diff --git a/README.md b/README.md
index b28c771..9abc972 100644
--- a/README.md
+++ b/README.md
@@ -165,9 +165,33 @@ The precise run configurations should be taken from the data spreadsheets that l
 
 ### Correctness testing
 
-Correctness can be verified using the [validate.py](./validate.py) script.
+To check that the benchmark software is working correctly, a matrix
+comparison job must be run on 1 GPU and 8 GPUs with no collocation (`qmode=1`), 10000
+total dofs (`ndofs_global`), and in both cases should produce the same
+output `ynorm` and `znorm` (within numerical roundoff precision). 
+For a problem with 10000 dofs, the numerical value of the `ynorm` and
+`znorm` should be 1.141577508 to 9 decimal places. The console output
+and the JSON file should be reported.
+
+The same correctness test should be performed with the CG operator on
+1 and 8 GPUS:
+
+- Correctness comparison with matrix result: `bench_dolfinx --mat_comp --cg
+  --ndofs_global=10000 --degree=3 --json mat_comp_cg.json`
+
+In this case, `ynorm` and `znorm` should be 167.5924472. Console output
+and JSON should be reported.
 
-The validation script should be run as follows and produce output similar to the following:
+For both these tests, the [validate.py](./validate.py) script can be used to check 
+the values of `ynorm` and `znorm` meet the accuracy requirements (see description
+below of how to use the script).
+
+### Benchmark run validation
+
+Benchmark runs can be verified using the [validate.py](./validate.py) script.
+
+The validation script takes as input the JSON and console output from the 
+benchmark code. For example:
 ```
 ./validate output.json output.out
  
@@ -178,49 +202,20 @@ The validation script should be run as follows and produce output similar to the
                nreps : 1000
          scalar size : 64
  
-  MAT COMP performance: 0.2957402083152624 Gdofs/s
+  Stencil performance: 0.2957402083152624 Gdofs/s
  
   Validation: PASSED
  
 
 ```
 
-Sanity check: The matrix comparison must be run on 1 GPU and 8 GPUs with no collocation (`qmode=1`), 10000
-total dofs (`ndofs_global`), and in both cases should produce the same
-output `ynorm` and `znorm` (within numerical roundoff precision). 
-For a problem with 10000 dofs, the numerical value of the `ynorm` and
-`znorm` should be 1.141577508 to 9 decimal places. The console output
-and the JSON file should be reported.
-
-For the acceptance tests, with `--qmode=0`, all GPU-based computations must
-yield the same answer as a CPU-based variant, subject to numerical
-roundoffs.
-
-The same correctness test should be performed with the CG operator on
-1 and 8 GPUS:
-
-- Correctness comparison with matrix result: `bench_dolfinx --mat_comp --cg
-  --ndofs_global=10000 --degree=3 --json mat_comp_cg.json`
-
-In this case, `ynorm` and `znorm` should be 167.5924472. Console output
-and JSON should be reported.
-
-
 ### Performance results
 
-In addition to testing for correctness, `validate.py` will also print the Computation Rate, which is the sole FoM for the benchmark.
+In addition to validating the benchmark run, `validate.py` will also
+print the Computation Rate, which is the sole FoM for the benchmark.
 The Computation Rate printed by `validate.py` corresponds to the
 total throughput in billion degrees of freedom per second (Gdofs/s).
 
-<!--
-The minimum problem size allowed is 200M DoFs at Q3 and 350M DoFs at
-Q6. Performance may improve with larger problems sizes, subject to
-memory available.
-
-The throughput tests can in principle be run on any number of GPU. The
-problem size can be increased to use more GPU memory.
--->
-
 ### Reference data
 
 #### LUMI-G (MI250x): Throughput in GDoFs/s for 2-64 nodes (8-256 GPUs)
@@ -295,6 +290,7 @@ The following changes to this document have been made since initial release:
 
 | <div style="width:90px">Date</div> | Change |
 |-----------:|--------|
+| 2026-06-09 | Fixes validate.py script and clarifies wording around correctness and validation |
 | 2026-06-05 | Removes incorrect `--mat-comp` option from suggested configurations |
 | 2026-05-29 | Correct validation script to support CG correctness test |
 
diff --git a/validate.py b/validate.py
index 93d7c2f..829663f 100755
--- a/validate.py
+++ b/validate.py
@@ -56,10 +56,6 @@ def parse_output( json_fname, console_fname ):
 print(f'                nreps : {d["nreps"]}')
 print(f'          scalar size : {d["fp"]}')
 
-if not d["is_mat_comp"]:
-    print(f'\n  ERROR: Benchmark must be run with --mat_comp')
-    valid = False
-
 if d["fp"] != 64:
     print(f'\n  ERROR: Benchmark must be run with 64-bit precision')
     valid = False
@@ -103,9 +99,9 @@ def parse_output( json_fname, console_fname ):
             valid = False
 
 if d["is_cg"] and valid:
-    print(f'\n  CG performance: {d["gdofs"]} Gdofs/s')
+    print(f'\n  Stencil+CG performance: {d["gdofs"]} Gdofs/s')
 else:
-    print(f'\n  MAT COMP performance: {d["gdofs"]} Gdofs/s')
+    print(f'\n  Stencil performance: {d["gdofs"]} Gdofs/s')
 
 print("\n  Validation:", ("PASSED" if valid else "FAILED") )
 print()