Conjecture 4 Research Map Stub

This conjecture has no atomic research nodes yet. Use ../index.md for the current big picture and ../../conjectures.md for the canonical statement.

First Node Tasks

1. Prove an exact-decoding separation before approximate decoding.
2. Replace average-case hardness by a cleaner worst-case hardness target if needed.
3. Use coherent information or another decoder-independent survival certificate as the first weaker theorem.

Node Policy

Add only theorem, reduction, source-extraction, or explicit gap nodes. Do not add generic background summaries here.