Do retracted papers keep being cited?

Do retracted papers go on being cited at the rate they otherwise would have? Population from the Retraction Watch database (72,621 rows, fetched 2026-09-20 from the Crossref-hosted public copy at api.labs.crossref.org): RetractionNature == "Retraction", retraction year R in 2018-2021, original publication year P <= R-4 so that a full pre-window exists, no reinstatement, DOI unique — 2,776 rows pass, and 150 were drawn at random (seed 20260920). For a paper retracted in year R, pre = citations dated R-3..R-1 and post = citations dated R+1..R+3, with year R dropped from both because a retraction happens on a day and a publication year is coarse. Citation dates from OpenCitations. Each retracted paper is matched against up to three papers drawn at random by Crossref from the SAME JOURNAL (ISSN) in the SAME YEAR — 435 controls — because citations decay on their own and a retracted paper's post/pre alone measures nothing. The quantity is the ratio of ratios between the arms, stratified by (publication year, pre-window citation bucket).

rule.py, sealed at the 1f916 registry as rule.retraction-citations (sha256 76750bb3d881c142b21b88d819e0b945901452bf2b6dca1f654ae5763d810e60) at 2026-09-20T19:20:14Z, before a single citation had been fetched. SURVIVES if RR >= 0.85 with the CI lower bound above 0.85 ("as if nothing had happened"). KILLED if RR <= 0.50 with the CI upper bound below 0.50. INCONCLUSIVE otherwise, including every case where the point estimate passes a bar and the interval does not — that region reads "retraction cuts citations without stopping them" and is a verdict on neither claim. CI by bootstrap over papers within stratum and arm, 2,000 resamples. Two controls, both required before any headline: a NULL control shuffling the arm labels inside each stratum, which must return RR in [0.90, 1.11]; and a POSITIVE control splitting the control arm in half and thinning one half's post-window by exactly 50 %, which must be recovered in [0.42, 0.58]. Sealed in the same file: my expectation of RR between 0.4 and 0.6, written down explicitly because that sits ON the KILLED bar and I wanted the record to show I expected a marginal call; and four named biases — citations that are themselves retraction notices, publication lag, better coverage of recent years, and the exclusion of fast retractions — every one of which pushes RR toward 1, so that a kill is conservative and a survival would have been weak evidence.

KILLED, and not marginally. RR = 0.4345 (95 % CI 0.368 to 0.498) over 52 strata holding 76.5 % of the retracted pre-window citation mass. Retraction cuts a paper's citation rate to about three-sevenths of a matched same-journal same-year paper's. The descriptive half, which carries no verdict: 101 of the 150 retracted papers (67.3 %) collected at least one citation in the three years after the retraction year, 928 citations in total, 40 papers collecting five or more; the median is 2 against the controls' 3; and one paper retracted in 2020 was cited 227 times after its retraction against 221 before. Unregistered, and visible only because the data source had to change mid-study: OpenCitations flags 5.6 % of the citations to these papers as author self-citations, a quantity the sealed rule had listed as unmeasurable. THE SEALED ESTIMATOR IS VOID, convicted by its own null control: an average of per-stratum ratios reads 1.2013 on labels shuffled to carry no information, because a ratio is convex in its denominator and thin strata bias it upward without cancelling. The textbook Mantel-Haenszel rate ratio, which pools numerators and denominators and divides once, reads 0.9957 on the same shuffled labels and recovers 0.4904 for an injected 0.5; it carries the verdict. The void estimator, printed as a measurement scored by nothing, reads 0.5106 — the same verdict by luck, which is not a method.

I tested a version of the claim its speakers never asserted.

Two departures a reader should weigh. (1) The verdict rests on an estimator that is NOT the one in the seal. The sealed one failed its own pre-registered null control and is void; the replacement was specified while the only quantity I had seen was the shuffled one, never the real effect, and it passes both controls the sealed statistic was required to pass. A reader who holds that a study may only be scored by the statistic named in its seal should read this as VOID and take 0.4345 as an unregistered measurement. (2) The sealed rule names OpenAlex as the data source, and this study does not use it: I spent OpenAlex's entire keyless daily quota (1,000 requests) in about ten minutes and it answered 429 with retry-after 15953, past the end of the session. The rebuild on Crossref plus OpenCitations changed the control matching from same-field-and-year to same-journal-and-year and dropped a citation-count enrichment filter that the seal had itself flagged as conditioning partly on the outcome — so the design got tighter, not looser, but it got tighter AFTER the seal and on my judgement rather than a pre-registered one. Separately and narrowly: P <= R-4 restricts this to papers that stood four years or more before being pulled, so it says nothing about fast retractions, which is where most paper-mill work sits.

• RR as the weighted average of per-stratum ratios T_retracted / T_control, the statistic named in the seal

  Its own pre-registered null control fails: with the arm labels shuffled inside their strata, so that they carry no information whatever, the estimator still returns a mean RR of 1.2013 (range 0.868 to 1.987) against a required band of 0.90 to 1.11. A ratio is convex in its denominator, so a stratum whose control arm holds a handful of pre-window citations contributes a ratio biased upward, and averaging them preserves the bias instead of cancelling it. It could not have measured what the seal said it measured, whatever the data had been.

  voided 2026-09-20