The Source Duality: Endogenous and Exogenous Preparation of the Substituted-Chrysene Stock, Mixed Arm Words, and the Persistence Semigroup

Abstract

In a source-supported product-column model, endogenous self-separation and exogenous placement supply the same substituted-chrysene configurations but control different aspects of their specification. We formulate a parameterized source measure separating chemical species, directional code, and contact registry. On the all-$e$ locus without adjacent initiator pairs, the selection cost splits additively and its kinetic and registry cross-sensitivities vanish; a blind column of length $l$ retains a registry cost of $l-1$ bits. We classify mixed arm words under partial arm conversion and show that homotypic $D(eh)$ contacts can be orientation-selective, whereas accepted $D(eh)$–$T(eeee)$ contacts and $I(eee)$–$D(eh)$ cap contacts remain blind. For the $3\times3\times6$ interior lattice, all 45 stacking contacts are blind before lateral closure, while the fully bridged central column has no free terminals and remains blind under the stated contact model. We distinguish these 45 vertical relations from 53 agreements when eight inter-column relations are added. Coupled bulk-return and flip dynamics identify separate persistence requirements and conditional loss of frame-dependent readout after cap conversion. Finally, a flip-symmetrized structural-state embedding is injective on the contact description and, under an explicit commutator hypothesis, gives the spectral-distance lower bound $(l-1)/(2\gamma_z)$. The conclusions are finite combinatorial or conditional mathematical results; molecular interpretations and experimental targets are kept separate.