Very interesting to see this concept distilled so cleanly!
@rijndael sketched what seems to me exactly the same idea in this thread describing a possible token standard using CAT called CatNip. Once you remove the ‘token’ parts, I think the singleton is precisely what’s left - and indeed, constant-size proof of ancestry was the goal.
There, he used CAT in (at least) two ways:
- carrying state via extra outputs (using introspection with the Schnorr trick)
- introspecting the parent’s Script based on its txid.
An opcode that allows a clean way of carrying state (like OP_CHECKCONTRACTERIFY) would avoid the Schnorr trick, but of course reading ‘inside’ a txid is trickier (perhaps not crazily so, though). There might be other ways of creating the singleton that do not require the txid.
The singleton primitive seems very interesting to me, as it would allow to generalize the concept of the ‘connector outputs’ (which are essentially a proof of ancestry at depth zero) used for example in Ark. I expect this will be very useful in trying to combine state-carrying UTXOs with Ark and other shared UTXO constructions.