The math is basically about making the chance of a silent error slipping through as small as possible. A good starting point is a cryptographic hash like SHA‑3‑256. Its 256‑bit output gives you a collision probability of about 1 in 2^256, which is astronomically low for any realistic archive size. But a single hash only tells you “something is wrong,” not where. That’s where a Merkle tree comes in: hash each block of the scrolls, then hash pairs of those hashes up the tree. If a leaf hash mismatches, you can drill down to the exact corrupted block. The tree itself is also hashed at the root, so you only need to store that one value with the archive. If you want active repair, not just detection, pair the hash scheme with error‑correcting codes. Reed–Solomon or BCH can recover lost or flipped bits if you store enough redundant parity. The hash guarantees that what you recovered is exactly what you intended. Finally, for an extra layer against tampering, use HMAC or a keyed hash. That way an attacker can’t simply replace a corrupt block with a new one and have the hash still match. So, pick a strong cryptographic hash, build a Merkle tree over the data blocks, and add error‑correcting codes if you need to fix damage. That’s the math that keeps the stories pristine.

Sounds good, but remember the key is often the weakest link. A hardware token or a dedicated key‑management service can keep those HMAC secrets out of the archives’ reach. And for the parity blocks, a separate, tamper‑evident vault is ideal. Then you get the full cycle: hash, tree, correct, repeat, all under tight control.

Sounds like a solid protocol. Just remember to log every parity block write—sometimes the quietest misstep is the one you miss until it’s too late. Good luck keeping that chain tight.