Information-Theoretic Mechanics of Survival in Maximum-Entropy Environments Static Minimax Disturbance Attenuation, Coordination-Deficit Costs, and the Placed Source as Categorical Right Adjoint

Abstract

We formulate a finite coordination between endogenous supply and exogenous registry preparation in the substituted-chrysene framework. A binomial slack count identifies the uniform $l$-site registry with $2^{l-1}$ states, while a dimensionless coordination-deficit comparison distinguishes unequal-inventory lattice costs from a physical free-energy minimization. For two explicit 18-carbon graphs, perfect-matching counts and one-orbital spectra give a zero-field chrysene--tetracene gap comparison; a perturbation-norm condition supplies a sufficient bounded-field extension. Independent Gibbs contacts define the coefficients of an explicit static disturbance surrogate. Its induced $L^2$ gain is minimized by equal allocation of a fixed total energy-splitting budget. Finite bias leaves positive entropy and full registry support. A reverse-inclusion category of supports containing a chosen target admits a natural adjunction with the discrete category of pointed species words, with identity monad; thermodynamic work bounds require a separate cyclic isothermal implementation. A three-component indicator functional characterizes feasible sequence, boundary and scaffold configurations without asserting a unique morphology. Finally, under a specified radius law, fixed scaffold and quaternary boundary alphabet, we prove a surface-capacity inequality for every integer $L\ge233$ and derive its asymptotic utilization. At $L=233$, the model compares $682$ interior bits with $4{,}754$ boundary bits. The resulting capacity budget is distinct from a gravitational entropy bound. The mathematical results are accompanied by reproducible verification and explicitly scoped Lean certificates, with molecular realization expressed through experimentally testable conditions.