", 14, TreeSA(ntrials = 1, niters = 2, βs = 1:0.1:40))  # fails!
+        ("Segmentation", 13, TreeSA(ntrials = 1, niters = 2, βs = 1:0.1:40)),
+        ("Segmentation", 14, TreeSA(ntrials = 1, niters = 2, βs = 1:0.1:40))
     ]
     for (problem_set_name, id, optimizer) in problems
         @testset "$(problem_set_name) problem set, id = $id" begin
             problem = problem_sets[problem_set_name][id]
             @info "Testing: $(problem_set_name)_$id"
             model = MMAPModel(read_model(problem); optimizer, evidence=read_evidence(problem), queryvars=read_queryvars(problem))
-            _, solution = most_probable_config(model)
-            @test solution == read_solution(problem)
+            logp, solution = most_probable_config(model)
+            reference_logp = log_probability(model, read_solution(problem))
+
+            # These external assignments are feasible lower bounds, not certified
+            # optima. A different assignment is valid when its objective is at
+            # least as good; the small tests above independently establish that
+            # the solver finds exact MMAP optima on exhaustively enumerable models.
+            @test log_probability(model, solution) ≈ logp
+            @test logp >= reference_logp || isapprox(logp, reference_logp)
         end
     end
 end