The POW miners of Bitcoin are mutually referred to as "oracle Turing machines" to update the longest chain. The growth of the longest chain rule is the actual implementation of over limit iterations. The digital signature chain UTXO/timestamp chain Blockchain, etc. are logical systems with infinite sequences. The three-layer PH structure composed of UTXO/POW/longest chain is a recursive convention between the computable and non computable Turing degree patterns.