module module high

`IndisputableMonolith.Unification.BlackHoleBandwidth`

This module defines black hole quantities in Recognition Science native units, starting from the Schwarzschild radius r_s = 2M and extending to horizon area, entropy, and bandwidth. Researchers unifying holographic bounds with RS cost functions would cite these definitions. It assembles direct translations of classical expressions using imported constants, cost, and recognition bandwidth primitives.

claim$r_s = 2M$ (Schwarzschild radius); horizon area $A = 4π r_s^2$; entropy $S = A/4$ in RS units; horizon bandwidth and demand derived from $k_R = ln(φ)$ and the 8-tick cadence.

background

The module imports Constants (τ₀ = 1 tick as fundamental RS time quantum), BoltzmannConstant (k_R derived from ledger bit cost), Cost (J-cost framework), and RecognitionBandwidth. The latter states: holographic bound (max information ∝ boundary area / (4 Planck areas)), recognition cost per bit k_R = ln(φ), ILG parameters C_lag = φ^{-5}, and 8-tick cadence where R̂ completes one cycle per 8τ₀. These supply the setting for black-hole extensions in RS-native units.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

Supplies the black-hole bandwidth layer that extends RecognitionBandwidth to gravitational horizons, linking the holographic bound and k_R = ln(φ) to classical expressions. It fills the unification step connecting area-law entropy to the recognition cost ledger, consistent with T7 eight-tick octave and D = 3 spatial dimensions from the forcing chain.

scope and limits

Does not derive the area law from RS axioms.
Does not treat Kerr or charged black holes.
Does not include quantum corrections or evaporation.
Does not compute numerical values beyond symbolic definitions.

depends on (4)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Constants.BoltzmannConstant module_import
IndisputableMonolith.Cost module_import
IndisputableMonolith.Unification.RecognitionBandwidth module_import

declarations in this module (19)

def schwarzschildRadius L48
def horizonArea L51
theorem horizonArea_pos L53
def bhEntropy L58
theorem bhEntropy_eq L60
theorem bhEntropy_pos L64
def horizonBandwidth L71
theorem horizonBandwidth_pos L74
def horizonDemand L85
theorem horizonDemand_eq L88
theorem horizonDemand_universal L95
def saturationRatio L112
theorem saturationRatio_pos L117
def hawkingTemp L133
theorem hawkingTemp_pos L135
theorem hawkingTemp_inv_mass L140
theorem hawking_contains_eight_tick L154
def excessBandwidth L170
theorem entropy_is_bandwidth_capacity L175