hawkingTemp
plain-language theorem explainer
The definition supplies the Hawking temperature T_H(M) = 1/(8πM) for a Schwarzschild black hole of mass M in natural units. Researchers in quantum gravity and black hole thermodynamics cite it when linking the classical formula to the eight-tick recognition cycle. It is introduced as a direct one-line assignment that embeds the 8-tick cadence from the recognition operator into the standard expression.
Claim. The Hawking temperature of a Schwarzschild black hole with mass $M$ is $T_H(M) = 1/(8 π M)$.
background
In the Black Hole Bandwidth module a black hole is the limiting case of maximal recognition saturation where the recognition operator is fully occupied at every scale. Horizon area is $A = 16π M^2$ and Bekenstein-Hawking entropy is $S_{BH} = 4π M^2$; recognition bandwidth at the horizon is then $R_{max} = S_{BH}/(k_R · 8 τ_0)$. The module states that the factor 8π contains the eight-tick cadence and that T_H is the recognition clock rate of the horizon.
proof idea
One-line definition that directly assigns the classical Hawking temperature formula, with the numerical factor 8 reinterpreted via the eight-tick cadence from upstream Recognition.Cycle3.M.
why it matters
This definition anchors the Hawking temperature inside the Recognition Science framework and is used by hawking_contains_eight_tick, which shows the 8 encodes the eight-tick cadence (T7). It supports the module claim that T_H is the recognition clock rate set by the 8-tick cadence divided by the horizon geometric scale, connecting to the eight-tick octave and the geometric π factor. It leaves open the question of deriving the temperature purely from bandwidth saturation without adopting the classical expression.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.