ConwayCert
The structure bundles three integer identities that certify the 24-dimensional Leech lattice representation of the Conway group Co₁ inside Recognition Science. Researchers working on sporadic groups or lattice embeddings in the phi-ladder would cite these facts to invoke the dimension and factorization without repeating the arithmetic. The definition simply records two constant definitions together with their equality established by direct computation.
claimA structure asserting that the Leech lattice dimension equals 24, that this dimension equals half the order of the 3-cube group, and that the dimension factors as $2^3 · 3$.
background
The module records structural integer facts for the Conway group Co₁ and its canonical 24-dimensional action on the Leech lattice. It states that the order of Co₀ is twice the order of Co₁, that 24 equals 2³ · 3, and that 24 also equals the order of the 3-cube group divided by 2. These identities are treated as decided arithmetic facts supporting later sporadic-group work in Recognition Science.
proof idea
The declaration is a structure definition whose three fields are filled by the constant definition of the Leech dimension, the definition of the half-cube order, and the decide tactic on their equality.
why it matters in Recognition Science
This certificate supplies the dimension and factorization facts required by the downstream construction of the Conway certificate. It supports the sporadic-group analysis in Recognition Science by linking the factor 2³ to the eight-tick octave and the factor 3 to spatial dimension D = 3. No open questions are addressed.
scope and limits
- Does not prove the existence of the Leech lattice.
- Does not derive the dimension from the Recognition Composition Law.
- Does not compute the full order of the Conway group.
- Does not connect these facts to mass formulas or the phi-ladder.
formal statement (Lean)
32structure ConwayCert where
33 leech_dim : leechDimension = 24
34 leech_half_b3 : leechFromCube = leechDimension
35 leech_factorisation : leechDimension = 2 ^ 3 * 3
36