IndisputableMonolith.Physics.QuantumComputingGatesFromRS
The module derives single-qubit Clifford gates from Recognition Science, establishing that the group cardinality equals 8. Quantum information researchers linking discrete symmetries to the RS forcing chain would cite it. The module supplies definitions for CanonicalGate and related objects plus a direct cardinality equality.
claimThe single-qubit Clifford group satisfies $|C_1| = 8 = 2^D$.
background
Recognition Science obtains D = 3 from the T0-T8 forcing chain, with T7 supplying the eight-tick octave whose period is 2^3. The module sits inside the physics derivations that embed quantum operations into the J-cost and phi-ladder structures. It imports Mathlib and introduces sibling definitions CanonicalGate, cliffordSingleQubit and QCGateCert to make the connection explicit.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the concrete link from the eight-tick octave (T7) to Clifford operations, feeding downstream gate-certification results in the RS physics layer. It closes one step in the program that recovers standard quantum gate counts from the Recognition Composition Law and the forced dimension D = 3.
scope and limits
- Does not treat multi-qubit Clifford groups.
- Does not derive non-Clifford gates.
- Does not address measurement or error correction.