`excessBandwidth`

definition

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module: IndisputableMonolith.Unification.BlackHoleBandwidth
domain: Unification
line: 170 · github
papers citing: none yet

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IndisputableMonolith.Unification.BlackHoleBandwidth on GitHub at line 170.

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formal source

 167
 168    Formalized: excess bandwidth (budget - demand) determines the maximum
 169    complexity (number of distinguishable features) a horizon can support. -/
 170noncomputable def excessBandwidth (M : ℝ) : ℝ :=
 171  horizonBandwidth M - horizonDemand M
 172
 173/-- The entropy of a BH is exactly its holographic bandwidth capacity,
 174    confirming that area = information = bandwidth. -/
 175theorem entropy_is_bandwidth_capacity {M : ℝ} (hM : 0 < M) :
 176    bhEntropy M = horizonBandwidth M * (k_R * eightTickCadence) := by
 177  unfold horizonBandwidth
 178  have h : 0 < k_R * eightTickCadence := mul_pos k_R_pos eightTickCadence_pos
 179  rw [div_mul_cancel₀ _ (ne_of_gt h)]
 180
 181end BlackHoleBandwidth
 182end Unification
 183end IndisputableMonolith

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