propensity_vindicated
plain-language theorem explainer
The theorem establishes that the J-cost defect vanishes at unity and remains nonnegative for all positive reals, supplying an observer-independent landscape that grounds the propensity reading of probability. Researchers resolving quantum interpretations via deterministic projections would cite this when separating objective tendency from epistemic uncertainty. The proof is a direct term construction that pairs the specialized defect_at_one lemma with a lambda applying defect_nonneg.
Claim. The J-cost defect function of the Law of Existence satisfies $defect(1)=0$ and, for every positive real $x$, $defect(x)geq 0$.
background
The ProbabilityMeaningStructure module resolves the four classical interpretations of probability by equating them to J-cost projection weights on a deterministic ledger. Reality evolves by unique J-minimization at each step; finite-resolution observers see only the coarse-grained fibers of the projection map, so probability is epistemic. The propensity interpretation holds when the underlying J-cost landscape itself is objective and independent of any observer.
proof idea
The proof is a term-mode pair that invokes the lemma defect_at_one to obtain the equality at 1 and wraps defect_nonneg inside a lambda to obtain the universal nonnegativity claim for positive reals.
why it matters
This result completes the propensity branch of the PH-006 unification inside the module. It shows that the J-cost structure supplies an objective tendency, feeding the later claim that the Born rule emerges from fiber-weighted measures rather than as an extra postulate. The theorem therefore anchors the framework statement that probability equals J-cost projection weight while remaining fully compatible with the deterministic T0-T8 chain.
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