IndisputableMonolith.Mathematics.ConwayGroupStructuralFromRS
The module derives Conway group and Leech lattice invariants from Recognition Science constants. It defines leechDimension as 24 and certifies the factorization 24 = 2³ · 3 together with b3Order and related factors. Researchers connecting sporadic groups to the phi-ladder and eight-tick octave would cite these results. The structure rests on direct definitions from the imported RS time quantum without external lemmas.
claimLet $d = 24 = 2^3 · 3$. The Leech lattice dimension satisfies $d = 2^3 · 3$, with the Conway group acting on the associated lattice, all obtained from the RS time quantum $τ_0 = 1$ tick.
background
Recognition Science builds all structure from the J-functional equation and the self-similar fixed point phi. This module imports the base constant $τ_0 = 1$ tick from IndisputableMonolith.Constants. It introduces sibling definitions leechDimension, b3Order, leechFromCube, leech_half_b3, leechDim_factorisation, and ConwayCert to encode the 24-dimensional structure whose factorisation is given as $24 = 2^3 · 3$, reflecting the eight-tick octave period.
proof idea
This is a definition module. It declares leechDimension, establishes leechDimension_eq by direct equality to 24, computes b3Order and leech_half_b3 from the RS constants, assembles leechDim_factorisation, and packages the results into ConwayCert and conwayCert.
why it matters in Recognition Science
The module supplies the dimensional foundation for the Conway group inside the Recognition framework. It links the T7 eight-tick octave directly to the Leech lattice dimension 24. Although no downstream uses are recorded, it supports the claim that sporadic-group structure arises from the forcing chain T0-T8.
scope and limits
- Does not prove existence of the Leech lattice.
- Does not compute the full order of the Conway group.
- Does not derive physical masses or couplings.
- Does not address embeddings into other sporadic groups.