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def definition def or abbrev high

G

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The RS-native gravitational constant is defined by direct substitution as G = λ_rec² c³ / (π ħ) with λ_rec the recognition length and ħ = φ^{-5}. Researchers deriving zero-parameter constants from the meta-principle cite it to close the Planck relation inside the forcing chain. The declaration is a one-line algebraic rearrangement of the lambda_rec definition.

claimIn RS-native units the gravitational constant is given by $G = λ_{rec}^2 c^3 / (π ħ)$, where $λ_{rec}$ is the fundamental recognition wavelength and $ħ = φ^{-5}$ is the reduced Planck constant.

background

Recognition Science fixes c = 1 and obtains ħ = E_coh τ₀ = φ^{-5} from the coherence energy in the eight-tick cycle. The recognition length λ_rec is set to the base length ℓ₀. The module supplies all constants in this native system so that the J-cost functional equation and Recognition Composition Law hold without external parameters.

proof idea

One-line definition that inverts the Planck-scale identity λ_rec = √(ħ G / c³) from Bridge.DataCore.lambda_rec and substitutes the RS-native ħ and c = 1.

why it matters in Recognition Science

Supplies the RS-native G required by cost_algebra_unique and cost_algebra_unique_aczel (T5 uniqueness of the cost function J). It also feeds the zero-parameter certificate ml_zero_parameter_certificate and the mass-to-light derivations. The form is consistent with the phi-ladder and the eight-tick octave.

scope and limits

formal statement (Lean)

 432noncomputable def G : ℝ := (lambda_rec^2) * (c^3) / (Real.pi * hbar)

proof body

Definition body.

 433

used by (40)

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

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depends on (9)

Lean names referenced from this declaration's body.