Lhbar0
plain-language theorem explainer
Loosest admissibility class for candidate action-quantum values: every real number is allowed. Anyone comparing unconstrained versus RS-native ħ cites this as the baseline carrier before gate-tightening. The body is a one-line structure instance setting the admissible set to the universe.
Claim. The loosest action-quantum admissibility class on $\mathbb{R}$ takes every real $h$ as admissible (the universal set), with label ``every candidate action-quantum value''.
background
In the maximal-forcing layer for the RS-native action quantum, a realization is a candidate real $h$ standing for a reduced Planck constant in the native gauge $\lambda_{\mathrm{rec}}=c=1$, tick $\tau_0$. An admissibility class is a named subset of such realizations: a set of allowed $h$ plus a string label.
This module is the sixth single-constant instantiation and reaches the quantum sector. The RS-native value is the parameter-free $\hbar=\varphi^{-5}$ (proved elsewhere as Constants.hbar_eq_phi_inv_fifth). The loose class admits every real; the gate class later pins $h$ exactly to that native $\hbar$.
Together with the native gravity coupling $\kappa=8\varphi^5$ and the $\alpha$ window, this is one of three native/dimensionless $\varphi$-expression surfaces: action normalization, gravitational coupling, and electromagnetic coupling.
proof idea
Definitional structure instance of AdmissibilityClass ℝ: the admissible field is Set.univ (every real), and the label is the fixed string naming the unconstrained candidate pool. No proof obligations beyond inhabiting the structure.
why it matters
Baseline of the action-quantum forcing sandwich. Downstream, the gate class restricts to ${h\mid h=\hbar}$, and the tightening map records that every gate-admissible value was already loose-admissible. Independence of the claim $h=\varphi^{-5}$ over the loose class is witnessed by $\hbar$ (satisfies) versus $0$ (fails, since $\varphi^{-5}>0$). Over the gate class the same claim is forced by wrapping the proved native identity. The effective-tightening theorem packages both sides: independent on the loose class, forced on the gate. This is the native action-normalization boundary, not an SI derivation of Planck's constant.
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