Equivariance of the Source Measure Off the Pure Limit: Contact Sensitivity, Channel Capacity, and the Invariance of Selection Cost

This paper quantifies how partial sidechain cleavage affects the orientation sensitivity and alignment selection cost of stacking contacts in a self-separating substituted-chrysene stock. In the one-reagent limit where every sidechain is a hydroxyethoxy arm, the registration filter of the self-separating source reads the alignment of a stacking contact solely through the initiator, pricing the exogenous supply of alignment at one bit per contact. Extending this analysis to mixed arm words generated by partial cleavage establishes the exact magnitude of orientation sensitivity across operating regimes and demonstrates that the unconditional alignment price of one bit per contact remains invariant. The orientation sensitivity exhibits a sharp quadratic onset. Writing σ(π_h) for the probability that a contact drawn from the admitted stream is orientation-sensitive when each arm is cleaved to the phenol h independently with probability π_h, exact arithmetic shows that σ is a degree-8 polynomial with rational coefficients. At the uncleaved limit, σ(0) = f_I² = 2.47 × 10⁻⁷, arising solely from initiator pairs; the linear correction carries a coefficient of 9.40 × 10⁻⁶, while the quadratic π_h² term dominates with a coefficient of 4.00009. Across the three standard operating points of the separation process, partial cleavage increases orientation sensitivity over the pure limit by factors of 1587, 36502, and 131037, such that a one per cent cleavage rate amplifies the source's orientation sensitivity by more than fifteen hundred. Despite this increase in sensitivity, the induced channel remains unbiased. Because the inversion involution ι fixes the disubstituted (D) and tetrasubstituted (T) families setwise and cleavage acts independently across arms, relabelling a unit's arm word via a ↦ a ∘ ι forms a measure-preserving involution of the stream that reverses the unit's presented pattern and exchanges the registration numbers at both of its contacts. These involutions generate all bit-flips of the alignment field, ensuring that the field's marginal distribution remains uniform at every cleavage probability π_h — holding exactly in the absence of the initiator, and within 2.83 × 10⁻⁷ bits per contact (one part in 3.54 × 10⁶) when the initiator is included. Consequently, the selection cost of ℓ − 1 bits holds across the entire cleavage regime, as partial cleavage opens an informational channel between the arm words and the alignment field without biasing the alignment state. Evaluating the capacity of this channel defines its operational utility. For any registration free energy Δ_rgy, the channel capacity is bounded above by σ bits per contact and approaches this bound in the high-energy limit, yielding at most 0.1620 bits across a codon-length column at an arm retention of π_e = 0.90, compared with the 5.0000-bit unconditional specification cost. Utilizing this mutual information requires an agent capable of reading the arm words along the column. Furthermore, while an orientation-sensitive contact distinguishes its two alignment states internally, assigning absolute labels still relies on an asymmetric reference frame: out of 53 nominal contacts in a heritable lattice column at π_e = 0.90, an average of 1.717 contacts are self-distinguishing while 96.76 per cent continue to reference the terminal cap, accompanied by a corresponding adjustment in overall arm efficiency to 0.9875.