Exchangeability and the Exclusion of Equilibrium Assembly: Necessary Conditions on Throughput, Entropy, and Fidelity in the Chrysene Formalism

This paper establishes the formal constraint set governing any exogenous placement system that supplies the alignment of a substituted-chrysene assembly, deriving six quantitative bounds from the established properties of the system and demonstrating that orientation fidelity requires active, non-equilibrium imposition. While prior analyses establish that an exogenous agent must supply the stacking alignment and determine its exact information price, this work characterizes the operational requirements that any physical placement mechanism must satisfy. The primary bound addresses orientation fidelity. On the self-separated stock, the registration weight of a contact is independent of its alignment bit at every contact except initiator–initiator pairs. A contact without a registration gap exhibits no Boltzmann preference between its two orientations, yielding an orientation error rate of 1/2 at every registration free energy. When partial sidechain cleavage renders a fraction σ(π_h) of contacts orientation-sensitive, the signed bias of the stream remains zero, so sensitive contacts likewise favour the target state half the time. Consequently, both contact classes exhibit an error rate of 1/2, fixing the mean orientation error rate of an equilibrium process at exactly 0.5 — uniformly in the registration free energy Δ_rgy and in σ. Relative to the permissible error budget of 1.01 × 10⁻⁵ for a period's anchor units, the equilibrium rate differs by a factor of 4.97 × 10⁴, and by a factor of 50 even under perfectly correlated failures, confirming that a placement system must actively impose orientation rather than relying on equilibrium discrimination. Five additional bounds specify the throughput, thermodynamic cost, sensing, and symmetry parameters of the placement process. First, the material feasibility relation specifies a total demand of 42,200 units per period, of which the 1,000 anchor units are placed directly into the heritable structure, while the remaining 97.6 per cent comprises lumen osmolyte and membrane lipid; this sets the placement rate on the order of one unit per second, inversely proportional to the period. Second, pricing a coded hexamer at 25.0 to 28.0 bits establishes an information cost of 4.17 to 4.67 bits per unit, corresponding to 3.23 kT at the Landauer limit — an energetic scale comparable to the stacking contact itself, representing 1.62 times a disubstituted contact at Δ = 1 and 0.81 of a tetrasubstituted contact. Third, a sensor coupling exclusively to the arm-registration pattern must evaluate 31 contacts per bit, independent of Δ. Finally, because the in-plane connectors are directed with one contraction per in-plane direction, the relative orientation freedom of an in-plane pair is 0, leaving a single collective flip per layer and 6 across the six-layer heritable box. Aligning the material demand with the minimum heritable genome length refines the baseline resource figure. Evaluating the demand formula at the minimum heritable length of L = 222 base pairs, rather than the nominal L = 200 base pairs, yields a per-period requirement of 43,762 units, representing a 3.7 per cent adjustment across the corresponding ledger entries.