k_B
plain-language theorem explainer
Boltzmann constant k_B is fixed at its exact SI value 1.380649 × 10^{-23} J/K. Researchers deriving Bekenstein-Hawking entropy or Hawking temperature from Recognition Science ledger capacity cite this anchor to link information measures to thermodynamic quantities. The definition is a direct numerical assignment with no further reduction steps.
Claim. $k_B = 1.380649 × 10^{-23}$ J/K
background
Module Quantum.BekensteinHawking targets QG-001 and QG-002: black hole thermodynamics from Recognition Science. Core results state S_BH = k_B A / (4 l_P²) with entropy proportional to horizon area, and T_H = ℏ c³ / (8π G M k_B). The constant supplies the conversion between ledger information capacity and thermodynamic entropy. Upstream anchors include G from Constants (G = λ_rec² c³ / (π ℏ)) and the identical k_B in ComputationLimitsStructure whose doc notes the Landauer energy k_B T ln(2) as minimum erasure cost.
proof idea
Direct definition that assigns the SI numerical value 1.380649e-23 to the real number k_B.
why it matters
The definition anchors the entropy formula S_BH = k_B A / (4 l_P²) in the module and feeds downstream results such as thermal_energy_at_unit_T (E_thermal = k_R at unit temperature) and room-temperature superconductivity certificates. It realizes the module claim that horizon area measures ledger capacity and supports the holographic bound. The placement closes the interface between RS-native constants and SI anchors for black-hole thermodynamics.
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