After posting this, I did a lot more research and I was finally able to find some publications with controlled experiments on Na+ neonatal/infant intake, mostly in animals of course, with a few human experiments when they were ethical to do so (e.g. testing two Na+ supplementation regime in Na+ deficient neonates).
[1]. Haycock, The influence of sodium on growth in infancy.
This review article quotes a number of experiments on rats and other animals, and to my untrained eye, the methodology looks to be gold standard. In one experiment, some populations of rats are apparently in completely indistinguishable environments, except that the concentration of Na+ is varied across these groups (Cl- is constant across all groups). Na+ deprivation seems to lead to growth delay, progressively larger dose of Na+ mitigate this delay up to a certain threshold where normal development is achieved. This article describes many more related experiments studying related aspects, e.g. showing that Na+ deprivation followed by adequate Na+ intake does not produce "catch-up" growth (the growth gap is permanent).
This paper also describes two experiments on human neonates. The first such experiment had substantial Na+ losses in the ileostomy fluid. There does not seem to be any controls, and no mention of blinding the clinicians. These infants failed to grow, which was remedied when the infants were provided with Na+ supplementation.
A second clinical experiment on humans is described. Premature neonates (<34 weeks) were provided either 4-5mmol/kg/day (treatment group) or 1-1.5/mmol/kg/day ("control" group) of Na+. The "control group" seems to have delayed growth compared to the treatment group. Further observations are described, comparing "mature" maternal milk against maternal milk of mothers whose infants are premature, and whey-based formula with high mineral contents. It wasn't clear to me how many of these experiments were double-blind controlled, but also the three treatments don't prove much about Na+ because so many other atoms and molecules vary between the three treatments.
Elsewhere in the literature, I've seen many mentions that <34 week preemies should receive Na+ supplementation, but >34 week preemies should not. Although it is scientifically correct in the abstract, not to give unproven treatments to patients, it may be that the question of Na+ sufficiency in mature neonates is an open problem. I was not able to find scientific evidence to support confident assertions that mature neonates and infants have sufficient Na+ intake from maternal milk. For example:
[2]. Strazzullo, Campanozzi, Avallone. Does salt intake in the first two years of life affect the development of cardiovascular disorders in adulthood?
[2] is a highly cited paper that sets out excellent protocols for the clinical setting. However, I am using [2] as an example because I feel that the wording they use is sometimes stronger than the scientific evidence that they have. This is par for the course in medicine, but as a mathematician, and for the context of my question, I am looking for unambiguous, objective, gold-standard science.
In [2], the authors write "The amount of sodium to be retained by an infant for proper physiological growth is largely covered by breast feeding (or low sodium formula milk) in the first six months..." However, according to my reading, they do not have gold-standard double blind controlled experiments on humans to prove this. One piece of their argument is to cite a rat experiments co-authored by Hancock (the author of [1]) and extrapolate to humans. Their argument is that rats need 0.3mmol/day, and they somehow conclude that therefore humans would need 0.9mmol/day. If that were the case, there is a good likelihood that maternal milk would indeed be sufficient, but this begs the question: why does maternal milk contain 60+mmol/L of Na+? Also, I am suspicious of this extrapolation, tripling from newborn rats to newborn humans.
Apart from the rat evidence, these authors attempt to link "salt preference" with later bad outcomes, but this is not the sort of science I am looking for. It suffers from the usual flaws. Observational studies can, at best, show correlations. You can never tell the direction of the causality, and you can never uncover confounding factor. My favorite way of teaching confounding factors and causation is the story of Bob, who always gets a headache after sleeping with his shoes on. Because of the time difference, people assume that Bob's shoes are magical headache-causing footwear but the reality is that Bob only sleeps in his shoes after partying at the pub.
I realize that if [2] had used confusing language like "we recommend no Na+ supplementation for mature neonates, although the question of Na+ sufficiency for such patients remains an open problem", that would be confusing for clinicians and it's a lot easier to publish papers that have a clear message.
My personal, unscientific opinion is that it is likely that mature neonates and young infants have sufficient salt, but it is also possible that they do not. Salt sufficiency is presumed because it is assumed that maternal milk is "perfect food" for neonates. But this is in tension with the consensus elsewhere that breastfed children are iron deficient. Would prehistoric infant mammals somehow get iron intake from their environments? Would they also get sodium intake from their environments? I don't think these questions have been answered, from what I can tell.
