Erasure Skew: A Measurement Program for the Power-Conditioning of Provenance Loss in Retrieval and Composition Systems

Standalone empirical white paper. Companion to Measuring Semantic Deviation (EA-GLAS-02, DOI 10.5281/zenodo.20271783). This paper specifies a measurement program for Erasure Skew (Ω): the degree to which provenance loss in a retrieval or composition system is conditioned on the power of the source. Where the Provenance Erasure Rate (PER) measures the magnitude of provenance loss, Erasure Skew measures its orientation — whether the loss falls evenly across sources or systematically strips low-power sources while preserving high-power ones. Conceptually Erasure Skew is the covariance of per-source provenance retention with source power; operationally it is estimated as the regression slope of per-source retention on a declared power coordinate, Ω = cov(w,ρ)/var(w), with the power coordinate defaulting to Retrieval Capital (RC) or a logged observable proxy. It is the second moment of PER: where PER measures how much provenance is lost, Erasure Skew measures whom the loss falls on. The paper does three load-bearing things. (1) Separability: a seed-fixed synthetic test demonstrates that the estimator recovers power-conditioning independently of mean provenance loss — two corpora with equal PER and opposite Ω — with a stated falsification condition; empirical separability on real output is pre-registered prediction P1. (2) Lineage: Ω relocates the fairness-of-exposure question (Singh & Joachims 2018; Diaz et al. 2020) from who is shown in a ranked list to whose authorship survives when composition dissolves the list into a single synthesized voice — the composition layer the exposure literature did not target — and maps (PER, Ω) onto the R1 lossy / R2 predatory / R3 witness regimes of the Three Compressions. (3) Placement: Ω enters the Formal Foundations operator algebra as candidate #11, the distributional companion to the surviving-provenance invariant; the pair (∮, Ω) measures accountable circulation and its equity, and the population-scale Single-Owner Discount is Ω's size-weighted population integral. The RESOLVE/MEASURE/REPORT procedure is executable and auditable, with logged limits: ground-truth provenance and the power coordinate must be supplied and logged; self-scoring must be validated externally; the estimator is undefined when var(w)=0 or n