newtonAccel
plain-language theorem explainer
Newtonian gravitational acceleration is defined by the classical inverse-square expression a = G_N M / r². Researchers deriving the saturation threshold a_sat in Recognition Science cite this when comparing demanded recognition rate against holographic bandwidth. The definition is a direct algebraic transcription with no lemmas or reductions.
Claim. Newtonian acceleration at distance $r$ from central mass $M$ is given by $a = G_N M / r^2$.
background
The Bandwidth Saturation module shows how recognition throughput limits force the ILG kernel to activate below a critical acceleration. Newtonian acceleration supplies the high-acceleration reference used to compute dynamical time T_dyn = 2πr/v and gravitational area A = 4π(2GM/a)². Upstream constants include the RS-native G derived from lambda_rec and k_R = ln φ, the cost per ledger bit that sets the holographic bound.
proof idea
The definition is a one-line algebraic expression that directly transcribes the inverse-square law: G_N * M / r ^ 2. No tactics or lemmas are applied; it serves as the explicit high-acceleration limit in the saturation condition.
why it matters
This definition anchors the Newtonian regime inside the ILG emergence argument. It feeds the saturation condition where demanded rate equals bandwidth, leading to the ILG time kernel w_t > 1 for a < a_sat. It connects directly to the eight-tick octave and phi-forcing chain by providing the classical limit that the recognition operator must recover above saturation.
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