# Contract — T3-synthesis (P0)

## Question
Does access to a generative-AI assistant shorten the time workers need to complete their tasks? Small evidence synthesis of five primary studies whose extracts are provided under `data/sources/`.

## Estimands
- The five printed values exactly as printed (estimate, uncertainty, sample, definition, locator).
- θ = ln(T_AI / T_noAI): log ratio of mean completion time with AI to mean completion time without AI, same tasks, randomised comparison (negative = faster with AI). Harmonised θ and SE(θ) per study where obtainable from printed quantities under TASK conventions:
  - log-time regression coefficient b → θ=b, SE=SE(b) (or CI width / 3.92);
  - % change c or ratio → θ = ln(1+c);
  - p-value only → SE ≈ |θ| / z_{1−p/2} (approximate, flagged);
  - stars / threshold / figure-only CI → harmonisable but not poolable;
  - not a time comparison AI vs no-AI on same tasks → not harmonisable.
- Inverse-variance FE and DerSimonian–Laird RE pooled θ over poolable studies, 95% CI with 1.96, Q (df=k−1), I² = max(0,(Q−df)/Q)·100, τ² = max(0,(Q−df)/C). Heterogeneity label low/moderate/substantial at 25/50. Significance = RE CI excludes 0. pooled_pct_change_re = 100(exp(θ_RE)−1).
- Assumptions: printed effects are unbiased estimates of the log time ratio for their populations/tasks; normal sampling distribution on log scale; p-value-derived SE assumes a Wald-type test on the same scale; RE assumes exchangeable study effects (very weakly identified with k=2).

## Required outputs
- out/table1.csv (5 rows; columns study, estimate_as_printed, uncertainty_as_printed, sample_as_printed, definition, locator, harmonised_estimate, harmonised_se, harmonisable, poolable, transformation, reason_if_not)
- out/figure1.png forest plot (harmonisable studies; no-SE studies as points; RE pooled)
- out/results.json keys: task_id, target_definition, items{S1..S5 with estimate_as_printed, uncertainty_as_printed, sample_as_printed, definition, locator, harmonisable, harmonised_estimate, harmonised_se, poolable, transformation, reason_if_not}, k_extracted, k_harmonised, k_pooled, fe_estimate, fe_se, fe_ci_low, fe_ci_high, re_estimate, re_se, re_ci_low, re_ci_high, q_stat, i2, tau2, heterogeneity_interpretation, pooled_significant_5pct, pooled_pct_change_re, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed
- out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues)
- out/analysis.py (regenerates results.json, table1.csv, figure1.png from data/ only, deterministic, prints the source lines it relies on)
- out/claims.json; out/exclusions.csv; out/state/*

## Information-availability rules
Only the extracts are admissible evidence. No remembered values from full papers, figures or elsewhere. Printed numbers reported exactly as printed; transformations only in harmonised columns.

## Invalidity / impossibility
- Fewer than 1 poolable study would make pooled keys impossible (they are non-nullable) — check.
- Using values not printed in extracts (e.g., METR CI from Figure 1) would invalidate.
- Pooling non-comparable outcomes (S5 output counts) would invalidate.