z8Size
plain-language theorem explainer
The definition sets the number of elements in the cyclic group of integers modulo 8 to 8. Analysts working on discrete Fourier transforms derived from Recognition Science would cite this cardinality when verifying the eight-tick structure. The value is assigned directly as a constant in the natural numbers.
Claim. \( |\mathbb{Z}/8\mathbb{Z}| := 8 \)
background
The module develops abstract harmonic analysis from Recognition Science by identifying five canonical locally compact groups whose count equals the configuration dimension D = 5. Within this, the discrete Fourier transform of order 8 operates on the cyclic group ℤ/8ℤ whose order is 2^3. Pontryagin duality identifies the dual of ℤ with the circle group S¹. The local setting requires |ℤ/8ℤ| = 8 = 2^3 by direct assignment.
proof idea
The declaration is a direct constant definition assigning the natural number 8.
why it matters
This supplies the group order required by the certificate structure for the harmonic analysis setup. It realizes the eight-tick octave of period 2^3 from the forcing chain step T7 and confirms D = 3 spatial dimensions. The parent theorem then proves the equality to 2^3, closing the verification that the group order matches the required power.
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