alpha_t
plain-language theorem explainer
The definition introduces the ILG mixing parameter as (1 minus the inverse of phi) divided by 2. Modelers of dark matter as spatial topological frustration cite it to set the scale of J-cost mixing in the ℤ³ carrier. The assignment is a direct real-number expression with no lemmas or reductions required.
Claim. The ILG mixing parameter is defined by $α_t = (1 - φ^{-1})/2$, where φ denotes the golden-ratio fixed point.
background
The module frames dark matter as diffuse phase-saturation in the ℤ³ carrier that produces nonzero Betti-1 homology at galactic scales. This is one spatial projection of the phantom sector; the ILG kernel encodes the resulting geometry. The parameter appears explicitly in the module key result that frustration regions couple only through the J-cost gradient.
proof idea
The declaration is a direct definition that evaluates the algebraic expression (1 - phi inverse) divided by 2. No lemmas are applied and the body contains no tactics.
why it matters
It supplies the concrete value required by the DarkMatterTopologyCert structure, which records alpha_t positive, alpha_t less than one half, and gravity-only coupling for every frustration region. The definition realizes the ilg_encodes_dm statement in the module documentation and links the spatial projection to the phi-ladder of the unified forcing chain.
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