hbar_action_identity
plain-language theorem explainer
The theorem asserts that the reduced Planck constant equals the product of coherence energy and the fundamental tick duration in RS-native units. Researchers deriving quantum constants from the Recognition Science forcing chain would cite this identity when linking minimal action to recognition events. The proof is a direct reflexivity step that follows immediately from the definitions of hbar and E_coh.
Claim. In Recognition Science units the reduced Planck constant satisfies $ħ = E_{coh} τ_0$, where $E_{coh} = φ^{-5}$ is the coherence energy and $τ_0$ is the duration of one fundamental tick.
background
Recognition Science works in native units with $c=1$ and derives constants from the J-function and phi-ladder. The coherence energy $E_{coh}$ is the lock constant $C_{lock}=φ^{-5}$. The time quantum $τ_0$ equals one tick and is set to 1. The module defines ħ directly as that product, consistent with upstream definitions of tau0 as the tick duration and hbar as $E_{coh}·τ_0$. The PrimitiveDistinction result supplies the axiomatic base from seven axioms to four structural conditions plus definitional facts.
proof idea
The proof is a one-line reflexivity step. It applies the definition of hbar directly equaling $E_{coh}$ times tau0, with no additional lemmas or tactics required beyond the prior definitions of those quantities.
why it matters
This fills THEOREM C-004.4, supplying the action quantum identity that interprets ħ as the minimal energy-time product for a recognition event. It anchors the phi-ladder constants (E_coh = φ^{-5}) and supports later derivations of alpha and mass formulas in the forcing chain. No open questions are directly closed here, but the identity completes the native-unit definition of ħ.
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