IndisputableMonolith.Chemistry.MaillardThresholdFromJCost
This module derives the Maillard threshold in chemical systems from the J-cost function, establishing that below threshold normal hydration equals recognition equilibrium. Chemists applying Recognition Science to reaction thresholds would cite it to link the forcing chain to observable hydration behavior. The module consists of definitions and supporting lemmas that separate equilibrium and positive-defect regimes without a single central theorem.
claimThe Maillard threshold is the J-cost value separating regimes where hydration level $h$ satisfies recognition equilibrium ($J(h)=0$) from regimes where defect distance is positive.
background
Recognition Science measures deviation from self-similarity via the J-cost function $J(x)=(x+x^{-1})/2-1$, introduced in the upstream Cost module. The present module applies this cost to hydration in the Maillard reaction, defining the threshold at which normal hydration coincides with recognition equilibrium. The DOC_COMMENT states the core relation: below threshold, normal hydration equals recognition equilibrium.
proof idea
This is a definition module, no proofs. It introduces the threshold via a collection of sibling definitions and lemmas that establish the equilibrium case below threshold, the positive-defect case above threshold, and symmetry properties.
why it matters in Recognition Science
The module supplies the J-cost foundation for chemical thresholds in Recognition Science and connects directly to the forcing-chain steps T5 (J-uniqueness) and T6 (phi fixed point). It provides the concrete link between the abstract cost function and the Maillard reaction without feeding any downstream theorems in the current graph.
scope and limits
- Does not compute a numerical value for the Maillard threshold.
- Does not incorporate temperature or kinetic effects.
- Does not address specific molecular reactants or products.
- Does not extend the threshold to non-hydration reactions.