diff --git a/solve.eigs b/solve.eigs
index bdedc8c..6d97afc 100644
--- a/solve.eigs
+++ b/solve.eigs
@@ -201,6 +201,14 @@ define pagerank(m, maxit) as:
     return [r, it]
 
 # ---- demo ----
+# zeros returns a numeric buffer since EigenScript#1093. Materialize only
+# for display so both list and buffer-backed solvers print their components.
+define display_vector(v) as:
+    local components is []
+    for i in range of (len of v):
+        append of [components, v[i]]
+    return components
+
 print of "=== iterative solvers: the predicate as a loop condition ==="
 print of "every loop runs until `report of change` is settled and HOLDs — the observer,"
 print of "not a magnitude tolerance, decides when to stop. (iters include the hold)"
@@ -210,9 +218,9 @@ A is [[4.0, -1.0, 0.0], [-1.0, 4.0, -1.0], [0.0, -1.0, 4.0]]
 bb is [3.0, 2.0, 3.0]
 rj is jacobi of [A, bb, 500]
 rg is gauss_seidel of [A, bb, 500]
-print of f"Jacobi        Ax=b -> {rj[0]}"
+print of f"Jacobi        Ax=b -> {display_vector of rj[0]}"
 print of f"              {rj[1]} iters"
-print of f"Gauss-Seidel  Ax=b -> {rg[0]}"
+print of f"Gauss-Seidel  Ax=b -> {display_vector of rg[0]}"
 print of f"              {rg[1]} iters  (fresh values -> fewer than Jacobi)"
 print of ""
 
@@ -224,6 +232,6 @@ print of ""
 # 3-node graph 0->{1,2}, 1->{2}, 2->{0}; column-stochastic. True stationary [0.4,0.2,0.4].
 G is [[0.0, 0.0, 1.0], [0.5, 0.0, 0.0], [0.5, 1.0, 0.0]]
 rr is pagerank of [G, 500]
-print of f"PageRank stationary distribution -> {rr[0]}  ({rr[1]} iters)"
+print of f"PageRank stationary distribution -> {display_vector of rr[0]}  ({rr[1]} iters)"
 print of ""
 print of "DONE"
diff --git a/tests/check_solver_output.py b/tests/check_solver_output.py
new file mode 100644
index 0000000..bdc1803
--- /dev/null
+++ b/tests/check_solver_output.py
@@ -0,0 +1,29 @@
+#!/usr/bin/env python3
+"""Check the three numeric vectors printed by the standalone solver demo."""
+import ast
+import math
+import re
+import sys
+
+output = sys.stdin.read()
+# A @ [1, 1, 1] = b; G @ [0.4, 0.2, 0.4] = [0.4, 0.2, 0.4], sum = 1.
+for label, expected in (
+    ("Jacobi", (1.0, 1.0, 1.0)),
+    ("Gauss-Seidel", (1.0, 1.0, 1.0)),
+    ("PageRank", (0.4, 0.2, 0.4)),
+):
+    rows = re.findall(r"^" + re.escape(label) + r"\s+[^\n]*?-> (\[[^\n]*?\])(?:\s|$)", output, re.M)
+    try:
+        if len(rows) != 1:
+            raise ValueError("expected one printed numeric vector")
+        values = ast.literal_eval(rows[0])
+        if len(values) != 3 or any(
+            type(value) not in (int, float)
+            or not math.isfinite(value)
+            or not math.isclose(value, want, rel_tol=0.0, abs_tol=0.0001)
+            for value, want in zip(values, expected)
+        ):
+            raise ValueError(f"incorrect components: {values!r}")
+    except (ValueError, SyntaxError, TypeError) as error:
+        sys.exit(f"FAIL: {label}: {error}")
+    print(f"PASS: {label} prints all three converged components")
diff --git a/tests/test_lab.sh b/tests/test_lab.sh
index 093590e..f2d7778 100755
--- a/tests/test_lab.sh
+++ b/tests/test_lab.sh
@@ -35,8 +35,7 @@ SOUT=$("$EIGS" solve.eigs 2>&1)
 echo "$SOUT"
 echo "$SOUT" | grep -q "DONE"                          || { echo "FAIL: solve.eigs did not finish"; exit 1; }
 echo "$SOUT" | grep -q "dominant eigenvalue -> 2"      || { echo "FAIL: power iteration eigenvalue wrong"; exit 1; }
-# PageRank true stationary is [0.4, 0.2, 0.4]
-echo "$SOUT" | grep -qE "0\.3999|0\.4000"              || { echo "FAIL: PageRank did not reach the stationary distribution"; exit 1; }
-# both linear solves reach ~[1,1,1]
-echo "$SOUT" | grep -q "0.9999"                        || { echo "FAIL: Jacobi/Gauss-Seidel did not converge to the solution"; exit 1; }
+# Check every component on its own named row; a number printed by another
+# solver must not mask a missing distribution or an incorrect component.
+printf '%s\n' "$SOUT" | python3 tests/check_solver_output.py
 echo "PASS: solvers converge via the predicate-driven loop (settled + hold)"