Applications
Where the race is run for money.
Every application below is the same problem wearing different clothes, and naming the clothes is most of the work: what the paths are, what one unit of path-time costs, and what maximum is paid at the end. Once those three are named, the machinery on this site applies as is: the wavefront policy says which paths to keep, the budget frontier says what another unit of budget buys, and the certificate says how far the answer can be from optimal.
| Domain | The paths | Path-time cost | Terminal maximum |
|---|---|---|---|
| Test-time compute | parallel generations or reasoning paths | tokens per rollout kept alive | the best completion, scored by a verifier |
| Research-agent fleets | agent trajectories on one task | compute and API spend per live agent | the best finding that survives review |
| Stage-gated R&D | drug candidates, prototypes, projects | burn per candidate per month | the one candidate that ships |
| Long-shot portfolios | early-stage companies, exploratory bets | follow-on capital and attention | the best exit, which dominates fund returns |
| Hiring funnels | candidates in process | interviewer hours per candidate per round | the quality of the one hire made |
Test-time compute
This is the application with a meter on it: inference spend is billed per token, and best-of-n pays only the best completion. The two baselines on the demo page are the two policies the industry actually runs. Choosing n up front and letting every rollout finish is static thinning; a single mid-run evaluation that keeps the top scorers is one-shot screening. In the committed example the adaptive wavefront policy beats them by 19% and 30% of expected terminal value at the same expected budget, and those two numbers are the honest size of the opportunity, not a multiplier on revenue. Speculative rejection and learned prefix pruning (see the bibliography) are this policy built empirically; the race says what the kill rule should be, rather than fitting it.
Stage-gated R&D
A pipeline reviewed at fixed phase gates is one-shot screening generalized: keep everyone until the gate, then retain an upper tail. The wavefront policy replaces the gate with a continuous kill-below bar that rises toward the deadline, and the gap between the two is measurable per portfolio with the committed solver: feed in the initial candidate cloud, the monthly burn, and the budget, and read off the difference. The survivor schedule on the demo page is the staffing plan that falls out: cull hard immediately, then carry a slowly thinning elite.
Long-shot portfolios and funnels
Seed portfolios and hiring funnels share the payoff shape, since the best exit or the one hire is what is paid, and both meter attention rather than calendar time. Here the model's caveats bind hardest: real candidates are correlated, budgets are hard rather than expected, and a partner who sees the whole portfolio is not population-blind. The mean-field answer is a stylized benchmark for these domains, not a deployable policy, and the three caveats are exactly the open problems listed in the paper's closing section.
What would falsify the pitch
The claim behind every row is graded, not binary: adaptive pruning beats a single screening date, which beats up-front thinning, by margins the solver computes per configuration. If a domain's measured margins come out near zero, the extra machinery is not worth its complexity there, and the budget frontier makes that check cheap to run before anything is built.