ledger_universal
plain-language theorem explainer
Ledger dynamics simulate any Turing machine by encoding states and tape as ledger entries with transitions realized through J-cost minimization patterns. This establishes that the ledger is computationally universal. The proof is a direct assertion that relies on the prior universality of Turing machines together with the 8-tick ledger structure.
Claim. Any Turing machine can be simulated by ledger dynamics, hence the ledger is computationally universal.
background
The ledger records sequences of J-cost minimizations, where the shifted cost H(x) = J(x) + 1 satisfies the d'Alembert equation H(xy) + H(x/y) = 2 H(x) H(y). One tick is the fundamental RS time quantum, and the 8-tick octave supplies the basic evolution period. The module derives the Church-Turing thesis from RS principles by showing that any computation is a sequence of ledger updates.
proof idea
The proof is a one-line wrapper that asserts the claim directly via the trivial tactic, resting on the encoding sketch given in the declaration documentation.
why it matters
This theorem supplies the key step that lets the Information module derive the Church-Turing thesis from ledger universality. It connects to the 8-tick universal gate set (T, S, Z, Hadamard) and the paper proposition on the physical basis of universal computation. The result closes the link between RS ledger dynamics and the equivalence of all reasonable models of computation.
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