IndisputableMonolith.Mathematics.AbstractHarmonicAnalysisFromRS
The module derives abstract harmonic analysis from Recognition Science by centering on the cyclic group of order 8. Researchers linking discrete group theory to the eight-tick octave in the forcing chain would cite it. The structure consists of group definitions, cardinality lemmas, and a certification object with no complex proofs.
claimThe cyclic group $\mathbb{Z}/8\mathbb{Z}$ satisfies $|\mathbb{Z}/8\mathbb{Z}|=8=2^3$, with LCGroup denoting the locally compact group structure and AbstractHarmonicAnalysisCert the derived certificate.
background
The module imports Mathlib for standard group and measure theory. It introduces LCGroup as the locally compact abelian group on the cyclic order-8 case, lcGroupCount for element enumeration, z8Size and z8Size_2cubed for the explicit cardinality result, and AbstractHarmonicAnalysisCert together with its constructor abstractHarmonicAnalysisCert. The local setting is the T7 eight-tick octave of the UnifiedForcingChain where the period equals $2^3$.
proof idea
This is a definition module, no proofs. It assembles sibling definitions and the direct cardinality statement from the doc-comment into a coherent package for downstream harmonic analysis.
why it matters in Recognition Science
The module supplies the group-theoretic substrate for abstract harmonic analysis derived from RS and feeds parent results on the eight-tick octave (T7) and the Recognition Composition Law. It closes the discrete-to-continuous bridge required by the forcing chain before mass formulas or alpha-band calculations are reached.
scope and limits
- Does not derive full Pontryagin duality or Plancherel theorems.
- Does not compute explicit Fourier transforms on the group.
- Does not link the group order to spatial dimension D=3 or constants.
- Does not address continuous locally compact groups beyond the order-8 case.