What a valid draw means, precisely

No hand-waving. These are the rules the engine enforces, and the source code that enforces them ships with the site.

Guarantees

The receipt

At shuffle time the full assignment is serialized, sorted, and hashed into a single SHA-256 Merkle root — the receipt. Each participant link carries one leaf of that tree plus its sibling path, so a link can prove membership in the commitment without exposing any other pairing. Verification is public on /verify/.

Limits (stated plainly)