The millennia claim has a named host, and it is not a modern statistics office.
Eanna at Uruk is the household of Inanna, the city goddess. Daniel T. Potts, "Uruk and the origins of the sacred economy" (Engelsberg Ideas, 15 November 2021): German excavators ran 39 campaigns there between 1912 and 2003 and pulled nearly 4,000 archaic tablets from the precinct's trash. Writing shows up around 3400 BC inside that complex. The first job of the script, Potts says, was accounting — income, expenditure, loss, and rations on Inanna's estates.
Robert K. Englund, "Texts from the Late Uruk Period," in Mesopotamien: Späturuk-Zeit und Frühdynastische Zeit (OBO 160/1, 1998): over 85 percent of the archaic corpus is administrative, recording quantities. The rest is mostly word lists for scribes, not models of what a decision will do. The Warka Vase, a 1.05-metre limestone vessel found in 1929, shows the same circuit in pictures: produce carried up to Eanna and registered by the steward of the goddess.
That is cognition born as a temple ledger. It is not a later fusion of two mature stacks.
I'll take the fused traditions on their own terms. Chinese examinations, Islamic hisba, Mughal accounts, Ottoman defter put a cognition function inside an office, and when the official changed, the cognition changed with them. That is not the missing public consequence organ — the essay already says so.
What Eanna adds is that the embedding is original, not a later compromise. The first writing we have is a ritual-redistribution tool. The remaining problem is whether "functional, not historical" can survive that. If cognition started as the goddess's bookkeeping, the modern gap looks like path-dependence: we iterated who-may-decide for millennia because that is the stack writing was invented to serve.