Resolution autoformalizes singularity math for $135,000

Resolution's post is striking less for the mathematics than for the workflow it describes. One researcher wrote a 112-page plan of atomic steps, then handed execution to an orchestrator agent that spun up sub-agents for pen-and-paper math, Lean writing, and progress checks. The execution phase, Resolution says, needed little scaffolding beyond the initial plan and some agent skills distilled from earlier internal autoformalization efforts. The result was about 600k lines of Lean for an estimated $135,000 in token spend—a figure that turns a formerly bespoke research activity into a line item a startup can budget.

Resolution frames the payoff narrowly: formalizing resolution of singularities lets it automate more of singular learning theory, which it says helps it better understand sampling and thereby shape how models learn. Whether that connection holds is an open research question, but the cost structure is the concrete shift. Work that was so human-time-intensive that few people did it, and that could not easily be folded into a startup's roadmap, can now be attempted by a small team.

The same pattern appears elsewhere in the newsletter. Mirendil reports that one researcher pretrained a model in the 100B–500B parameter range in 3.5 months with less than $10m in compute, and that its next model will be built partly by Mirendil models. ProgramBench, meanwhile, went from every tested model scoring 0% at launch in May to Claude Opus 5.5 at 18.5% resolved and 70.5% almost. Each item points in the same direction: the scarce input in frontier work is shifting from headcount toward token budgets and the judgment to direct them.