Methods: citation history and h-index forecast

How CiteVector gets its data, how it rebuilds a dated citation and h-index history, and how it forecasts citations, h-index and i10-index. The same summary appears at the bottom of every dashboard.

Live profile data

The CiteVector server fetches the public Google Scholar profile page and its publication list, sorted by citations, 100 rows per page. Results are cached for six hours. Each load also records one observation per day in CiteVector's own history, so the trajectory keeps growing even for profiles the Wayback Machine rarely captures.

Google Scholar limits automated access. When a live fetch fails, CiteVector falls back to a cached copy, then to the latest Wayback Machine capture (exact metrics, but only the 20 papers shown on that page), and says which source it used. You can also save the profile page from your own browser and drop the HTML file on the home page; it is parsed in your browser and not uploaded.

Wayback Machine history

The Wayback Machine's CDX index is queried for every archived URL of the profile: any hl= language, with or without view_op=list_works. One snapshot per calendar month is kept. The raw archived HTML is fetched with the id_ flag, which skips the Wayback toolbar rewriting, and the metrics table is parsed with the same parser used for live pages. Snapshots whose metrics table cannot be read are listed but not plotted. See h-index history for what this produces.

Per-paper citation forecast

Each paper follows Equation 3 of Wang, Song and Barabási, "Quantifying long-term scientific impact", Science 342 (2013):

• m = 30, the constant the paper fixes for every publication.
• Φ is the standard normal cumulative distribution function.
• t is in days. In the paper's time unit a publication's impact time is T* = e^μ, and μ above 9 would mean an impact time of more than 20 years, so days are the consistent unit.
• Immediacy μ and longevity σ are fixed. A Scholar profile has no per-paper citation times, so μ and σ cannot be fitted from a history the way the paper does (supplementary section S2.3). They are set to the values the paper reports as typical: T* = 3 years, so μ = ln(3 × 365.25), the impact time it describes as stable across the journals it tracked; and σ = 1.2, the longevity of the paper fitted in its main text.
• Fitness λ is solved exactly so that Equation 3 at the paper's observed age equals its current citation count. Every earlier or later count is Equation 3 at that age.
• Uncited papers have λ = 0, which is what the paper's likelihood gives when no citations have arrived.
• Publication dates are set to mid-year, because the profile exposes only the year. A paper published in the current year is assumed to be six months old, so that λ is not solved at an age where Φ is close to zero and the forecast would explode.

From papers to h-index and i10-index

At each year-end, from up to 12 years back to five years ahead, CiteVector evaluates every paper's curve, then recomputes total citations, the h-index (the largest h such that h papers each have at least h citations) and the i10-index (papers with at least 10 citations) from those per-paper counts. The forward projection is anchored so the current year equals the values Scholar shows today. Past values on the projection chart are model reconstructions, not Scholar history.

When the publication list is incomplete and no longer than the current h-index or i10-index, past values cannot be reconstructed, so only the forward segment is drawn, starting from today's real values. That understates the trend, and the dashboard says so. See the h-index predictor for what the forecast covers and its limits.

Models considered and not used

Xiao et al. (IJCAI 2016) propose a Hawkes-process model of citation counts. It needs each citation's timestamp plus a covariate vector, which a Scholar profile does not contain, so it is not applied.

Peer percentile

The dashboard's "h-index among peers" tile and the report's "Standing among peers" section are exact counts from OpenAlex, not samples. Two peer groups are used for each topic. The first is every OpenAlex author with at least 10 works in that topic, the population a committee usually has in mind; this is the group behind the dashboard tile. The second, shown in the report, is the subset whose total works count lies between half and double the researcher's, a strict stand-in for career stage (OpenAlex does not expose a first-publication year for peers) that leans towards senior authors because OpenAlex counts preprints and versions as works. The percentile is the share of the group with a strictly lower h-index (or fewer citations). Both the researcher and the peers are measured with OpenAlex's own figures, which run below Google Scholar's because OpenAlex indexes fewer sources. Percentiles depend on the topic chosen, so the report shows up to three. The self-citation share is the fraction of OpenAlex works citing the researcher's most-cited papers that list the researcher as an author.

Attention badges

The top 20 papers by citations are matched to DOIs by title search on OpenAlex (best match with bigram similarity above 0.6). Altmetric and Dimensions badges are embedded by DOI; a paper with no DOI match shows no badge.