Potential objections to the full explanation

As to be expected for any work of this size, there are several possible objections to the reasoning and conclusions presented here. This section lists the most important of them and offers answers where appropriate. Informed comments and criticism are always welcome.

The statistical base is weak
    This is essentially Arthur Snyder's criticism. With two fragments in one group and three in the other, how can one calculate any reasonable statistics? The surprising fact is that although that may be a legitimate criticism of earlier work, when the heterogeneity was still thought to be 24%, it is no longer valid. The agreement of the observed 3% heterogeneities of the groups with the 3%–5% for other groups of tiny particles effectively increases the statistical base significantly, and the orderly decrease in heterogeneity with shrinking particle size solidifies the significance of these numbers by showing that they are part of an organized framework. The one-in-a-million probability that these numbers arose by chance also works to strengthen their significance.

Wrong model of mixing?
   To understand the unusual nature of the heterogeneities of Sb in WCC/MC bullets, I had drawn an analogy to the swirling of brown and yellow batter when preparing a marble cake. In the Providence Conference of April 1999, I referred to it as the "mixing bowl" theory. Tony Marsh claimed that this idea was fatally flawed, and proposed his "nugget" theory instead. As far as I can tell, the nugget theory says only that the core of a bullet can be viewed as a series of little nuggets stacked against each other, whose concentrations can differ significantly within bullets, to the point that a nugget from one bullet can match one from another bullet just as well as one from its own bullet. This is a way of characterizing heterogeneities within WCC/MC bullets rather than of explaining how those heterogeneities arose.
    Neither the "mixing bowl" nor the "nugget" model is central to the validity of the tight groups; they offer explanations for the large-scale heterogeneities that do not apply to the tiny scale from which the five fragments were actually drawn. They are peripheral information.

Proof or hypothesis?
    How can the new explanation be considered as proof if it is based on a working hypothesis (that multiple tiny fragments are homogeneous because they come from very near each other on single breaks in fragmenting lead cores)? This question is easy to resolve. The near-uniformity of composition (heterogeneity if 2%-3%, including analysis) is a fact; only its ultimate cause is not. The meaningfulness of the two tight groupings of the five assassination fragments rests on the fact of the low heterogeneities, not on their cause.

Quarters of one bullet overlap (in Sb) those of other bullets
    This is an older objection that refers to the well-known fact that antimony in a quarter of one bullet may occasionally overlap antimony in a quarter of another bullet. It is usually presented as something that kills Guinn's work completely. This objection is invalid for at least three reasons: (1) Guinn himself recognized it, and expressed his conclusions accordingly. (2) Matches are always expressed in terms of probabilities rather than the absolutes that this objections implies. In working out the probabilities, the entire distribution of antimony concentrations from both objects is taken into account, not just individual values. (3) Last and most importantly, this objection is now obsolete because we know that heterogeneities at the scale of quarters of bullets are no longer relevant to actual heterogeneities of groups of fragments. It may have been marginally relevant at one time, but no longer.

Wouldn't more analyses of background WCC/MC bullets be in order if Guinn had grossly mismeasured their heterogeneities?
    No, for two reasons. The first is the premise of this question, that Guinn had grossly mismeasured the heterogeneities in his test bullets. There is absolutely no evidence for such a charge. First, a NAA pioneer of Guinn's rank must always be given the benefit of the doubt—he obviously knew how to measure antimony! Second, his measurements agreed extremely well with the FBI's earlier data.
    The second reason that additional analyses of test WCC/MC bullets are unwarranted is relevance—variations over quarters are nor relevant to the much smaller scale at which fragments are formed. (See discussion under "Resolving the logical incompatibility.")

Too risky when a whole explanation hangs on one calculation that the two tight groups could not have arisen by chance?
    Isn't it awfully risky to build an entire explanation one one negative calculation (that the two tight groups could not have arisen by chance)? It may be risky in principle, but in this case the calculation is so straightforward and the result so far beyond any risk of being invalidated that we can feel secure about it.

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