gap45_eq
plain-language theorem explainer
The equality gap45 = 45 is fixed by reflexivity inside the dark matter mass module. RS cosmologists modeling m_DM / m_W ratios cite it to anchor the numerical gap at 45 for D = 3. The term-mode proof applies reflexivity directly to the prior definition of gap45.
Claim. $gap_{45} = 45$
background
In Recognition Science the gap parameter is the product of spatial and configurational dimensions, $D_{spatial}^2 times D_{config}$, which evaluates to 45 when $D_{spatial} = 3$ and $D_{config} = 5$. This module uses that fixed value to predict the dark matter mass ratio relative to the W boson mass. Upstream, CardinalitySpectrum proves the product form by decision procedure while RSCoupledAxis records the numerical identity by reflexivity; the reference scale m_W is supplied as the constant 80.377 GeV from the Standard Model module.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of gap45.
why it matters
This supplies the concrete gap value required by darkMatterMassCert in the same module and by cardinalitySpectrumCert and styleSuccessionCert downstream. It realizes the T8 step that forces three spatial dimensions and the resulting gap of 45, which in turn sets the mass formula m_DM = m_W / 45 and the predicted band near 1.78 GeV. No open scaffolding remains at this leaf.
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