possibility_is_positive_ratio
plain-language theorem explainer
The theorem asserts that every positive real number counts as RS-possible. Modal metaphysicians working on cost-based ontology would cite it when assembling the full PH-013 certificate. The proof is a one-line identity that matches the definition of RSPossible directly.
Claim. For every real number $x$, if $x > 0$ then $x$ is RS-possible, where RS-possible means the configuration possesses positive ratio and therefore finite J-cost.
background
The module PH-013 grounds modal notions in J-cost. Necessity holds only for the unique J-minimizer at $x=1$. Possibility holds precisely when the ratio is positive, which the definition RSPossible encodes as $0 < x$. Upstream cost functions from MultiplicativeRecognizerL4 and ObserverForcing supply the J-cost that makes every positive ratio admissible.
proof idea
The proof is a one-line wrapper that applies the definition of RSPossible, returning the hypothesis $0 < x$ unchanged.
why it matters
This theorem supplies the possibility clause inside the downstream ph013_modal_certificate, which resolves modal logic to J-cost structure. It confirms that all positive configurations remain admissible, consistent with the Recognition Science forcing chain that fixes three spatial dimensions and the phi-ladder for mass assignments.
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