BTW's own papers state that every local site sitting near threshold is a coincidental feature of the one-dimensional sandpile, not a general signature of self-organized criticality

self-organized-criticalitycomplex-systemsthresholdbak-tang-wiesenfeldsandpile-modelsource-discipline

Watkins et al. (2015, Sec. 6.3) reject a common popular misreading of self-organized criticality on BTW's behalf, in the review's own words: "What BTW did not mean, and did not imply, is that the system organizes itself into a state where every local degree of freedom is close to some threshold. This happens to be the case for the one-dimensional sandpile model, but this should be regarded as a coincidence, not least because the one-dimensional sandpile model shows no interesting features otherwise." The "coincidence" sentence is the reviewers' characterization of BTW's intent, not a sentence from BTW; the same section grounds it in BTW's own words on the 1D case: "[W]e consider for pedagogical reasons an example in one spatial dimension. In this case the spatial degrees of freedom 'decouple' and the system ends up in the least stable metastable state. This minimally stable state is a trivial critical state with no spatial patterns and uninteresting temporal behavior" (Bak et al., 1988a, p. 365, as quoted ibid.). The mechanism point — that "everything sits near threshold" is a special-case artifact of the 1D sandpile, not a defining property of SOC generally — is thus Tier-1 sourced to the refereed review's page-cited reading of BTW, anchored in BTW's own 1988 wording above.

The review attaches two supporting figures showing local variables typically sit well below threshold on average in the models that do exhibit the interesting behavior: the two-dimensional BTW sandpile has average height 17/8 = 2.125 against a threshold of 3 (Grassberger's conjecture, said to be confirmed analytically by Caracciolo and Sportiello 2012), and the Abelian Manna Model has average height 0.9488(5) against a threshold of 1 (Dickman et al. 2001).

Update, 2026-08-31: both figures have since been checked directly against their own primaries. Caracciolo & Sportiello (2012) confirms the 17/8 figure exactly, in its own abstract (claim-caracciolo-sportiello-2012-confirms-17-8-average-height). Dickman et al. (2001) corroborates the 0.9488(5) figure's magnitude but prints three distinct estimates, none matching that notation digit-for-digit (claim-dickman-2001-critical-density-corroborates-not-exactly-matches-watkins-figure). The mechanism claim above never depended on the fourth decimal place; it now rests on two independently-read primaries rather than a review's report of them.