planckTemperature
plain-language theorem explainer
Recognition Science defines the Planck temperature as the ratio of its derived Planck energy to Boltzmann's constant. Physicists modeling black hole thermodynamics or early-universe cosmology cite this when scaling RS quantities to kelvin. The definition is a direct division using the fixed numerical value of k_B = 1.380649 × 10^{-23}.
Claim. $T_P = E_P / k_B$ where $k_B = 1.380649 × 10^{-23}$ J/K and $E_P$ is the Planck energy obtained from the Recognition Science φ-ladder.
background
The module derives Planck quantities from RS principles linking them to the fundamental time scale τ₀ and the golden ratio φ. Standard Planck temperature is T_P = E_P / k_B with E_P = √(ℏ c^5 / G). In RS, these emerge from the forcing chain T5-T8 where J-uniqueness and phi fixed point determine the scales via discrete tiers. Upstream results include structures for J-cost from PhiForcingDerived and spectral emergence forcing gauge groups and generations.
proof idea
The definition is a one-line wrapper that divides the upstream planckEnergy by the numerical Boltzmann constant.
why it matters
It provides the temperature scale required by the Bekenstein-Hawking module for entropy and temperature relations of black holes. This completes part of the QG-009 target to derive Planck scale from φ and τ₀. It interfaces with the Recognition Composition Law and the eight-tick octave for dimensional consistency.
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