Cao (2025) credits Andrey Kolmogorov with an independently-developed, near-identically-titled extrapolation theory in 1939, alongside Wiener's own

cyberneticsnorbert-wienerkolmogorovextrapolationcold-war-scienceunverified

Xuenan Cao's 2025 paper on the mathematical genealogy of LLM "hallucination" (see claim-cao-2025-traces-llm-hallucination-to-wieners-1941-42-missile-extrapolation-math) reports, in her own words, that Soviet mathematician Andrey Kolmogorov developed a body of extrapolation theory in 1939 with an "almost identical title" to the concept Wiener would later apply to missile prediction and, through Cao's argument, to language modeling. The title Cao gives is "Interpolation and Extrapolation of Stationary Series" (1939); per Cao's own footnote and works-cited, the 1939 original appeared in French as "Sur l'interpolation et l'extrapolation des suites stationnaires" (C.R. Acad. Sci., Paris, 208), with Russian (1941, adding "random"/"zufälligen") and German versions following — the English near-identical title is the rendering Wiener's citation and Cao use. Cao frames this as independent, near-simultaneous discovery on both sides of what would become the Iron Curtain, rather than transmission in either direction — a different shape from the vault's other Cold War science-transfer notes (e.g. the Song Jian/Forrester lineage), which trace one-directional copying.

Unverified layer. Cao further reports, citing historian Benjamin Peters (2016), that Wiener came to show Kolmogorov "grudging deference" as an intellectual peer despite the political divide. This characterization is asserted in Cao's own voice but rests on her citation of a secondary source (Peters 2016, 40-41), and has not been independently checked against Peters or a Wiener-Kolmogorov primary exchange — it is recorded here as reported, flagged [unverified-secondary-citation], and does not raise to the level of a load-bearing fact this note rests on. The load-bearing claim — that near-identical extrapolation theory arose independently in 1939 on both sides — is Cao's own statement and clears the sourcing floor for a historical/biographical claim on a Tier 1 source.