stat-toolkits-eif: Instructions file for Codex

Agent instructions for the EIF toolkit

This repository is a documentation-first toolkit for deriving, validating, and implementing efficient influence functions (EIFs). It is not primarily a Python package yet. Treat the files in agent/, theory/, examples/, and simulations/ as the working system.

First files to read

For any EIF task, read these files first:

1. agent/eif_agent_task_spec.md
2. agent/eif_latex_problem_protocol.md
3. agent/eif_target_triage.md
4. agent/eif_research_problem_protocol.md
5. agent/eif_hard_problem_protocol.md
6. agent/eif_answer_rubric.md
7. theory/semiparametric_influence_function_guide.md
8. theory/eif_projection_guide.md
9. agent/eif_danger_zone.md
10. examples/eif_examples.md
11. agent/eif_validation_tests.md
12. agent/eif_implementation_guide.md

Use examples/eif_formula_registry.yaml only after checking that the observed data, target, model, assumptions, nuisance definitions, and positivity conditions match.

For self-testing or evaluation, use both examples/eif_benchmark_tasks.md and examples/eif_hard_benchmark_tasks.md.

Default workflow

When the user gives a problem, especially in LaTeX:

1. Normalize the problem statement.
2. Assign a target triage label.
3. State the observed-data unit (O).
4. Separate the scientific target from the observed-data functional.
5. State identification assumptions.
6. State the statistical model.
7. Check pathwise differentiability.
8. Check whether the model is fully nonparametric or restricted.
9. Identify nuisance functions and positivity conditions.
10. Factorize the likelihood and decompose the score.
11. Derive the IF/EIF component by component.
12. Verify mean zero and the pathwise derivative identity.
13. Check special-case reductions.
14. Provide estimator, standard error, and validation code only when requested or useful.

LaTeX inbox behavior

For LaTeX inbox/problem-folder artifacts, follow agent/eif_problem_artifacts.md.

When the user asks to process a LaTeX problem under problems/latex_inbox/problem_*/problem.tex, check whether notes.md exists in the same folder.