possibility_status
plain-language theorem explainer
The definition supplies a status report string summarizing the grammar of possibility in Recognition Science modal logic, with P(c) as the set of finite-cost reachable configurations and modal operators box and diamond. Logicians working on RS modal interpretations cite it for an overview of J-stasis, actualization, and identity fixed-point results. The implementation is a direct string literal definition with no lemmas or reductions.
Claim. The status report for the grammar of possibility is the string constant containing the summary of core concepts: $P(c)$ as the set of configurations $y$ reachable from $c$ with finite transition cost under $J$, the operators $□p$ (necessary) and $◇p$ (possible), and theorems on identity preferring stasis together with cost-decreasing actualization.
background
The module introduces the possibility operator on configurations. From the referenced definition, Possibility(c) collects those y where y.time equals c.time plus one octave step and the combined J-cost of the transition plus J(y) does not exceed the stasis cost from c. This rests on the J function, J-transition, and J-stasis already available in the foundation layer. Upstream results supply auxiliary lists such as the seven narrative plot families and the eight kinship systems, which supply concrete examples of reachable configurations in the modal setting.
proof idea
The definition is a direct string literal assembled by concatenation of fixed lines. No lemmas are invoked and no tactics are used; the body simply returns the pre-written ASCII report.
why it matters
The definition supplies a compact human-readable anchor for the modal layer built on the possibility operator and J-cost minimization. It records the foundation-complete status for the grammar of possibility and references the identity fixed-point and actualization results that descend from the forcing chain. With zero downstream uses it functions purely as documentation rather than a theorem node.
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