inevitability_holds
plain-language theorem explainer
The theorem establishes that the concrete inevitability structure is inhabited by exhibiting explicit witnesses for phi uniqueness, defect characterization, and finite costs. Researchers formalizing the no-alternatives claim in Recognition Science would cite this to confirm that the J-cost framework admits a zero-parameter realization. The proof is a direct term construction that packages three prior lemmas into the required structure.
Claim. There exists a structure satisfying: a unique positive real solution to $x^2 = x + 1$, the condition that defect vanishes if and only if the argument equals 1 for all positive reals, and the property that every real cost bound is exceeded by the defect function near zero.
background
The module bridges abstract inevitability slogans such as zero-parameter and no-alternatives with concrete CPM and cost definitions. ConcreteInevitability is the structure whose fields are phi uniqueness, the defect characterization defect(x) = 0 iff x = 1 for x > 0, and the nothing-infinite condition that rules out infinite costs. The upstream inevitability theorem states that any alternative zero-parameter framework deriving observables must either match the RS cost and selection or violate at least one necessity gate.
proof idea
The proof is a term-mode construction that directly supplies the structure. It invokes the phi uniqueness lemma for the first field, the defect-zero equivalence for the second field, and the lemma that nothing can have infinite cost for the third field.
why it matters
This declaration makes the abstract-to-concrete equivalence concrete, supporting the core RS inevitability claim that alternatives either reduce to the same cost structure or violate a gate. It realizes the T5 J-uniqueness and T6 phi fixed-point steps of the forcing chain inside a single inhabited structure. The module doc-comment notes that the equivalence links INEV_DIMLESS and INEV_ABSOLUTE to specific J-minima and single-calibration conditions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.