Jcost_second_deriv_positive
plain-language theorem explainer
The theorem establishes that the second derivative of the J-cost equals x to the negative third power and is strictly positive for every positive real x. Researchers resolving determinism via unique minimizers in constrained ledger updates would cite this convexity fact. The proof is a direct one-line application of the positivity tactic to the explicit term x^{-3}.
Claim. For every real number $x > 0$, the second derivative of the J-cost satisfies $J''(x) = x^{-3} > 0$.
background
The module formalizes the resolution of determinism versus apparent randomness. The J-cost function is strictly convex on $(0, ∞)$, so every constrained optimization (ledger update) possesses a unique minimizer; the next state is therefore uniquely determined by the current state. Finite-resolution observers see only a lossy projection of this deterministic process, which appears random, and the Born rule emerges as the projection of the J-cost landscape onto that resolution.
proof idea
The proof is a one-line wrapper that applies the positivity tactic directly to the term $x^{-3}$.
why it matters
This supplies the strict-convexity ingredient for the unique-minimizer principle inside the determinism argument (F-007). It anchors the claim that deterministic J-cost minimization produces a unique actualized configuration, with apparent randomness arising only from observer projection. The result sits upstream of the unique_minimizer_principle sibling and supports the overall chain from strict convexity to Born-rule emergence.
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