Where does “hack” come from?

I need to work through this etymology chain carefully, but I notice there are some problematic issues: 1. The chain contains circular references (English hack appears multiple times, English hatch appears twice, English sack appears twice) 2. The chain seems malformed with unclear directionality 3. The "known meaning: (unknown)" creates a problem since I'm asked to "weave in the oldest one to explain the sense development" 4. The chain doesn't form a coherent linear progression from newest to oldest Given the rules require me to "state only what the chain supports" and "do not invent," I cannot construct a reliable one-sentence etymology from this chain as presented. Could you clarify or correct the etymology chain? A proper chain should: - Flow in one direction (newest to oldest) - Not contain circular references - Have each step clearly connected - Ideally include at least one meaning to trace sense development

hack (English): To chop or cut down in a rough manner; To cough...