IndisputableMonolith.Physics.PlanckConstantFromRS
The module Physics.PlanckConstantFromRS fixes the coherence exponent at k=5 to produce explicit RS-native expressions for ħ and G. Physicists tracing constants from the J-function and phi-ladder cite these definitions when converting between RS units and laboratory values. The module is a short sequence of definitions and positivity statements that import the time quantum τ₀ from Constants and specialize the scaling.
claimThe module sets the coherence exponent $k=5$, yielding $\hbar_{RS}=\phi^{-5}$, $G_{RS}=\phi^5/\pi$, and the Einstein relation in RS-native units with $c=1$ and $\tau_0=1$.
background
Recognition Science obtains all constants from the J-cost functional equation and the self-similar fixed point phi. The upstream Constants module supplies the base time quantum $\tau_0=1$ tick. This module specializes the coherence exponent to the integer value 5, which places ħ on the phi-ladder at rung -5 and G at rung +5, consistent with the eight-tick octave and D=3 geometry.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the explicit constants ħ_RS and G_RS that enter the mass formula yardstick * phi^(rung-8+gap(Z)) and the alpha band (137.030,137.039). It realizes the T5 J-uniqueness step by fixing k=5, providing the numerical anchors used in downstream derivations of physical relations such as the Einstein relation.
scope and limits
- Does not derive the integer value k=5 from the J-equation.
- Does not include numerical conversion factors to SI units.
- Does not address higher-order corrections beyond the phi-ladder.
- Does not prove uniqueness of the exponent choice.