universalGateSet
plain-language theorem explainer
The declaration defines a four-element list naming the quantum gates supplied by the eight-tick phase structure. Researchers working on the physical Church-Turing thesis from ledger universality cite this list to ground universal computation in Recognition Science. The definition enumerates the gates by their rotation angles and tick counts, with the Hadamard entry obtained from superposition.
Claim. The universal gate set is the list containing the T gate for a rotation by $π/4$ in one tick, the S gate for $π/2$ in two ticks, the Z gate for $π$ in four ticks, and the Hadamard gate realized by superposition.
background
Recognition Science obtains the Church-Turing thesis from ledger universality: every computation is a sequence of ledger updates under the eight-tick period. The tick is the fundamental RS-native time quantum, set to 1. The shifted cost H satisfies H(x) = J(x) + 1 and converts the Recognition Composition Law into the d'Alembert equation H(xy) + H(x/y) = 2 H(x) H(y).
proof idea
This is a definition that directly constructs the list of gate strings. It assigns rotation angles to T, S, and Z using multiples of the tick constant and places the Hadamard entry via the superposition rule already present in the ledger model.
why it matters
The definition supplies the concrete gate set required by the physical Church-Turing thesis developed in the same module. It realizes the eight-tick octave as the source of a universal gate set for quantum computation. The module targets the paper proposition on the physical basis of universal computation.
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