z8Size
plain-language theorem explainer
z8Size defines the natural number 8 as the order of the cyclic group ℤ/8ℤ. Analysts studying discrete Fourier transforms on cyclic groups or the eight-tick structure in Recognition Science would cite this constant when certifying harmonic analysis. The definition is a direct literal assignment, with the relation to 2 cubed established separately by a decision procedure.
Claim. The cardinality of the cyclic group $ℤ/8ℤ$ is defined to be 8.
background
The module Abstract Harmonic Analysis from RS identifies five canonical locally compact groups (ℝ, ℤ, S¹, ℚ_p, GL_n(ℚ)) with configuration dimension D = 5. It treats DFT-8 as harmonic analysis on the cyclic group ℤ/8ℤ whose order is 8, equivalently 2 cubed, and notes Pontryagin duality relating the dual of ℤ to the circle group S¹. The Lean code confirms the group order by decision with zero sorries or axioms.
proof idea
This is a direct definition that assigns the literal constant 8 to z8Size. No lemmas are applied and no tactics are used.
why it matters
z8Size supplies the group order required by the AbstractHarmonicAnalysisCert structure to assert equality with 2 cubed. It anchors the connection to the eight-tick octave (period 2^3) at forcing-chain step T7 and supports derivation of three spatial dimensions at T8. The module uses the definition to ground harmonic analysis in the RS framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.