Existing-codebase changes: z3 algebra missed the quality margin and used more tokens
Here the design docs start already written for the existing application. Across three repeat runs, neither Prose docs nor Algebraic docs + z3 lifted the score by the threshold in any stage. Algebraic docs + z3 used more tokens than No docs in every run.
Results at a glance
| Run | Arm | Average score | Stages compared | Tokens | Time | Python CC |
|---|---|---|---|---|---|---|
| E024 run 1 | No docs | 0.310 | 5 of 5 | 10.01M (best in run) | 0:50:31 (best in run) | 3.27 (best in run) |
| Prose docs | 0.312 (+0.002) (best in run) | 17.16M (+71%) | 0:55:44 (+10%) | 3.27 | ||
| Algebraic docs + z3 | 0.304 (−0.006) | 14.93M (+49%) | 0:59:38 (+18%) | 3.27 | ||
| E024 run 2 | No docs | 0.310 | 5 of 5 | 12.05M (best in run) | 0:50:09 | 3.27 |
| Prose docs | 0.346 (+0.036) (best in run) | 12.19M (+1%) | 0:48:45 (−3%) (best in run) | 3.27 | ||
| Algebraic docs + z3 | 0.318 (+0.008) | 16.61M (+38%) | 1:01:11 (+22%) | 3.27 (best in run) | ||
| E024 run 3 | No docs | 0.294 | 5 of 5 | 12.21M (best in run) | 0:53:28 (best in run) | 3.27 |
| Prose docs | 0.308 (+0.014) (best in run) | 14.07M (+15%) | 0:57:44 (+8%) | 3.27 | ||
| Algebraic docs + z3 | 0.292 (−0.002) | 15.34M (+26%) | 0:54:31 (+2%) | 3.27 (best in run) |
Scores average the stages every arm of the run scored: the stages compared. Tokens and time are each run’s builder totals over every stage it worked. Brackets compare with No docs. Highlighted values mark the highest quality score and lowest recorded tokens, time, and Python CC within each run; ties share the highlight. This does not mean the success rule passed. Python CC means the recorded mean cyclomatic complexity of the Python code’s functions, classes, and methods at the final stage. It includes vendored code where present.
What changed in this condition
The agent extends an existing application inside about 400,000 lines of vendored code, over five stages of imperative prompts.
Control
No docs
No design method and no starting design. Before coding, it writes its own method, then its designs.
Comparison
Prose docs
The prose method, and the existing application’s finished design in prose in place of the starting charters.
Hypothesis arm
Algebraic docs + z3
The algebraic method with z3 installed, and the existing application’s finished design in algebra, with its z3 files, in place of the starting charters. Every proof must pass when a stage ends.
Runs: 3 (E024 run 1, E024 run 2, E024 run 3), repeats of one setup.
Builder model: gpt-6-sol · medium
Agent harness: codex-cli. Judge: claude-opus-5-5-high.
Stage evidence
Not supported. Each part of the rule must hold in every run.
Stages:
duplicate-name-checkentry-supersessionrevise-informationagent-token-telemetryontology-audit
| Run | Arm | Met | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|---|
✗ Algebraic docs + z3 must score at least 0.1 above No docs in every graded stage, in every run: not met | |||||||
| E024 run 1 | Algebraic docs + z3 | 0 of 5 | −0.02 | +0.02 | +0.03 | 0.00 | −0.06 |
| E024 run 2 | Algebraic docs + z3 | 0 of 5 | −0.01 | +0.01 | +0.06 | −0.03 | +0.01 |
| E024 run 3 | Algebraic docs + z3 | 0 of 5 | 0.00 | −0.07 | +0.04 | 0.00 | +0.02 |
Each cell is the arm’s score minus the other arm’s at that stage. ✓ marks a stage that meets that part of the rule; Met counts them, of the stages with a value.
Noise. Between runs that repeat the same setup, the same arm’s score at the same stage moved by a median of 0.03 and at most 0.11, over 15 comparisons; 2 moved by 0.10 or more, the rule’s threshold.
Details
The prediction, set before the runs
The test card names the arms as follows: control is No docs, semantic is Prose docs, algebraic_solver is Algebraic docs + z3; total_tokens is tokens and elapsed_s is time.
Prediction. The algebraic_solver arm’s quality score exceeds the control’s by at least 0.1 in each stage; tokens and time are recorded as secondary measures.
Falsifier. The algebraic_solver arm’s quality score is no higher than the control’s. A positive difference below 0.1 is inconclusive.
Measured: Each arm’s judged score at each stage. Quality Δ is the arm’s score minus No docs. A stage meets the quality target at +0.1 or above. Every counted check must pass in every run.
z3
| Run | Arm | Last stage | Proof goals | Proved | Disproved | Undecided | Stages the agent ran z3 |
|---|---|---|---|---|---|---|---|
| E024 run 1 | Algebraic docs + z3 | 5 | 222 | 222 | 0 | 0 | 3 of 5 |
| E024 run 2 | Algebraic docs + z3 | 5 | 201 | 201 | 0 | 0 | 4 of 5 |
| E024 run 3 | Algebraic docs + z3 | 5 | 187 | 187 | 0 | 0 | 3 of 5 |
After each stage, the system runs z3 on the proof goals in the design’s z3 files and counts those it proves, disproves or leaves undecided. The counts are from the last stage that has them; — means none were recorded. The last column counts stages in which the agent itself ran z3.
Runs
E024 run 1 — gpt-6-sol · medium
Run ID: run-20260924T013909Z-79df517b
Started: 2026-09-24
Harness status: completed
Every arm finished every stage.
E024 run 2 — gpt-6-sol · medium
Run ID: run-20260924T013934Z-a085b261
Started: 2026-09-24
Harness status: completed
Every arm finished every stage.
E024 run 3 — gpt-6-sol · medium
Run ID: run-20260924T014000Z-e4983936
Started: 2026-09-24
Harness status: completed
Every arm finished every stage.
Source data
View condition E024 in G001.json. The run IDs above identify the counted runs. See Data and methods for the export method and limits.