siddhartha-gadgil/leanaide/03-source-study

Skill: Source Material Analysis

Goal: Dissect relevant mathematical literature to extract techniques, reusable lemmas, limitations, and possible extensions. Write findings to artifacts/02_literature_review.md.

Instructions: For each provided proof or theorem snippet:

1. Structural Mapping: Map which original hypothesis is used to justify which line in the proof.
2. Hypothesis Stress-Testing: Identify what specifically breaks in the proof if a key hypothesis is dropped.
3. Generalization: Can the hypotheses be weakened? (e.g., from compact to locally compact).
4. Aha! Moment: Distill the core trick of the paper into 1-3 sentences.
5. Examples and Counterexamples: Extract examples, counterexamples, sharpness examples, and boundary cases used by the source. Record which hypothesis each example tests.
6. Research Leads: If in exploratory mode, list plausible extensions, sharpness questions, examples to compute, and nearby open-ended questions. Clearly label speculative leads as speculative.