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def definition def or abbrev high

configDim

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The definition fixes the configuration dimension at 5 for RS cosmology calculations. Researchers deriving the first CMB acoustic peak multipole would cite it to obtain ℓ₁ = 44 × 5 = 220 exactly. It is a direct numerical assignment with no lemmas or computation.

claimThe configuration dimension is defined as the constant 5.

background

In the RS framework the configuration dimension counts the total degrees of freedom in a recognition event: D spatial dimensions plus one temporal dimension plus one ledger-balance dimension. For the standard D = 3 case this yields exactly 5. The present module uses this value to express the first acoustic peak as the product of the baryon rung (44) and configDim. Upstream, the same identifier appears in IntegrationGap as d + 2 and in CoalitionSizeFromConfigDim as the base for 2^D - 1 coalition types.

proof idea

Direct constant definition; no tactics or upstream lemmas are invoked.

why it matters in Recognition Science

This supplies the numerical factor required by the CMBCert structure and the firstPeak definition to certify ℓ₁ = 220 and the second-peak ratio band. It realizes the T8 step of the forcing chain by embedding D = 3 spatial dimensions into the cosmology module. The value propagates into etaB_pos and the counterfactual rung derivations in EtaBExactRungDerivation.

scope and limits

Lean usage

theorem peak_decomposition : firstPeak = baryonRung * configDim := rfl

formal statement (Lean)

  28def configDim : ℕ := 5

proof body

Definition body.

  29
  30/-- ℓ₁ = baryonRung × configDim = 220. -/

used by (23)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (4)

Lean names referenced from this declaration's body.