Suppose you found an _error-detecting code_ $f(H(m), m')$ (forget random oracles, second-preimage resistance, _etc._) with the following properties:

1. $|H(m)| = O(1)$, _i.e._ the checksum overhead is independent of the message length.
2. $f(H(m_0 \mathbin\| m_1), m_0) = f(H(m_0 \mathbin\| m_1), m_0 \mathbin\| m_1) = 1$
3. $f(H(m_0 \mathbin\| m_1), m_0 + \delta) = 0$ with high probability when $\delta \ne 0$
4. $f(H(m_0 \mathbin\| m_1), m_0 \mathbin\| (m_1 + \delta)) = 0$ with high probability when $\delta \ne 0$

This would be an astonishing development in coding theory, because it would mean that we could detect fine-grained errors in any message on the planet just by hashing them all into a short $|H(m)|$-bit string as follows:

1. Check every book $m_0, m_1, m_2, \dots$ out of the Library of Alexandria.
2. Concatenate them all into one giant message $m_0 \mathbin\| m_1 \mathbin\| m_2 \mathbin\| \cdots$, encoded appropriately so that the colophon of the previous book doesn't get confused with the title page of the next book.
3. Compute $h = H(m_0 \mathbin\| m_1 \mathbin\| m_2 \mathbin\| \cdots)$ and store it somewhere safe—replicate it at libraries around the world, put it in the blockchain, tattoo it on your forehead, _etc._
4. Whenever you're concerned that a cosmic ray might have dislodged a piece of type and thereby caused a typo into one of the books in the library, check $f(h, m'_0)$, which, if there was an error in $m'_0$ from $m_0$, will fail with high probability, in which case get book 0 reprinted; otherwise, check $f(h, m_0 \mathbin\| m'_1)$, which, if there was an error in $m'_1$ from $m_1$, will fail with high probability, in which case get book 1 reprinted; and so on.

Archivists still put checksums on individual pieces of data, instead of merging into one collaborative cabal of archiveborg with a single checksum for all the world's data, so I don't think that breakthrough in coding theory has been found yet.