Thank you for your reply. Its a valid question and we can both theorize at this point and of course use our discussions as fuel to help build more robust solutions.
The way the solution has been designed is that it starts life as an L2 working as a parallel system (think like lightning network) works as a parallel system on top of Bitcoin.
As some point when a cryptographically relevant quantum computer comes to fruition and is capable of attacking Bitcoin and this is observed by the community / us / everyone on the blockchain that this has happened the L1 Bitcoin chain as we know it can no longer be trusted. Blocks can be rearranged so on and so forth.
At this point the parallel system that was working as backup becomes the new L1. Its capable of it as it has its own consensus, its own independent blockchain.
When I say “working as a backup” the concept is more akin to a third wheel that continuously is working and supporting but if one of the other wheels gets punctured it can be relied upon to continue functioning as normal and as a replacement to the wheel that was punctured - in other words people can use it now on testnet and mainnet once it launches to quantum wrap their BTC.
I am aware of the article you referenced regarding SIKE. Our system uses FIPS240 ML-DSA which for all intents and purposes at present is considered by NIST approved and went through their rigorous verification process.