The first conversion case ended with a proposed lesson: before interpreting an aggregate conversion move, recompute the pooled rate from counts and split mix from within-channel change. This follow-up asks whether that lesson changes the next analysis, or becomes a story the agent repeats without checking.
Synthetic teaching case. An isolated Codex agent completed it after the first case, without the answer key. Sequential tasks in one agent are not independent sessions or a benchmark.
The second question
Conversion recovered in the next comparable period. Same grain and counting rules: one row per period and exclusive channel, sessions not unique people. The baseline is the earlier case's current period. No intervention log, costs, or user-level records.
| Period | Channel | Eligible sessions | Signups | Conversion |
|---|---|---|---|---|
| Baseline | Direct | 2,000 | 220 | 11.0% |
| Baseline | Paid | 8,000 | 400 | 5.0% |
| Current | Direct | 4,000 | 440 | 11.0% |
| Current | Paid | 6,000 | 360 | 6.0% |
Baseline pooled rate: 620 / 10,000 = 6.2%. Current: 800 / 10,000 = 8.0%. The movement is +1.8 percentage points.
What retrieval should change
A useful plan cites the earlier lesson, verifies that channel attribution is still exclusive and complete, and adds the mix/rate reconciliation before treating "recovery" as the previous decline in reverse. Direct is still 11%. Paid rises from 5% to 6%. Paid's share of sessions falls from 80% to 60%.
One exact decomposition, assigning the interaction to mix:
Mix contribution
= (40% − 20%) × 11% + (60% − 80%) × 5%
= +1.2 percentage points
Within-channel contribution
= 40% × (11% − 11%) + 60% × (6% − 5%)
= +0.6 percentage points
Total = +1.2 + 0.6 = +1.8 percentage points
The earlier decline was mostly mix. This recovery is mix plus a paid-rate improvement. Repeating "it was mix last time" would miss half the movement and treat a past observation as a mechanism that has to recur.
The other exact ordering reallocates the interaction and still sums to +1.8; the trial record notes the isolated agent used it. Both are arithmetic identities. Neither identifies a product or campaign cause.
What the saved run did
The agent's proposed lesson stays scoped to the measurement rules and marks itself proposed. Its follow-up plan cites that lesson and adds the composition check. Its answer reports a partial mix reversal and improved paid conversion.
That is the Compound Engineering bar applied to analytics: capture a demonstrated lesson, retrieve it on a later question, and show the check that changed. "I considered prior learnings" is not enough.
Run it yourself
Finish the first conversion case, then ($learn-from-analysis and $plan-analysis in Codex):
/learn-from-analysis Capture the acquisition-mix lesson from the
conversion analysis you just ran. Keep it scoped, link the evidence,
and mark it proposed.
/plan-analysis Conversion recovered from 6.2% to 8.0%. Plan the
follow-up using that lesson and
https://raw.githubusercontent.com/patrickjmorris/aftergrid/main/examples/skills-lab/data/conversion-followup.csv
State which lesson applies, which check it adds, and what would
invalidate it. Then run the plan.
From a checkout, node examples/skills-lab/verify.mjs checks the arithmetic. Inspect the follow-up CSV and case brief. Analysis that compounds is the essay.