horizonBandwidth
plain-language theorem explainer
horizonBandwidth defines the maximum recognition bandwidth at a Schwarzschild black hole horizon of mass M as Bekenstein-Hawking entropy divided by the product of the recognition Boltzmann constant and the eight-tick cadence. Researchers deriving black hole thermodynamics from holographic information bounds or Recognition Science saturation arguments would cite this when equating area to processing capacity. It is a direct algebraic definition that combines the entropy expression with the fixed recognition cycle constants.
Claim. The recognition bandwidth at the horizon of a black hole with mass $M$ is $R_h(M) = S_{BH}(M) / (k_R · 8τ_0)$, where $S_{BH}(M) = 4πM^2$ is the Bekenstein-Hawking entropy, $k_R = ln φ$ is the recognition Boltzmann constant, and $8τ_0$ is the duration of one full recognition cycle.
background
The module frames black holes as the limiting case of maximal recognition saturation, where every holographic bit at the horizon is consumed by gravitational dynamics. Relevant definitions include the recognition Boltzmann constant $k_R = ln φ$, the fundamental cost per ledger bit, and the eight-tick cadence $8τ_0$, the minimum time to complete one recognition event. The Bekenstein-Hawking entropy is given by $bhEntropy M = horizonArea M / 4 = 4πM^2$ in natural units with Planck length set to 1.
proof idea
This is a one-line definition that divides the black hole entropy by the product of the Boltzmann constant and the eight-tick cadence.
why it matters
This definition supplies the bandwidth capacity used in downstream results such as entropy_is_bandwidth_capacity, which equates entropy directly to bandwidth times processing time, and excessBandwidth, which formalizes the no-hair theorem via zero excess capacity. It realizes the module claim that black holes achieve maximal saturation, linking to the eight-tick octave (T7) and explaining Hawking temperature and information conservation. It closes the loop from area to entropy to bandwidth within the Recognition Science framework.
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