Hello, here's a small idea to combine merkel tree with timestamped message signature to bind p2pkh adress to quantum resistant scheme so user do not need to rush to move bitcoin before qday, in a space efficient form.

Universal P2PKH freeze — At a defined block height, all P2PKH outputs become unspendable via classical ECDSA.

Pre-freeze claim — Before the freeze, owners sign a claim containing their Bitcoin address and a new post-quantum public key of their choice. The claim is ECDSA-signed, proving classical ownership while quantum computers don't yet exist.

Merkle-batched publication — Claims are batched into Merkle trees. Only the 32-byte root goes on-chain via OP_RETURN. One transaction covers large amount of claims.

Post-freeze spending — To spend a frozen output, provide: the original claim, a Merkle inclusion proof linking it to a pre-freeze root, and a signature from the post-quantum key committed in the claim. 

No claim, no spend — Any P2PKH output with no registered claim before the freeze height is permanently frozen until a future recovery mechanism is defined by the community.

I do not have enough knowledge to find the ideal scheme or implementation that fulfill those requirements sadly. 

1 - Stewart I, Ilie D, Zamyatin A, Werner S, Torshizi MF, Knottenbelt WJ. Committing to quantum resistance: a slow defence for Bitcoin against a fast quantum computing attack. R Soc Open Sci. 2018 Jun 20;5(6):180410. doi: 10.1098/rsos.180410. PMID: 30110420; PMCID: PMC6030263.
https://pmc.ncbi.nlm.nih.gov/articles/PMC6030263/

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