theory-to-toy-cases

Theory to Toy Cases

Make the idea concrete before scaling it up.

Workflow

1. Restate the abstract claim in the smallest possible setting.
2. Build 2-5 minimal cases:
   • a friendly case where the idea should work
   • a boundary case
   • a failure case
   • a misleading case that appears to work for the wrong reason
3. If useful, write a tiny simulation or symbolic example.
4. Compare predicted behavior vs actual behavior.
5. Extract what the toy case teaches about the full problem.

Good toy cases

Prefer cases that are:

• low-dimensional
• analytically tractable
• numerically checkable
• likely to expose hidden assumptions

Rules

• Do not use toy cases as proof.
• Say what scales and what does not.
• If a toy case fails, treat that as signal, not annoyance.

Output shape

Return:

• Abstract idea
• Minimal setup
• Cases
• What each case shows
• Implication for the full research question
• What the toy cases cannot establish