Five-stage builds: algebraic docs missed the quality margin and used more tokens

Generation · fresh codebase · 5 imperative stages · Result: not supported

Question: Do algebraic design docs improve coding agents' quality, token use, or time against no supplied docs and prose docs?

The agent grew one application over five stages of sequential imperative prompts, each in a new container that reused the previous container’s environment. Algebraic docs moved up in some stages and down in others, always by less than the threshold, against No docs and against Prose docs. It used the most tokens of the three arms in both runs.

Results at a glance

RunArmAverage scoreStages comparedTokensTimePython CC
E015 · gpt-6-astra · xhighNo docs0.370 (best in run)4 of 520.47M (best in run)2:11:12 (best in run)4.11
Prose docs0.362 (−0.008)22.82M (+12%)2:18:53 (+6%)4.09 (best in run)
Algebraic docs0.363 (−0.007)35.88M (+75%)2:57:17 (+35%)4.26
E016 · gpt-6-sol · mediumNo docs0.3124 of 515.00M1:00:286.35 (best in run)
Prose docs0.325 (+0.013) (best in run)14.25M (−5%) (best in run)0:50:33 (−16%) (best in run)7.32
Algebraic docs0.310 (−0.003)20.49M (+37%)1:06:58 (+11%)7.14

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 stage immediately before Rust conversion.

What changed in this condition

The agent grows the application from an empty repository over five stages of imperative prompts. The last stage converts it to Rust. Each run uses a different builder model, to test the result at different model sizes.

Control

No docs

No design method and no starting design. Before coding, it writes its own method, then its designs.

Comparison

Prose docs

A design method in prose, and four starting charters in prose that define the application’s core concepts: checks, operations, the ontology and telemetry.

Hypothesis arm

Algebraic docs

A design method in algebra (capability contracts, Hoare triples, laws and proofs), and the same four charters in algebra, each with a written proof.

Runs: 2 (E015, E016), one per builder model.

  • E015: gpt-6-astra · xhigh
  • E016: 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:

  1. initial-build
  2. telemetry-add
  3. parity-substrate
  4. process-ontology
  5. rust-conversion
RunArmMet12345
✗ Algebraic docs must score at least 0.1 above No docs in every graded stage, in every run: not met
E015 · gpt-6-astra · xhighAlgebraic docs0 of 4+0.05+0.02−0.05−0.05both failed
E016 · gpt-6-sol · mediumAlgebraic docs0 of 40.00+0.08−0.08−0.01both failed

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. “failed” means that arm’s grade failed at that stage, so the stage has no score.

Noise. No two runs here repeat the same setup. In this group’s repeated runs, the same arm’s score at the same stage moved by a median of 0.03 and at most 0.11.

Details

The prediction, set before the runs

The test card names the arms as follows: control is No docs, semantic is Prose docs, algebraic is Algebraic docs; total_tokens is tokens and elapsed_s is time.

Prediction. The algebraic arm’s quality score exceeds the semantic arm’s by at least 0.1.

Falsifier. The algebraic arm’s quality score is no higher than the semantic arm’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. The prediction above names Prose docs; the condition result uses the No docs control.

Runs

E015 — gpt-6-astra · xhigh

Run ID: run-20260923T223518Z-020373a4
Started: 2026-09-23
Harness status: failed

The Algebraic docs arm’s grade failed at stage 5 (rust-conversion): cargo test failed. The No docs arm’s grade failed at stage 5 (rust-conversion): cargo test failed. Every earlier stage was graded.

E016 — gpt-6-sol · medium

Run ID: run-20260923T223651Z-b952ede3
Started: 2026-09-23
Harness status: failed

The Algebraic docs arm’s grade failed at stage 5 (rust-conversion): cargo test failed. The No docs arm’s grade failed at stage 5 (rust-conversion): cargo test failed. Every earlier stage was graded.

The harness marks a run failed when any arm’s grade fails. That stage has no score for that arm; the run’s other stages still count.

Limits

  • The two runs used different builder models, so they are not repeats.
  • Both runs lost the final stage’s comparison: at least one of the two arms failed its Rust grade.

Source data

View condition E015-E017 in G001.json. The run IDs above identify the counted runs. See Data and methods for the export method and limits.