The partial expectation GK maps to higher moments, up to the infinite moment (the extremum) dealt with in extreme value theory.

This is a technical claim in Taleb's 2023 work: the partial-expectation measure GK maps to higher moments, up to the infinite moment (the extremum) dealt with in extreme value theory. True: the paper defines GK and gives a derivation or correct argument showing that GK relates to higher moments, with the limiting case corresponding to the maximum or extremum studied in extreme value theory, and nothing shows the mathematics to be wrong. Mostly true: the relationship holds but is shown only heuristically or under conditions such as a particular distribution class. Mixed: the mapping holds for finite higher moments but the link to the extremum is unsupported, or the reverse. Mostly false: the mathematics shows only a loose analogy, not a mapping. False: the stated mapping is mathematically incorrect.

Set before the research began.

1. E1 What You See and What You Don't See: The Hidden Moments of a Probability Distribution arXiv (Nassim Nicholas Taleb) · April 2020 Own record

   “Using extreme value theory, we examine the properties of the hidden tail and calculate its moments of order p.”

2. E2 Evaluating probabilities without model risk arXiv (ar5iv rendering)

   “This is significant since the partial expectation already shows what the traditional Markov’s inequality does with the higher moments.”

3. E3 An Introduction to Extreme Order Statistics and Actuarial Applications H. N. Nagaraja, Ohio State University (2004 ERM Symposium lecture slides) · 26 April 2004

   “Suppose the top 100p% of the population are selected and one is interested in the average of the selected group.”

4. E4 The Role and Nature of High Impact Events (Black Swans): Technical Commentary and Empirical Data Scribd (copy of Taleb's Edge technical appendix) Own record

   “Mandelbrot and I used extreme value theory to get the same result: the Extrememum/Mean stays significant until we hit a huge N.”

5. E5 Evaluating probabilities without model risk ar5iv (arXiv HTML render) · 11 November 2019

   “In actuality, partial expectation cannot be calculated; however, it may be estimated by \(X_{n,n}/n\), where \(X_{n,n}\) is the maximum of an \(n\)-sample.”

6. E6 The Fourth Quadrant - Technical Appendix, Nassim Nicholas Taleb, Edge - 09 Scribd Own record

   “Mandelbrot and I used extreme value theory to get the same result: the Extrememum/Mean stays significant until we hit a huge N.”

7. E7 The Fourth Quadrant - Technical Appendix, Nassim Nicholas Taleb, Edge - 09 Scribd Own record

   “Note: What do we mean by "Infinite Kurtosis" or "infinite moment"? It simply means that the number is unstable; it does not converge as observations lengthen; its measurement is sample dependent.”

8. E8 An Introduction to Extreme Order Statistics and Actuarial Applications (lecture slides) H. N. Nagaraja, 2004 ERM Symposium, Chicago (hosted at National Taiwan University) · 26 April 2004

   “is the α of the parent distribution representing the tail thickness.”

9. E9 On the Shadow Moments of Apparently Infinite-Mean Phenomena Springer (record hosted on TU Delft research portal) · 2018 Own record

   “We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean.”

10. E10 Extreme Value Theory QuantMemo · 30 May 2026

    “Extreme value theory fills that hole: limit theorems about the largest observation rather than the sum, whose content is that a tail has a universal shape with only a handful of knobs, whatever generated the data.”

11. E11 Extreme Value Theory: Fuhgetaboudit fooledbyrandomness.com (Nassim N. Taleb) · 3 November 2025 Own record

    “Now let us generate, exactly as before, but change the distribution, with N random powerlaw distributed variables Zi, with tail exponent m=3,”

None of the evidence contains the 2023 paper's definition of GK or any derivation linking it to higher moments and to the extremum. E2 and E5 discuss partial expectations, Markov's inequality, and estimating the partial expectation from the sample maximum, but neither mentions GK or derives the claimed mapping. E1, E4, E6, E7, E9 and E11 are Taleb's own earlier or related writings on extreme value theory and hidden moments, and they do not address GK. E3, E8 and E10 are general extreme-value background. So the evidence does not settle the claim either way.