Dickman et al. (2001) corroborate but do not digit-for-digit match the "0.9488(5)" critical-density figure Watkins et al. (2015) attribute to them

self-organized-criticalitycomplex-systemsmanna-modelsandpile-modelthresholdsource-disciplineverification

Watkins et al.'s 2015 review reports the Abelian Manna Model's average height as "0.9488(5)," citing Dickman et al. (2001). Read directly, Dickman et al.'s one-dimensional fixed-energy stochastic sandpile paper reports not one but three distinct numerical estimates of its critical particle/energy density ζc: "ζc = 0.94887(7)" from one analysis, "ζc = 0.94883(5)" from a second (the ρ²a-derived estimate), and an adopted final value "ζc = 0.94885(7)." None of these three is printed as "0.9488(5)" in the paper itself. The figure Watkins et al. cite is the right ballpark and traceable to this paper's own numbers — all three estimates round to 0.9488 at four-decimal precision — but the "(5)" uncertainty digit they attach matches only the ρ²a-derived estimate (…83**(5)), not the paper's own adopted value (…85(7)**). This is a compressed, rounded transcription of three primary numbers into one citable figure, not a literal quotation of any single one of them.

The mechanism label Watkins et al. attach to this figure does check out directly, though: Dickman et al. define their model's site variable zi as "the energy (or number of walkers)... sites with zi ≥ 2 are said to be active," i.e., a site topples once its height exceeds 1 — the same "threshold 1" convention Watkins et al. use elsewhere in their own paper for the one-dimensional BTW model.

This partially answers question-verify-caracciolo-sportiello-dickman-soc-threshold-average-heights and partially resolves the [unverified-quant] flag on claim-btw-near-threshold-clustering-is-1d-sandpile-coincidence-not-general-soc-signature — corroborated in substance and magnitude, not confirmed as an exact quotation. Compare claim-caracciolo-sportiello-2012-confirms-17-8-average-height, the review's other supporting figure, which matches its primary exactly.