planck_mass_temperature
plain-language theorem explainer
Planck-mass black holes exhibit Hawking temperatures approximating the Planck temperature under Recognition Science. Quantum gravity researchers would cite this when aligning RS scales with standard Planck units. The proof is a one-line wrapper that applies the trivial tactic.
Claim. For a black hole of mass equal to the Planck mass $m_P$, the Hawking temperature satisfies $T_H(m_P) ≈ T_P$.
background
The module derives black hole thermodynamics from Recognition Science by equating horizon area to ledger information capacity and temperature to the effective τ₀ timescale at the horizon. Core targets are the Bekenstein-Hawking entropy S_BH = k_B A / (4 l_P²) and the temperature T_H = ℏ c³ / (8π G M k_B). Upstream structures supply phi-tier nuclear densities from NucleosynthesisTiers.of and fundamental periods from Breath1024.T.
proof idea
The proof is a term proof consisting of the trivial tactic applied directly to the statement of approximate equality.
why it matters
This fills the Planck-mass case in the QG-001 and QG-002 derivation of black hole thermodynamics from information theory. It aligns with the phi-ladder mass formula and constants such as ħ = φ^{-5}. No downstream uses are recorded.
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