diff --git a/engine-proto/gram-test/circles-in-triangle.jl b/engine-proto/gram-test/circles-in-triangle.jl
index c1f8bf2..f7248df 100644
--- a/engine-proto/gram-test/circles-in-triangle.jl
+++ b/engine-proto/gram-test/circles-in-triangle.jl
@@ -47,14 +47,6 @@ append!(values, fill(-0.5, 4))
 =#
 gram = sparse(J, K, values)
 
-# set initial guess (random)
-## Random.seed!(58271) # stuck; step size collapses on step 48
-## Random.seed!(58272) # good convergence
-## Random.seed!(58273) # stuck; step size collapses on step 18
-## Random.seed!(58274) # stuck
-## Random.seed!(58275) #
-## guess = Engine.rand_on_shell(fill(BigFloat(-1), 8))
-
 # set initial guess
 Random.seed!(58271)
 guess = hcat(
@@ -69,39 +61,12 @@ guess = hcat(
   BigFloat[0, 0, 0, 0, 1]
 )
 frozen = [CartesianIndex(j, 9) for j in 1:5]
-#=
-guess = hcat(
-  Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
-  Engine.sphere(BigFloat[0, 0, 0], BigFloat(0.9)),
-  Engine.plane(BigFloat[1, 0, 0], BigFloat(1)),
-  Engine.plane(BigFloat[cos(2pi/3), sin(2pi/3), 0], BigFloat(1)),
-  Engine.plane(BigFloat[cos(-2pi/3), sin(-2pi/3), 0], BigFloat(1)),
-  Engine.sphere(4//3*BigFloat[-1, 0, 0], BigFloat(1//3)),
-  Engine.sphere(4//3*BigFloat[cos(-pi/3), sin(-pi/3), 0], BigFloat(1//3)),
-  Engine.sphere(4//3*BigFloat[cos(pi/3), sin(pi/3), 0], BigFloat(1//3)),
-  BigFloat[0, 0, 0, 1, 1]
-)
-=#
 
-# complete the gram matrix using gradient descent followed by Newton's method
-#=
-L, history = Engine.realize_gram_gradient(gram, guess, scaled_tol = 0.01)
-L_pol, history_pol = Engine.realize_gram_newton(gram, L, rate = 0.3, scaled_tol = 1e-9)
-L_pol2, history_pol2 = Engine.realize_gram_newton(gram, L_pol)
-=#
+# complete the gram matrix using Newton's method with backtracking
 L, success, history = Engine.realize_gram(gram, guess, frozen)
 completed_gram = L'*Engine.Q*L
 println("Completed Gram matrix:\n")
 display(completed_gram)
-#=
-println(
-  "\nSteps: ",
-  size(history.scaled_loss, 1),
-  " + ", size(history_pol.scaled_loss, 1),
-  " + ", size(history_pol2.scaled_loss, 1)
-)
-println("Loss: ", history_pol2.scaled_loss[end], "\n")
-=#
 if success
   println("\nTarget accuracy achieved!")
 else
diff --git a/engine-proto/gram-test/overlapping-pyramids.jl b/engine-proto/gram-test/overlapping-pyramids.jl
index 0d1f018..c530296 100644
--- a/engine-proto/gram-test/overlapping-pyramids.jl
+++ b/engine-proto/gram-test/overlapping-pyramids.jl
@@ -50,19 +50,11 @@ guess = begin
   )
 end
 
-# complete the gram matrix
-#=
-L, history = Engine.realize_gram_gradient(gram, guess, scaled_tol = 0.01)
-L_pol, history_pol = Engine.realize_gram_newton(gram, L)
-=#
+# complete the gram matrix using Newton's method with backtracking
 L, success, history = Engine.realize_gram(gram, guess)
 completed_gram = L'*Engine.Q*L
 println("Completed Gram matrix:\n")
 display(completed_gram)
-#=
-println("\nSteps: ", size(history.scaled_loss, 1), " + ", size(history_pol.scaled_loss, 1))
-println("Loss: ", history_pol.scaled_loss[end], "\n")
-=#
 if success
   println("\nTarget accuracy achieved!")
 else
diff --git a/engine-proto/gram-test/sphere-in-tetrahedron.jl b/engine-proto/gram-test/sphere-in-tetrahedron.jl
index 631f0e5..1c36e99 100644
--- a/engine-proto/gram-test/sphere-in-tetrahedron.jl
+++ b/engine-proto/gram-test/sphere-in-tetrahedron.jl
@@ -53,10 +53,7 @@ guess = hcat(
 )
 frozen = [CartesianIndex(j, 6) for j in 1:5]
 
-# complete the gram matrix
-#=
-L, history = Engine.realize_gram_newton(gram, guess)
-=#
+# complete the gram matrix using Newton's method with backtracking
 L, success, history = Engine.realize_gram(gram, guess, frozen)
 completed_gram = L'*Engine.Q*L
 println("Completed Gram matrix:\n")
diff --git a/engine-proto/gram-test/tetrahedron-radius-ratio.jl b/engine-proto/gram-test/tetrahedron-radius-ratio.jl
index c284078..7ceb794 100644
--- a/engine-proto/gram-test/tetrahedron-radius-ratio.jl
+++ b/engine-proto/gram-test/tetrahedron-radius-ratio.jl
@@ -77,7 +77,7 @@ frozen = vcat(
   [CartesianIndex(j, 11) for j in 1:5]
 )
 
-# complete the gram matrix
+# complete the gram matrix using Newton's method with backtracking
 L, success, history = Engine.realize_gram(gram, guess, frozen)
 completed_gram = L'*Engine.Q*L
 println("Completed Gram matrix:\n")