The Partition Concordance: Arm Additivity Measured against the Open Literature, and the Reassignment of Purity to the Structural Filters
Year: 2026
Type: article
Abstract: Article 79 exports a substituted chrysene from a hydrophobic bulk into an aqueous stock phase and rests that export on $H_{\mathrm{add}}$, under which each polar arm lowers the unit's transfer free energy by an amount depending on the arm type alone. Its Target 14.1 asks for the per-arm enhancement $q$ to be measured. Nothing in the corpus has been tested against a number measured by anyone else. This paper does that. Because $H_{\mathrm{phase}}$ makes the stock phase aqueous and the bulk polyaromatic, Article 79's partition coefficient is an organic-to-aqueous coefficient, so it is the reciprocal of an octanol/water coefficient up to the reference solvent: the concordance is an identification and not an analogy. We then observe that Article 79's ordering theorem is a one-line consequence of $H_{\mathrm{add}}$ and therefore carries no empirical content of its own; the content is in the hypothesis, which separates into three claims. Against $6$ single-laboratory increments and $28$ compiled aromatics we find: every arm lowers the coefficient, so the sign claim holds; the increment does not decay with arm count, so the ladder claim holds; and the increment depends on the locant and not on the arm type alone, failing the third claim by $0.42$ log units, which is $60\%$ of one whole arm. Monotonicity survives all three, since the weakest increment is still $-0.58$. Target 14.1 is discharged at $q=5.05$ per hydroxyl arm, $q^{4}=651$, and we show this is a lower bound. Carrying a benzene-measured increment to a four-ring core needs a hydrogen-bonding substituent tested across ring count, which a nonpolar control cannot supply; we supply one, and it is flat to $0.11$ log units over one to three rings. Against this, $H_{\mathrm{bulk}}$ is refuted and withdrawn. It asserts that an unarmed competitor cannot outrun the chrysene into the stock phase; $11$ of $19$ measured competitors do, naphthalene by a factor of $324$, because aqueous affinity tracks size and size carries no arm. Restricting the competitor set to four-ring polyhexes does not rescue it. Article 79's architecture survives, because its Scholium already routes purity through admission and registry rather than through partition; what changes is that the load on those two filters is now quantified, and that one proposition which did use $H_{\mathrm{bulk}}$ is left unavailable for a realistic bulk. We close by showing the four arm types are not commensurable: ionizing an arm is worth $3.6$ neutral arm installations, so the single-arm-type ladder understates the real arc by orders of magnitude. The measurement bounds the ionization shift only, not the whole increment of an ionizable arm, and the figure is carried by estimated rather than measured entries; both limits are marked where the number is used.
Source: Annals of the Chrysene Formalism
DOI: 10.68366/qxw27909
Author: Charles Schaper
Language: English
Subfield: Health, Toxicology and Mutagenesis
Field: Environmental Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7224856637