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Bitcoin Is Not One Computation Object: Script Boundedness, UTXO State, and Transaction-Chained Universality

Year: 2026
Type: preprint
Abstract: "Bitcoin is Turing-complete" is ill-posed until one names the object, rule set, and enforcement tier, where the rule set includes script composition, not just opcodes. Our result is era-resolved: whether Bitcoin can enforce a covenant turns on the opcode set, the composition, and the resource model, which never simultaneously admitted the covenant we exhibit on mainnet. The deployed genesis validator composed scripts in one pass with a permissive OP_RETURN, so every output was bypass-spendable and the 2009 chain sits at the Recorded tier (Lemma 3, [C-executed]). Under a sound two-phase composition the genesis opcodes express a consensus-enforcing OP_PUSH_TX covenant (OP_CAT plus wide arithmetic bind the spending transaction through OP_CHECKSIG), which we run through the compiled interpreter on the rule set R*. Reading the bitcoin/bitcoin source shows R* never ran on mainnet: sound two-phase composition first shipped at v0.3.7 (31 July 2010), but the same hardening imposed a 201-non-push-opcode limit genesis lacked, and the covenant needs 254 opcodes (its two mandatory endianness reversals alone are 197), so its output is unspendable there. The two axes briefly coexisted at v0.3.7-v0.3.8, but the covenant needs a third thing, opcode-budget headroom, removed at the same moment; commit 4bd188c (15 August 2010) then disabled the opcodes and cut the numeric cap. So our covenant is off mainnet at every version, and R* is counterfactual. Even the bare binding is 224 non-push opcodes, golfable toward 216, still above 201; whether any covenant reaches 201 is open (the optimistic counting baseline of about 155 sits below 201, turning on an unproven reversal rate), while every covenant we build is rejected. The contribution is a definitional discipline plus an artifact adjudicating the covenant capability on R*, its genesis refutation, and the three-factor bracket.
DOI: 10.5281/zenodo.21384415
Language: English
Open Access status: green
OpenAlex ID: W7168352022
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