module module moderate

`IndisputableMonolith.Unification.BandwidthSaturation`

This module defines the effective gravitational area A(a) together with saturation acceleration and bandwidth kernel objects that link Newtonian gravity to recognition bandwidth limits. Unification researchers modeling low-acceleration deviations or holographic information bounds would cite these objects. The module is a collection of definitions and elementary positivity statements.

claimThe effective gravitational area is $A(a) = 4π (GM/a)^2$. Saturation acceleration is the scale at which recognition bandwidth reaches its holographic limit; the bandwidth kernel is unity at saturation.

background

The module sits inside the Unification domain and imports the RecognitionBandwidth framework. That framework states the holographic bound (maximum information proportional to boundary area over four Planck areas), the recognition cost per bit $k_R = ln φ$, the ILG parameters $C_{lag} = φ^{-5}$ and $α = (1-1/φ)/2$, and the eight-tick cadence. The Constants module supplies the RS time quantum $τ_0 = 1$ tick; the Cost module supplies the underlying J-cost structure.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The definitions supply the acceleration-dependent area and dynamical-time objects required to implement ILG modifications at long times, extending the five core elements listed in the RecognitionBandwidth module. They prepare the saturation threshold that later unification statements use to recover Newtonian behavior above a critical acceleration.

scope and limits

Does not derive G or α from the forcing chain.
Does not treat multi-body or relativistic regimes.
Does not compute explicit numerical saturation thresholds.
Does not address quantum corrections to the area formula.

depends on (4)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Constants.ILG module_import
IndisputableMonolith.Cost module_import
IndisputableMonolith.Unification.RecognitionBandwidth module_import

declarations in this module (16)

def gravArea L49
theorem gravArea_pos L52
theorem gravArea_inv_sq L60
def dynamicalTime L69
def newtonAccel L73
def saturationAccel L90
theorem saturationAccel_pos L93
theorem saturationAccel_well_defined L98
theorem high_accel_newtonian L108
theorem low_accel_saturated L129
def bandwidthKernel L151
theorem kernel_unity_at_saturation L155
theorem kernel_gt_one_when_saturated L161
theorem kernel_lt_one_when_sub L168
theorem Clag_is_coherence_quantum L181
theorem alpha_is_bandwidth_exponent L190