The Source: Substitution-Initiated Self-Separation of the Substituted-Chrysene Stock from a Polyaromatic Bulk, and the Supply It Delivers to the Protocell

The protocell articles take their substituted-chrysene stock as a boundary condition. Article 77 admits the 6,12-, 3,6,12- and 3,6,9,12-substituted families and places their manufacture, enrichment and self-separation outside its problem; Article 65 reduces the steady cycle to an inequality on a pool rate it does not supply; Article 40 records that an infinite admissible distance does not imply a physical scission, and states the dynamical scission theorem as a target. This paper supplies the source upstream of all three. Chrysene in a polyaromatic bulk is brominated, the 6- and 12-positions first and together and the 3-position next, as the filing's experiment reports; each bromine is replaced through an oxalate and reduced to a hydroxyethoxy arm; each polar arm lowers the unit's transfer free energy out of the bulk, so separation is initiated by substitution. We model the bulk as a finite absorbing chain on the substitution degree, prove the exit distribution in closed form, and show that one design equation, $k_3=e_2(R_T/R_D)(1+e_3/k_4)$, matches the exported stream to the protocell's demand at efficiency $0.998437$ in the illustration. The fast fourth step this requires is a stated design requirement, priced against initiator loss by $k_4/k_3=q\rho^\ast/(x(1+x))$ with $x=e_3/k_4$: the illustration asks $18{,}511$, and tolerating five per cent of surplus initiator lowers that to $18.5$. Selectivity against the polyaromatic background does not rest on the arming step being selective, and a second filter of a different kind is what makes that so. The exported units stack into columns, and because the four substitution positions sit on a core of $C_{2h}$ symmetry the arms of one unit fall over the arms of the next, so a column carries continuous arm registrations; a guest that cannot present the pattern breaks $\nu$ of them at each of two contacts and is excluded by $e^{-2\nu\Delta_{\mathrm{rgy}}}$. Article 40's enumeration of the four-ring polyhexes denies the pattern to every four-ring competitor. Partition, which acts on solvation, cannot discriminate an armed competitor from an armed chrysene at the same arm count; registry, which acts on geometry, can, and it is what protects the disubstituted stream. An unselective arming reagent therefore raises the stock-phase impurity concentration, in which the column bound is linear, and changes nothing structural. With returns disallowed the bulk empties exponentially, the admissible stock retains weight $0.998901$, and the exports of degree below two form a dynamically isolated waste class, discharging Article 40's Target 49 for this realisation in the classical sector. Article 77's predicate, which admits by substitution family and full specification, already accommodates every arm the source makes, so no widening and no arm-scheduling hypothesis is required. The supply interface adds a demand vector, a throughput in expectation, an upstream carbon ledger in which the oxalate is the only incorporated carbon reagent, and a necessary condition for diffusion-limited delivery.