Evaluators often produce correct labels via flawed reasoning, a critical failure for agentic systems gating actions, routing reviews, or supplying training feedback. Standard evaluation only verifies final label correctness, ignoring whether judgment changes stem from valid evidence, consistent rules, or proper rule applicability. We formalize evaluator reasoning accountability via three core sources: grounds, norms, and authority. Varying these sources yields an eight-cell counterfactual judgment cube to characterize judgment updates. We define judgment receipts as minimal source replacement sets that reproduce revised verdicts to explain judgment transitions. We derive certification cost bounds for black-box evaluators and present ReasonBench, a policy and logical reasoning benchmark with verifiable receipts covering 19,520 cases and 7,200 controls. In frozen evaluations, Qwen3-1.7B reaches 98.41% receipt accuracy, while cube prediction scores 96.99%, a consistent 1.42-point drop validated by Qwen3-0.6B replication. Strong standard accuracy masks severe robustness flaws. Meaning-preserving source permutations reduce valid receipt recovery to 54.8% and 49.2% for direct and cube prediction. Models trained on simple single-source changes retain 93.75% verdict accuracy but recover only 7.16% of receipts for complex multi-source updates. Permutation retraining boosts consistency to 96.6% yet worsens cube prediction deficits. Structured counterfactual supervision fails to guarantee robust reasoning. We show reason-aware evaluation must decouple prediction and certification, reporting transformation consistency alongside standard accuracy for trustworthy evaluator auditing.
Figures & tables
Source
Question at the interface
Nearest CS reading
Example revision
Grounds G
What happened, as accepted?
evidence; input record
A verified timestamp replaces an estimate
Norms N
What follows from the grounds?
decision rule
A refund window moves from 14 to 30 days
Authority A
May this norm govern this case?
rule scope; applicability
A regional office gains cross-border jurisdiction
Table 1
Figure 1: The certification workflow. The cube is an executed audit object relative to a declared source interface. A model-generated cube is a prediction of this object, not its certificate.
Table 1: Surface and chance diagnostics on the locked test. The character model and majority target use the full unbalanced training split; the random rows are analytic expectations.
Method
Revised-verdict accuracy
Exact receipt-family accuracy
Seeds
Direct verdict
99.10% (0.30)
—
5
Direct receipt
99.27% (0.05)
98.41% (0.06)
5
Judgment cube
97.42% (0.33)
96.99% (0.44)
5
Rationale receipt
98.29%
97.75%
1
Table 2: Locked-test outcomes. Parentheses give seed standard deviation in percentage points. The rationale row is descriptive (one seed).
Figure 2: Locked-test predictive accuracy. Axes are focused and stated, because zero-based bars would conceal the observed differences.
Diagnostic on locked gold changes
Direct receipt
Judgment cube
Exact receipt accuracy
97.30%
95.54%
Revised-verdict minus receipt accuracy
1.54 pp [0.24, 3.42]
0.90 pp [-0.62, 2.45]
Wrong receipt given both endpoints correct
1.66% [0.26, 3.61]
1.85% [0.47, 3.57]
Eligible seed-example observations
6,609
6,337
Table 3: Verdict–receipt separation. Intervals use the paired hierarchical bootstrap over seeds and source units.
Figure 3: Failure rates on the locked test. Drift and inertia whiskers show seed standard deviation; conditional receipt-error whiskers are 95% cluster-bootstrap intervals.
Locked subgroup
Cases per seed
Direct receipt
Judgment cube
Cube minus direct
Minimum size 1
904
98.21%
96.17%
-2.04 pp [-4.79, -0.27]
Minimum size 2
335
95.40%
93.85%
-1.55 pp [-4.06, 0.24]
Minimum size 3
101
95.45%
95.45%
0.00 pp [-0.99, 1.19]
Not receipt-ambiguous (includes stable cases)
1,980
98.38%
96.81%
—
Multiple minimal receipts
420
98.52%
97.86%
-0.67 pp [-1.87, 0.29]
Table 4: Exact receipt accuracy by structure. Intervals are shown for the prespecified paired subgroup comparisons. Rows differ in structure and source composition at once; they are not isolated causal effects.
Figure 4: Structural subgroups. Whiskers show seed standard deviation.
Split
Cases per seed
Direct receipt
Judgment cube
Cube minus direct (95% CI)
Locked
2,400
98.41%
96.99%
-1.42 [-2.87, -0.30]
Mixed operator
288
81.81%
78.61%
-3.19 [-8.61, 2.36]
Language
1,200
80.50%
68.40%
-12.10 [-16.35, -7.50]
Reserved structural
912
99.41%
96.27%
-3.14 [-5.92, -0.86]
Proof depth
912
96.73%
82.19%
-14.54 [-19.34, -8.00]
Table 5: Exact receipt accuracy under distribution shift. Effects are percentage points from paired hierarchical bootstrap estimates. The reserved structural split is not an unseen-composition test.
Paired control
Required relation
Direct receipt
Judgment cube
Inverse transition
Endpoint pair swaps
47.22%
42.97%
Source-order permutation
Receipt unchanged
54.77%
49.18%
Irrelevant distractor
Receipt unchanged
98.63%
93.43%
Table 6: Paired-consistency rates. Each relation is evaluated on 2,400 paired locked transformations per seed. Controls are transformations, not an additional independent sample.
Figure 5: Distribution versus presentation changes. Left: absolute receipt accuracy with seed-SD whiskers. Right: the semantic relation required by each paired transformation.
Direct receipt
Judgment cube
Metric
Frozen
Augmented
Frozen
Augmented
Locked: receipt, all cases
98.39% (0.05)
98.07% (0.25)
96.99% (0.38)
92.36% (1.86)
organizational (6 clauses)
93.29% (0.20)
92.25% (1.12)
87.67% (1.39)
68.52% (8.18)
logical (96 worlds)
100.00% (0.00)
99.91% (0.06)
99.93% (0.06)
99.89% (0.15)
Locked: receipt, changes only
97.31% (0.07)
96.62% (0.44)
95.50% (0.35)
88.26% (3.19)
Locked: revised verdict
99.26% (0.02)
99.25% (0.04)
97.40% (0.35)
92.75% (1.70)
Table 7: Post-hoc permutation-augmented training. Frozen columns restate the seed-11/37/71 subset of the primary runs, so columns are paired within each target; parentheses give seed standard deviation in percentage points. Consistency rows are paired-consistency rates against the locked parents; indented rows split the measure by source stratum. The augmentation targets only the order transformation.
Method
Realized accepted-change coverage
Reason debt
Correct gold-change recall
Direct receipt, 80% target
81.97%
0.27%
81.61%
Judgment cube, 80% target
85.54%
0.16%
84.30%
Direct receipt, 100% target
99.94%
2.26%
98.60%
Judgment cube, 100% target
99.98%
3.48%
94.58%
Table 8: Selected locked-test operating points. Thresholds are fitted on calibration data; coverage, debt, and recall are seed means.
Figure 6: Selective accounting. Low debt at partial coverage should be read together with the lost gold-change recall.
Split and metric
Cases per seed
Direct receipt
Judgment cube
Cube minus direct (95% CI)
Unseen compositions: revised verdict
1,440
93.75% (0.91)
66.94% (0.50)
-26.81 pp [-30.95, -22.70]
Unseen compositions: receipt, all cases
1,440
36.62% (0.11)
37.22% (0.57)
+0.60 pp [-0.37, 1.61]
Unseen compositions: receipt, changes only
968
7.16% (0.06)
9.57% (0.70)
+2.41 pp [0.35, 4.50]
Unseen compositions plus greater depth: revised verdict
576
99.83% (0.30)
59.20% (3.25)
-40.63 pp [-45.78, -36.57]
Unseen compositions plus greater depth: receipt, all cases
576
33.33% (0.00)
33.33% (0.00)
0.00 pp [0.00, 0.00]
Unseen compositions plus greater depth: receipt, changes only
384
0.00% (0.00)
0.00% (0.00)
0.00 pp [0.00, 0.00]
Table 9: Post-freeze true-composition holdout. Parentheses give seed standard deviation; intervals use the same paired source-unit bootstrap as the primary study. Changed-only rows use conditional denominators.
Split and metric
Cases per seed
Direct receipt
Judgment cube
Cube minus direct (95% CI)
Locked: revised verdict
2,400
99.15% (0.25)
96.76% (0.95)
-2.39 pp [-4.75, -0.49]
Locked: receipt, all cases
2,400
98.06% (0.06)
96.79% (1.01)
-1.26 pp [-3.08, -0.04]
Locked: receipt, changes only
1,340
96.79% (0.22)
95.12% (1.24)
-1.67 pp [-4.36, 0.15]
Language shift: revised verdict
1,200
95.44% (1.18)
92.97% (3.00)
-2.47 pp [-8.02, 2.66]
Language shift: receipt, all cases
1,200
78.64% (2.68)
70.97% (1.64)
-7.67 pp [-11.09, -3.71]
Language shift: receipt, changes only
662
63.24% (3.98)
50.15% (5.39)
-13.09 pp [-18.80, -4.96]
Table 10: Post-freeze Qwen3-0.6B replication. Parentheses give seed standard deviation; effects use paired source-unit bootstrap intervals; changed-only rows show conditional denominators.
Figure 7: Primary and secondary target comparisons. Left: zero-based separation between verdict and changed-case receipt accuracy under unseen source combinations. Right: clustered 95% intervals; composition and capacity rows are post-freeze secondary evidence.
Method
Trainable parameters
Mean training time
Peak reserved memory
Generated tokens/example
Direct verdict
17.43M
53.8 min
12.05 GiB
7.00
Direct receipt
17.43M
53.6 min
12.57 GiB
14.02
Judgment cube
17.43M
53.2 min
12.60 GiB
6.70
Rationale receipt
17.43M
52.7 min
11.43 GiB
22.22
Table 11: Compute and generation cost. Primary rows average five seeds; the rationale row has one. Hardware concurrency makes wall time descriptive rather than platform-independent.