planck_mass_rs
plain-language theorem explainer
The definition sets the Planck mass in RS-native units to the square root of the product of the reduced Planck constant and speed of light divided by the gravitational constant. Researchers deriving mass scales from the phi-ladder after the unified forcing chain would cite it to connect coherence energy to gravitational curvature. The definition is a direct algebraic substitution of the pre-derived constants c_rs = 1, ħ_rs = φ^{-5} and G_rs = φ^5.
Claim. In RS-native units the Planck mass is defined by $M_P := √(ℏ_rs ⋅ c_rs / G_rs)$, where $ℏ_rs = φ^{-5}$, $c_rs = 1$ and $G_rs = φ^5$.
background
The module derives the fundamental constants from the Recognition Science foundation via the composition law, J-uniqueness and the phi fixed point. Speed of light c_rs is the ratio of unit length to unit time and equals 1. Gravitational constant G_rs emerges as the curvature extremum and equals φ^5 in native units. Reduced Planck constant ℏ_rs equals φ^{-5} from coherence energy times the fundamental time scale.
proof idea
Direct definition that inserts the already-established expressions for ℏ_rs, c_rs and G_rs into the classical Planck-mass formula and applies the square-root operation.
why it matters
This definition supplies the input mass scale for the downstream theorem planck_mass_eq, which confirms M_P = φ^{-5}. It completes the constant-derivation chain that begins with the composition law and reaches the eight-tick octave and D = 3. The result places the Planck mass at rung -5 on the phi-ladder, consistent with the mass formula yardstick ⋅ φ^(rung - 8 + gap).
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