IndisputableMonolith.Unification.BlackHoleBandwidth
The module supplies black-hole quantities in RS-native units for the Recognition Science unification. It defines the Schwarzschild radius, horizon area, entropy, bandwidth, and demand using the recognition cost per bit. Physicists studying holographic bounds or black-hole thermodynamics would cite these definitions. The module consists of direct definitions and elementary positivity lemmas with no complex proofs.
claimIn RS-native units the Schwarzschild radius is $r_s=2M$. Horizon area is $A=4\pi r_s^2$. Entropy is $S=A/(4\ln\phi)$ with recognition cost $k_R=\ln\phi$. Horizon bandwidth and demand are expressed via the holographic bound and 8-tick cadence.
background
Recognition Science derives all physics from the J-cost functional and Recognition Composition Law. Upstream Constants fix the time quantum $\tau_0=1$ tick. BoltzmannConstant derives the ledger bit cost $k_R=\ln\phi$ from the fundamental recognition cost. RecognitionBandwidth connects the holographic bound (maximum information proportional to boundary area over four Planck areas) to the ILG parameters $C_{\rm lag}=\phi^{-5}$ and the 8-tick octave.
The module imports these four modules and sits inside the Unification domain. It translates black-hole geometry into ledger terms using the same recognition cost that appears in the holographic bound.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the black-hole bandwidth and demand functions that complete the holographic sector of the Recognition Science unification. It realizes the area-law entropy using the recognition cost $k_R=\ln\phi$ supplied by the upstream RecognitionBandwidth module. The definitions stand ready for downstream saturationRatio calculations that close the information-gravity loop.
scope and limits
- Does not derive the area law from the J-functional.
- Does not compute numerical values for astrophysical black holes.
- Does not include quantum corrections or higher-curvature terms.
- Does not connect to the phi-ladder mass formula or T5-T8 forcing chain.
depends on (4)
declarations in this module (19)
-
def
schwarzschildRadius -
def
horizonArea -
theorem
horizonArea_pos -
def
bhEntropy -
theorem
bhEntropy_eq -
theorem
bhEntropy_pos -
def
horizonBandwidth -
theorem
horizonBandwidth_pos -
def
horizonDemand -
theorem
horizonDemand_eq -
theorem
horizonDemand_universal -
def
saturationRatio -
theorem
saturationRatio_pos -
def
hawkingTemp -
theorem
hawkingTemp_pos -
theorem
hawkingTemp_inv_mass -
theorem
hawking_contains_eight_tick -
def
excessBandwidth -
theorem
entropy_is_bandwidth_capacity