The Tier-1 SOC literature places threshold-driven interaction among self-organized criticality's sufficient ingredients, not among its three logically necessary conditions

self-organized-criticalitycomplex-systemsthresholdsdidtnecessary-sufficientsource-discipline

Watkins et al. (2015, Sec. 7) draw an explicit two-list distinction the vault's existing Tier-3-sourced framing does not carry — "SOC's phenotype" (necessary) versus "SOC's genotype" (sufficient), with "necessary" meant "strictly in the logical sense (they define SOC: if and only if all of them are observed, one is faced with SOC)." The three necessary phenotype conditions, quoted directly (Sec. 7.1), are: "1. Non-trivial scaling (finite size scaling; no dependence on a control parameter). 2. Spatio-temporal power law correlations. 3. Apparent self tuning to the critical point." Thresholds do not appear on this list. They appear instead among the sufficient genotype ingredients hypothesized to produce SOC (Sec. 7.2): "In most SOC models the non-linearity is realized as a threshold in the interaction, i.e. activity can spread only when some local dynamical variable exceeds a threshold" — item "4. Non-linear interaction (required by 1), normally in the form of thresholds."

This corrects, rather than confirms, the "local thresholds are necessary but not sufficient" phrasing that claim-engineered-threshold-is-not-self-organized-criticality inherited from a Tier-3 course project (Golyk 2012): the Tier-1-adjacent literature's own necessary/sufficient split puts thresholds on the sufficient side from the outset, not on a necessary list they then fail to complete. See claim-soc-necessity-of-threshold-driven-interaction-remains-open-question for whether thresholds are also necessary — a separate, and still open, question in this same source.