gravArea
plain-language theorem explainer
GravArea defines the effective area A(a) = 4π(G_N M / a)^2 of the sphere where Newtonian acceleration equals a for mass M. ILG and bandwidth saturation researchers cite it when equating dynamical recognition demand to holographic capacity. The definition is a direct algebraic match to the Newtonian sphere surface.
Claim. The gravitational area is given by $A(a) = 4π (G_N M / a)^2$.
background
The Bandwidth Saturation module derives ILG gravity from recognition throughput limits. When Newtonian dynamics require more recognition events than the holographic bound permits, the system batches updates over 8-tick cycles. GravArea supplies the area term A(a) in the saturation condition that equates demanded rate M / T_dyn to available bandwidth A / (4 ℓ_P² · k_R · 8 τ_0).
proof idea
This is a direct definition. It expands immediately to the product of 4π and the square of the ratio G_N M over a.
why it matters
GravArea anchors the area comparisons in high_accel_newtonian and low_accel_saturated, which establish Newtonian behavior above saturationAccel and ILG activation below it. It supplies the A term in the critical acceleration derivation from the module's saturation condition, connecting to the holographic bound and the eight-tick octave in the Recognition Science forcing chain.
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