BoltzmannFalsifier
plain-language theorem explainer
A record structure that packages a concrete experimental counterexample to the J-cost derivation of the Boltzmann distribution. A physicist auditing the Recognition Science thermodynamics module would cite it when measured probability ratios deviate by more than 10% from the predicted exp(-β ΔE) form. The definition is a plain four-field structure whose only content is the explicit deviation inequality.
Claim. A falsifying instance consists of a system label $s$, measured ratio $r_m$, predicted ratio $r_p = e^{-β ΔE}$, and the predicate $|r_m - r_p|/r_p > 0.1$.
background
The module derives the Boltzmann distribution $P_i = e^{-β E_i}/Z$ from Recognition Science's J-cost functional, treating lower J-cost states as more probable under a fixed total-cost constraint. Temperature appears as the Lagrange multiplier conjugate to the cost constraint, and entropy maximization follows from counting microstates at fixed J-cost. Upstream, probability is taken from the Born-rule definition in QuantumLedger and the transition-probability definition in SMatrixUnitarity; both supply non-negative real values that the present structure compares against the exponential form.
proof idea
This is a structure definition with no proof body; it simply declares four fields and embeds the deviation inequality as a field proposition.
why it matters
The structure supplies the concrete falsification interface required by the module's target claim that the Boltzmann form emerges from J-cost minimization. It directly addresses the paper proposition on statistical mechanics from Recognition Science and leaves open the empirical question of whether any physical system meets the 10% deviation threshold.
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