What exactly is a "conclusive association" in Astronomy? Phys.org's Astronomers use slime mold model to reveal dark threads of the cosmic web says

A computational approach inspired by the growth patterns of a bright yellow slime mold has enabled a team of astronomers and computer scientists at UC Santa Cruz to trace the filaments of the cosmic web that connects galaxies throughout the universe.
Their results, published March 10 in Astrophysical Journal Letters, provide the first conclusive association between the diffuse gas in the space between galaxies and the large-scale structure of the cosmic web predicted by cosmological theory.

This links to Joseph N. Burchett et al, Revealing the Dark Threads of the Cosmic Web, The Astrophysical Journal (2020)
Kudos for the use of the slime mold model, this organism is a gift that keeps on giving to not only biologists but a wide range of other fields https://www.google.com/search?q=slime+mold+growth+modeling which includes computing, network analysis, transportation and even cosmology.
Astronomy differs from some other fields of science in that most hypotheses must be tested by observation of naturally occurring phenomena, it's hard to test them through carefully designed experiments. While particle physicists can &quot;throw large hadrons&quot; at each other under controlled conditions, astronomers can't similarly &quot;collide white dwarfs&quot; in the laboratory.
Question: In the results described in the ApJ Letter, was there such a thing as a &quot;conclusive association&quot;? Is that even a thing? Or was there simply a similarity as defined by some metric which the authors believe to be reasonably objective?
A &quot;conclusive association&quot; is an oxymoron; for example, &quot;brawling love&quot;, &quot;loving hate&quot; (these first two are from Shakespeare), &quot;act naturally&quot;, or &quot;jumbo shrimp&quot;. An association is a vague term while conclusive is very specific and means proven without a doubt.
The underlying journal article does not claim the authors have provided a &quot;conclusive association between the diffuse gas in the space between galaxies and the large-scale structure of the cosmic web predicted by cosmological theory.&quot; That is what the press release claims. Press releases are not subject to peer review. Press releases can, and oftentimes do, use over flowery speech.
The underlying journal article does claim that &quot;statistics of absorption by the intergalactic medium (IGM) via spectroscopy of distant quasars support the model yet have not conclusively tied the diffuse IGM to the web.&quot; This is true. The implication is that the authors' model has conclusively tied the diffuse IGM to the web. The author do not explicitly make this claim in the journal paper. Suppose the authors had make this claim in early versions of the paper. If that was the case, peer reviewers would inevitably have said to remove this claim on the basis that &quot;conclusive&quot; is an extremely strong word in science.
Even if peer review had allowed that claim, it would still be dubious. Many scientific press releases claim that the research being reported is ground shaking and conclusive. Don't take press releases as fact. Only a tiny few scientific papers show something that is ground shaking and conclusive. Those that do do so (e.g., Einstein's annus mirabilis papers) are very few and very far between.