Applications
Candidate domains, ranked by how cleanly they fit the race abstraction: many latent competitors, an expensive process, an extremal observation.
The selection criterion discovered along the way: find problems with thousands of latent competitors where an expensive process reveals a winner. Each domain below is scored informally on three axes — is the first-event structure exact, is the leave-one-out question physically meaningful, and is ground-truth simulation available to validate a surrogate against.
Chemical kinetics and kinetic Monte Carlo
The cleanest fit. A KMC step is a race among escape channels, with the exponential assumption baked in; catalysis and surface-reaction networks routinely involve thousands of channels whose rates are themselves expensive (DFT-computed) quantities. The surrogate question: infer latent propensities from observed first-event frequencies and predict the effect of blocking pathways (poisoning a catalytic site) or adding them — without recomputing the rate table. IIA violations from correlated barriers are exactly what a non-exponential Thurstone race can capture. Ground truth is cheap to generate synthetically, making this the first testbed.
Fracture and weakest-link failure
A stressed material fails at the weakest of millions of bonds — an argmin observation over a latent strength field. Weibull statistics is the classical IIA-style shortcut; real materials show correlated disorder and stress redistribution that break it. The leave-one-out question is native here: “what if this bond (or fiber, in fiber-bundle models) were absent or reinforced?” And the elastic response side is quadratic, so the rank-one cavity applies literally to the stiffness matrix: one factorization yields every single-bond-removal compliance change.
Glasses and rare-event dynamics
A supercooled liquid relaxes through whichever local rearrangement happens first — a race among soft spots. The cavity method is already the theoretical language of this field, which cuts both ways: the identity is known, but the computational framing (one solve, all cavities) may still pay in Hessian-based analyses of inherent structures, where mode-by-mode or site-by-site deletion studies are common.
Nucleation and first-passage percolation
Nucleation sites compete to form the critical nucleus first; first-passage percolation races paths through random media. Both produce winner-plus-time data of exactly the form Q3 of the program studies, and both have well-understood limiting regimes (extreme-value theory) to check surrogates against.
Resistor, elastic, and flow networks
Not a race but a pure rank-one-cavity playground: the graph Laplacian's pseudo-inverse contains every single-edge and single-node removal response. Effective resistances, current redistributions after a line failure, and contingency screening in power grids are all leave-one-out scalars — $O(1)$ each after one solve. The $N-1$ (and $N-2$) contingency analyses of power engineering are the leave-$k$-out identity by another name; the audit in Q1 will establish how much of current practice already exploits it.
Defects and vacancies in solids
Vacancy formation energies and defect interactions are classic remove-one-and-recompute calculations. Within a harmonic model, the leave-$k$-out identity prices every defect pair at a $2\times 2$ inversion — the compressed defect ensemble of Q4. The open question is how far the harmonic downdate tracks the relaxed (anharmonic) answer, and whether it works as a screening layer for full calculations.
Beyond physics
The same abstraction — thousands of latent competitors, an expensive process, a winner — recurs in commerce (auctions, product search, one item chosen from thousands), reliability (first component to fail), and model selection (first hypothesis to validate). These are deliberately out of scope here but kept in view: the point of naming the repository after the computational object's physical home, rather than any single application, is that results should transfer.