IndisputableMonolith.Mathematics.AbstractHarmoniAnalysisFromRS
The module certifies that ℤ/8ℤ carries a locally compact group structure with exactly eight elements. Researchers deriving the discrete octave symmetry in Recognition Science cite it to anchor the 2^3 period. Content consists of group definitions, cardinality lemmas, and a direct certification theorem.
claim$\mathbb{Z}/8\mathbb{Z}$ is a locally compact abelian group with cardinality $8=2^3$.
background
The module imports Mathlib to access the locally compact group type LCGroup. It introduces lcGroupCount, z8Size, and z8Size_2cubed to record that the cyclic group of order 8 has size exactly 2 cubed. AbstractHarmonicAnalysisCert packages the certification that abstract harmonic analysis applies to this finite group. The local setting is the discrete symmetry layer required by the eight-tick octave step of the Recognition Science forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the group-theoretic object required by the eight-tick octave (T7) in IndisputableMonolith.Foundation.UnifiedForcingChain. It feeds downstream constructions that use the period-8 structure to derive spatial dimension D=3 and the phi-ladder mass formula.
scope and limits
- Does not derive the Recognition Composition Law.
- Does not compute physical constants such as alpha or G.
- Does not treat continuous or non-abelian groups.
- Does not address the Berry creation threshold or Z_cf.