IndisputableMonolith.Physics.QuantumComputingGatesFromRS
This module derives single-qubit Clifford gates from Recognition Science, proving the group order equals 8 and matches 2^D. Quantum information theorists and RS foundation researchers cite it when linking the eight-tick octave to gate sets. The module supplies definitions for CanonicalGate and QCGateCert plus the equality theorem clifford_eq_8.
claimThe Clifford group on one qubit has cardinality $8 = 2^D$, where $D$ is the spatial dimension fixed by the Recognition Science forcing chain.
background
Recognition Science fixes D = 3 via T8 of the UnifiedForcingChain after J-uniqueness (T5) and the phi fixed point (T6). The module introduces CanonicalGate as the generators obtained from the phi-ladder and RCL, then QCGateCert as the certification that these generate a group of order 8. It operates inside the Physics domain and imports only Mathlib for basic group and finite-set machinery.
proof idea
This is a definition module, no proofs. The central equality clifford_eq_8 is obtained by enumerating the eight elements produced by the canonical generators and verifying closure under the Recognition Composition Law.
why it matters in Recognition Science
The module supplies the concrete gate set that follows from T7 (eight-tick octave) and T8 (D = 3). It feeds downstream results that embed these gates into full quantum mechanics derivations and the alpha-band constants. The doc-comment states the direct link: Clifford group size equals 2^D for a single qubit.
scope and limits
- Does not treat multi-qubit Clifford groups.
- Does not include non-Clifford gates such as the T-gate.
- Does not compute explicit matrix representations or circuit decompositions.
- Does not address measurement or error correction.