One pool, many targets: a conservation layer and what archival data can identify

2026-09-30

AI Summary

This study addresses the absence of finite-pool conservation constraints when interpreting RISC occupancy independently. We construct a differentiable scalar balance layer and propose a conservation operator with a unique positive root alongside a redistribution theorem, employing implicit differentiation to realize the redistribution of conservation equations. By integrating differentiable programming with thermodynamic affinity modeling, this work reveals rank invariance under fractional occupancy. The project provides reusable conservation operators whose predictive value is validated through historical data auditing; however, current empirical evidence has not yet confirmed that the coupling mechanism yields additional predictive gains.

Abstract

Pairwise guide--transcript scores do not enforce conservation of a finite guide-loaded RISC pool when they are interpreted independently as occupancies. We formulate a differentiable scalar equilibrium layer: one conservation equation with a unique positive root and exact implicit gradients. It yields a redistribution theorem, a qualified high-resource limit, an analysis of the retrieval approximation, and a conditional rank-invariance result: within one construct at one dose, rankings by fractional occupancy cannot distinguish equilibrium from independent scoring. We therefore audit the two experiments that proposition leaves open, dose and cross-context, on archival off-target data. Corrected thermodynamic affinities associate weakly with measured repression in the direction a working predictor requires, but a paired permutation test and a construct-cluster bootstrap do not establish added predictive value from the coupling: what survives their differing permutation-null baselines is \GapNet{}, a descriptive \GapNetOverSE{} of the equilibrium association's cluster standard error. The dose fits are heterogeneous and frequently violate the model-implied exponent constraint, which is superlinear rather than sublinear, so these data do not identify the competition parameter. A saturable compression of the competitor set holds both accuracy targets on held-out guide families but is not faster at the size measured. The contribution is a reusable conservation operator and the experimental information needed to test it. The code for this study is available at https://github.com/shadi97kh/One-Pool-Many-Targets.

Problem

• RISC pool conservation
• off-target prediction
• guide-transcript scoring
• thermodynamic equilibrium
• archival data

Innovation

• differentiable equilibrium layer
• conservation operator
• implicit gradients
• GapNet
• saturable compression