Stable Transfer Geometry of the Substituted Chrysene Network: H-Infinity Transformation Metrics, Dissipative Well-Posedness, and Survival Under Persistent Disturbance

Abstract

We construct a family of distances on the admissible domain of the Chrysene Formalism and determine which metric axioms each satisfies. The central object is the unitary-orbit H-infinity distance between the transfer realizations of two structural forms, together with its path closure over admissible transformations; it is an extended pseudometric, and its zero set is exactly the relation of transfer isomorphism, which is shown to be logically independent of isomorphism of the underlying molecular graphs. The construction requires a well-posedness result: the worst-case norm of a transfer operator built from the directional Hamiltonian is generically infinite, and we prove that it is finite precisely when the active region carries no mode that is energetically embedded in the continuum of a second fibration yet orthogonal to every channel into it. The dissipation making this possible is not postulated but computed, as the coupling-weighted density of states of that fibration, and the norm it removes from the admissible sector is shown to be transferred rather than destroyed. Two statements follow: a radius within which a form may be transformed and remain robustly stable, and a common-storage condition under which arbitrary admissible switching among forms preserves a uniform gain bound. Frozen-form stability is shown by counterexample not to imply the latter. The choice of the worst-case over the mean-square norm is justified by four independent arguments, including an explicit resonance family inside the axioms' own data; a self-adjoint perturbation class for which the worst-case norm is instead the wrong measure is identified, and an exact margin supplied for it. Invariance of the admissible domain is shown to be a peak-gain statement not controlled by the worst-case norm, so that survival, the conjunction of robust stability with that invariance, is certified here in two separate halves and by no single certificate. An explicit witness realization with closed-form values is given, the formalism's own explicit model being shown to have infinite gain. Fourteen non-implications, twelve new deferred targets, a concordance table recording five corrections to the prior corpus, and a self-identified defect ledger are stated.