IndisputableMonolith.Unification.BandwidthSaturation
The BandwidthSaturation module defines the effective gravitational area A(a) and saturation acceleration in Recognition Science unification. It links the Newtonian sphere of radius GM/a to bandwidth limits set by the phi-ladder and ILG lag. Researchers deriving low-acceleration modifications or holographic gravity bounds cite these objects. The module consists of direct definitions plus elementary positivity and well-definedness statements.
claimThe effective gravitational area is $A(a) = 4π (GM/a)^2 = 4π G^2 M^2 / a^2$, the spherical surface at which Newtonian acceleration equals $a$. Saturation acceleration is the value at which the bandwidth kernel reaches unity under ILG parameters $C_{lag} = φ^{-5}$.
background
Recognition Science sets the fundamental time quantum τ₀ = 1 tick. The upstream RecognitionBandwidth module states the holographic bound (max information proportional to boundary area over 4 Planck areas), recognition cost per bit k_R = ln(φ), and ILG parameters C_lag = φ^{-5}, α = (1−1/φ)/2 together with the 8-tick cadence. This module introduces gravArea as the Newtonian reference area, dynamicalTime, newtonAccel, and saturationAccel as the point where recognition bandwidth saturates the inverse-square law.
proof idea
This is a definition module, no proofs. Definitions are stated directly from the Newtonian sphere condition and the bandwidth kernel supplied by the RecognitionBandwidth import; positivity and well-definedness statements follow by elementary algebra on the phi-ladder quantities.
why it matters in Recognition Science
The module supplies gravArea and saturationAccel that feed the kernel_unity_at_saturation claim and the transition between high-accel Newtonian and low-accel saturated regimes. It fills the concrete gravitational objects required by the RecognitionBandwidth unification step that connects holographic bounds to the eight-tick octave and ILG lag.
scope and limits
- Does not derive G or α from the forcing chain.
- Does not include quantum corrections or Planck-scale effects.
- Does not treat time-dependent or cosmological evolution.
- Does not prove equivalence to general relativity.
depends on (4)
declarations in this module (16)
-
def
gravArea -
theorem
gravArea_pos -
theorem
gravArea_inv_sq -
def
dynamicalTime -
def
newtonAccel -
def
saturationAccel -
theorem
saturationAccel_pos -
theorem
saturationAccel_well_defined -
theorem
high_accel_newtonian -
theorem
low_accel_saturated -
def
bandwidthKernel -
theorem
kernel_unity_at_saturation -
theorem
kernel_gt_one_when_saturated -
theorem
kernel_lt_one_when_sub -
theorem
Clag_is_coherence_quantum -
theorem
alpha_is_bandwidth_exponent