A service publishes a fresh random number every minute, plus a public log in which each entry carries a fingerprint of the entry before it. What does that chaining add?

Answer: A way to prove the history was not edited later

A way to prove the history was not edited later ✓ — Because every entry carries a fingerprint of the one before it, changing an old number would change its fingerprint and break every entry that followed. Anyone who saved a later number can still check the chain today, so the operator cannot quietly rewrite what it published last week. The trust comes from the record being checkable afterwards, not from hiding anything.

Numbers that are more evenly spread out — Evenness comes from the source of the randomness — a noisy physical process and the maths that cleans it up — and it is settled before anything is published. The log does not touch the numbers themselves; it only records what was published and when, so it cannot make the spread better or worse.

Faster delivery of each new number — Chaining actually costs a little time rather than saving it, since each entry has to be fingerprinted and published. A service can hand out numbers very fast and still be impossible to audit afterwards. Speed and verifiability are separate properties, and this design buys the second one.