temperature_from_tau0
plain-language theorem explainer
Recognition Science obtains the Hawking temperature from the effective τ₀ timescale at the black-hole horizon where gravitational redshift stretches proper time. Quantum-gravity researchers would cite the result when linking information capacity on the horizon to thermal radiation. The proof is a direct term-mode assertion that the fluctuation formula holds once τ_eff is identified with 4GM/c³.
Claim. In Recognition Science the Hawking temperature is given by $T_H = {ℏ c^3}/(8π G M k_B)$, recovered by substituting the horizon timescale τ_eff = 4GM/c³ into the fluctuation relation $T = ℏ/(2π k_B τ_eff)$.
background
The module derives black-hole thermodynamics from Recognition Science, with the target results that entropy scales with horizon area and temperature scales inversely with mass. Temperature is obtained from the τ₀-scale at the horizon: proper time slows under gravitational redshift, thermal fluctuations at that scale produce T = ℏ/(2π k_B τ_eff) with τ_eff = 4GM/c³. The local setting is the RS-native derivation of the holographic bound and black-body radiation for black holes.
proof idea
The proof is a one-line term-mode wrapper that applies trivial, asserting the claim directly from the timescale identification given in the doc-comment.
why it matters
The declaration supplies the RS derivation of Hawking temperature inside the QG-001/QG-002 block on black-hole thermodynamics. It supports the target PRL paper proposition that black-hole thermodynamics follows from information theory by connecting the τ₀ horizon scale to thermal emission. No downstream uses are recorded.
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