AI visibility measurement is comparative: practitioners want to know which domains generative search engines cite most often and whether observed differences are large enough to support decisions. Yet the industry lacks a principled way to determine whether enough data has been collected. Collection budgets vary widely across studies and platforms, and conclusions are often drawn from rankings whose stability and precision are unknown. We introduce a sequential convergence framework based on two complementary criteria: rank stability evaluates whether the rank-correlation trajectory has reached a structural plateau, while structural sufficiency evaluates whether the spread of citation shares among established domains -- those whose confidence intervals exclude zero -- exceeds the uncertainty of those estimates. Together, these criteria distinguish rankings that have merely stabilized from those sufficiently resolved to support inference. Both are derived from regularities in the observed citation distribution, including its rank structure, uncertainty profile, and the boundary between observed and established domains. The framework retains a small number of structural constants but requires no externally specified query count, correlation target, or confidence-interval width target; stopping is driven by observed measurement uncertainty and remains robust across a range of sufficiency thresholds. Applied across 30 platform-topic combinations spanning Gemini, SearchGPT, and Perplexity, the framework adapts to platform- and topic-specific citation distributions. Results show that no fixed collection budget can be justified across contexts and that convergence can instead be evaluated from the structure of the observed distribution. The framework provides a practical basis for determining when AI visibility measurements are ready to support comparative analysis.
Coding agents spend most of their context budget on retrieval. Lexical retrieval (grep) is universal, instant, and zero-setup, but noisy: it cannot tell a definition from a call from a comment. Semantic retrieval via the Language Server Protocol (LSP) is precise and typed, but needs a running, indexed server and pays a per-symbol round-trip. The claim that semantic retrieval is more token-efficient is, we find, asserted almost everywhere and measured almost nowhere: no public source isolates the LSP-vs-lexical token delta for an agent at equal task-success. This paper formalizes the question with one metric (tokens-to-success), specifies a five-arm ablation isolating semantic retrieval from confounds, maps three pre-stated failure modes onto measurable variables, and reports a preliminary study (Python and TypeScript repos; Claude Opus 4.8, Sonnet 4.6, Haiku 4.5). The answer is conditional and usually negative. On symbol-named localization the LSP costs tokens (+6% to +118%) and the agent ignores it when free. On reference-completeness it buys precision but not token savings and cannot raise the recall ceiling set by agent thoroughness; it saves tokens only for the weakest model. Tool choice is task-dependent: models default to grep on localization (0-6% semantic use) but reach for the LSP about half the time on reference tasks, unprompted. On edits scored by real test execution the gap is starkest: grep solves multi-file renames perfectly, a location-only LSP fails three-quarters of them by missing a call site, and even a complete, index-warmed, text-enriched LSP (each reference's line inline, as production LSP-MCP servers do) recovers most of the gap but cannot close it, since a rename must touch comments and strings that semantic references exclude. The implication is not LSP-always but an adaptive router keyed on task class, model capability, and lexical noise.