Respectfully, I think you're missing the complications outlined in the rest of the thread. The difficulty in the biosciences and even in chemistry and some physics is that they can't really be formalized in the way that is necessary to construct these "chains of proof".
The scientific literature is an ongoing conversation anchored by rigorous experimental facts and data. But rigorous doesn't mean it's clean like a mathematical proof. In fact, most science approaches its "proofs" in quite a different way than math. For example, as far as science would be concerned P!=NP in complexity theory. We've done the experiment many times, tried different things, it's pretty much true. But it's still not mathematically proven because there isn't a formal proof.
That's not to say it's invalid to expect more rigor, or that we wouldn't all love to have "chains of proof" and databases and signatures for data etc. It's that it's simply not practical given how noisy and complex biological systems are. In contrast to math, you pretty much never know the full complement of objects/chemicals/parameters in your experimental space. You try to do the right controls to eliminate the confounding variables, but you're still never fully in control of all the nobs and switches in your system. That's why usually you need multiple different experiments tackling a problem from multiple different approaches for a result to be convincing.
Formalized systems would be great, but I don't think we're even close to understanding how to properly formalize all of those difficulties and variables in a useful way. And it may not even be possible.