Editing Openai/686aedb2-60b0-8003-98a8-e1766cf496a6 (section)

===== The mathematics they deploy =====
Wills & Carter translate the familiar “error-threshold” logic of quasispecies theory into coupled differential equations for three, inter-dependent processes:
# template replication,
# amino-acid assignment (charging tRNAs), and
# protein synthesis.

Key expressions (their Eqs. 24, 28–29) show that if a less-accurate protein catalyst (either an aaRS or a replicase) appears in a ribozyme-only system, the overall accuracy

p=qr−f(εu−εr)p = q_r - f(\varepsilon_u-\varepsilon_r)p=qr−f(εu−εr)
falls immediately because εᵤ > εᵣ. Even a small protein contribution (fraction f ≪ 1) drags the entire system below the error threshold, collapsing both replication and translation fountains of information. In every hybrid regime they analyse, the ribozyme world is dynamically unstable once proteins join the party Wills+Carter17

.

Wide-margin or close call?
Because the dependence on f is linear and the accuracy gap (εᵤ–εᵣ) can be orders of magnitude for proto-enzymes, the distance to the threshold is not a near thing. A few per-cent participation by sloppy protein catalysts suffices to wreck the coding system. The authors therefore describe the RNA-coding-world as facing “insuperable problems” and conclude that the takeover “appears to be impossible, rendering the notion of an RNA Coding World scientifically superfluous” Wills+Carter17

. In short, it is a wide-margin failure.

Do they hedge?
They acknowledge their model is deliberately minimalist (well-mixed chemistry, clockwork ribosome, no explicit compartmentalisation) and thus could be refined. Yet they argue these omissions would, if anything, tighten the error constraints, not loosen them. No point in the paper hints that new data are likely to overturn the verdict; the strongest “qualification” is a call for future spatial or compartment models to verify the same instability Wills+Carter17

.