q3Exponent
plain-language theorem explainer
Q₃, the recognition lattice in three dimensions, is assigned exponent 2. Researchers formalizing algebraic structures on the Recognition Science lattice cite this constant when certifying the five canonical structures for dimension D. The definition is a direct assignment that encodes the group property of (ℤ/2ℤ)³.
Claim. The exponent of the group $Q_3$ is $2$.
background
The module derives algebraic structures from Recognition Science by treating Q₃ as the lattice with cardinality 8 = 2³ = 2^D. It forms the abelian group (ℤ/2ℤ)³ whose every element satisfies x² = 1, hence exponent 2. This supplies the numerical value used alongside q3Size = 8 to certify exactly five algebraic structures (group, ring, field, module, algebra).
proof idea
The declaration is a direct definition that assigns the natural number 2.
why it matters
AbstractAlgebraCert references this definition to record q3Exponent = 2 as one of three facts establishing five algebraic structures on Q₃. The value aligns with the eight-tick octave of period 2³ in the forcing chain and with T8 fixing D = 3 spatial dimensions. It closes a small certification step in the abstract-algebra extraction from the recognition lattice.
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