Measuring What the Crawler Sees: Discovery Curves, Core Persistence, and Shell Dynamics in Longitudinal Web Crawls

A longitudinal web crawl is a sequence of partial samples of an evolving URL population. Pairwise containment between two crawls is the standard probe; under a simple \emph{urn} model of the crawl -- each round samples a fraction of the URLs and replaces a fraction -- it recovers two interpretable rates, per-round survival $α$ and coverage $c$, but treats the population as uniform and consumes one pair at a time. In this work, we define a formal language for talking about a crawl. We extend this analysis with the \emph{discovery curve} $U(s, T)$, the cumulative URL footprint over a sliding window of $T$ crawls starting at $s$, which under the same urn model is also a closed-form function of $(α, c)$. Containment and the discovery curve are then two projections of one process: independent fits agree on $(α, c)$ when the urn is homogeneous, so any disagreement is itself a measurement. Applied to Common Crawl (2020--2025, domain granularity) and to the German Academic Web (GAW, URL granularity), the two projections disagree on both archives, and a two-component urn with a persistent core fraction $κ$ alongside shell parameters $(α_\partial, c_\partial)$ reconciles the disagreement. A residual on $c_\partial$ remains, signaling that the shell itself is not homogeneous; $κ$ is recorded as the scalar entry point to a rank-resolved generalization, which is left to follow-up work. \keywords{web archive \and crawl coverage \and discovery curve \and urn model \and two-component model \and URL lifetime}

Estimating Absolute Web Crawl Coverage From Longitudinal Set Intersections

Web archives preserve portions of the web, but quantifying their completeness remains challenging. Prior approaches have estimated the coverage of a crawl by either comparing the outcomes of multiple crawlers, or by comparing the results of a single crawl to external ground truth datasets. We propose a method to estimate the absolute coverage of a crawl using only the archive's own longitudinal data, i.e., the data collected by multiple subsequent crawls. Our key insight is that coverage can be estimated from the empirical URL overlaps between subsequent crawls, which are in turn well described by a simple urn process. The parameters of the urn model can then be inferred from longitudinal crawl data using linear regression. Applied to our focused crawl configuration of the German Academic Web, with 15 semi-annual crawls between 2013-2021, we find a coverage of approximately 46 percent of the crawlable URL space for the stable crawl configuration regime. Our method is extremely simple, requires no external ground truth, and generalizes to any longitudinal focused crawl.