dim_G
plain-language theorem explainer
Newton's gravitational constant G receives the dimensional signature [L³ T^{-2} M^{-1}]. Researchers deriving Planck units or checking consistency in Recognition Science would reference this assignment. The definition directly instantiates the Dimension record with length exponent 3, time exponent -2, and mass exponent -1.
Claim. The gravitational constant $G$ carries the dimensional signature $[L^3 T^{-2} M^{-1}]$.
background
The module establishes a dimensional analysis framework for Recognition Science in which every quantity carries a signature [L^a, T^b, M^c]. The Dimension structure records these three integer exponents for length, time, and mass. Fundamental units are the tick τ₀, recognition length ℓ₀ = c τ₀, and golden ratio φ, from which constants including G are derived self-consistently.
proof idea
This definition is a one-line wrapper that applies the Dimension constructor to the exponents 3, -2, -1.
why it matters
It supplies the dimensional signature required to verify the Planck length √(ℏG/c³), Planck time √(ℏG/c⁵), and Planck mass √(ℏc/G) formulas inside the Recognition Science derivation of G = λ_rec² c³ / (π ℏ). The assignment aligns with the module's goal of obtaining all constants from τ₀, ℓ₀, and φ while respecting D = 3 spatial dimensions.
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