economic_inevitability_statement
plain-language theorem explainer
This definition supplies the economic phrasing of inevitability in Recognition Science by equating existence to stable minimization under a unique coercive cost. Researchers deriving physics from cost foundations cite it when contrasting RS against zero-parameter alternatives. The declaration assembles the statement through direct string concatenation with no lemma applications or computational steps.
Claim. Existence equals the stable minimizer of coercive aggregation under the unique cost function $J$, where $J(0^+)=∞$ and $J(1)=0$. All physical laws arise from this minimization rather than from external decree.
background
The module formalizes inevitability structure under the CPM/cost foundation, relocating degrees of freedom so that selection occurs by minimizing a unique cost. Key definitions include the cost function $J$ (uniquely fixed by symmetry, convexity, and normalization as $J(x)=½(x+x^{-1})-1$) and the selection rule that existence holds when defect approaches zero under coercive projection. Upstream results supply the inevitability theorem: any alternative zero-parameter framework deriving observables must reduce to the RS cost and selection or violate at least one necessity gate.
proof idea
The declaration is a direct definition that concatenates four sentences into a single string. No lemmas or tactics are invoked; the body simply assembles the economic phrasing of the core insight.
why it matters
This definition supplies the economic phrasing for the inevitability theorem, which asserts that alternatives must violate a necessity gate such as cost uniqueness (T5) or the selection rule. It anchors the framework claim that selection happens by minimizing unique $J$ and connects to the eight-tick octave and $D=3$ derivations downstream. The statement touches the open question of whether every zero-parameter framework reduces to RS.
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