hbar_positive
plain-language theorem explainer
The theorem establishes that the reduced Planck constant ħ in RS-native units is strictly positive. Researchers modeling quantum dynamics or information bounds in the Recognition Science framework would cite it to guarantee that the action quantum supports positive energies and forward time evolution. The proof is a one-line wrapper that directly invokes the positivity lemma for ħ expressed as φ^{-5}.
Claim. $0 < ħ$ where $ħ = φ^{-5}$ in RS-native units with $c = 1$ and $τ_0 = 1$ tick.
background
The Constants module defines the reduced Planck constant as ħ = cLagLock · τ₀ with τ₀ the fundamental RS time quantum equal to one tick. The upstream lemma hbar_pos proves 0 < ħ by applying mul_pos to the positivity of cLagLock and tau0, which rests on φ > 1. This local setting treats ħ as the RS-native action quantum required for quantum dynamics.
proof idea
This is a one-line wrapper that applies the hbar_pos lemma from the same module.
why it matters
It corresponds to THEOREM C-004.2, ensuring positivity of the action quantum for quantum dynamics in the Recognition Science constants chain. The result follows from the phi-ladder where φ > 1 forces ħ = φ^{-5} > 0 and aligns with the eight-tick octave and D = 3 structure. No direct downstream uses are recorded, leaving open whether it will be invoked in information or mechanism-design modules.
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