free_energy_monotone_status
plain-language theorem explainer
The free_energy_monotone_status definition assembles a hardcoded list of proof statuses for the Recognition Science free energy monotonicity results. A researcher tracking the RS analogue of the Second Law consults this list to distinguish fully proven components from those still scaffolded. The definition is a direct list literal that records the current status of push-forward preservation, partition function, data processing inequality, coarse-graining decrease, and the H-theorem.
Claim. The status of free energy monotonicity is the list pairing each component with its status: push-forward preservation of probability as theorem, partition function preservation as scaffold, data processing inequality as scaffold, coarse-graining decrease of free energy as scaffold, and recognition H-theorem as proven.
background
The module proves that Recognition Free Energy is non-increasing under coarse-graining and equilibration, forming the Recognition Science version of the Second Law. Upstream results include the data processing inequality (coarse-graining reduces distinguishability of distributions via log-sum inequality on fibers) and the H-theorem (free energy decreases monotonically toward the Gibbs measure via the variational identity F_R(p) = F_R(Gibbs) + TR * D_KL(p || Gibbs)). The definition also references the push-forward and partition function constructions from the same module.
proof idea
This is a definition that constructs a list literal of status pairs. It directly enumerates the five items without invoking tactics or lemmas beyond the sibling declarations already present in the module.
why it matters
This definition tracks completion of the thermodynamic stability results that realize the Second Law analogue in the Recognition framework. It surfaces the main results listed in the module documentation (coarse-graining decrease, relaxation decrease, arrow of time) and highlights which components remain scaffolded. No downstream uses exist yet; the list serves as an internal progress marker for the monotonicity chain.
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