Papers

Foundation

• Cotton, P. (2021). Inferring Relative Ability from Winning Probability in Multientrant Contests. SIAM Journal on Financial Mathematics 12(1), 295–317. The fast ability transform: a lattice construction of the winner-of-many distribution, each entrant priced against its leave-one-out field, $O(N)$ overall. Everything on this site applies that machinery to a new domain.

Working papers & notes

• Kinetic Surrogates via Fast Ability Transforms — in preparation. Outline in the paper directory. The two leave-one-out identities (multiplicative for races, rank-one for quadratic systems), the racing-to-kinetics dictionary, and first numerical evidence on synthetic kinetic Monte Carlo.
• Correlated Races for First-Passage Kinetics — experiments complete, note in preparation. Code and figures in exp01 and exp03. Brownian narrow-escape simulation: blocking absorbing windows redistributes flux to geometric neighbors (TV 0.08 from proportional), an IIA violation no independent race captures — but a geometry-informed correlated race, with correlation length calibrated on a held-out intervention, predicts the redistribution to the simulation noise floor (TV 0.009, a ~9× error reduction).
• Temperature Transfer of Kinetic Surrogates — experiment complete. Code and figures in exp04_kramers_transfer. Langevin barrier-crossing with 12 disordered channels: Arrhenius rescaling halves the transfer error at kT 1.0→0.7 and →0.55; the noise law (Gumbel vs Gaussian) is second-order. The follow-up (exp05) is an informative negative: the correlated race leaves transfer error unchanged — correlation repairs deletion counterfactuals, not global parameter shifts, so deletion and transfer are orthogonal failure axes for kinetic surrogates.
• The Compressed Defect Ensemble of a Disordered Elastic Network — experiment complete, note in preparation. Code and figures in exp02_glass_cavity. All 784 single-site pinning responses of a random spring network from one inverse in 9 ms (∼870× over re-solving), 4,000 defect-pair interactions from 2×2 downdates in 35 ms, exact to 1e-13; exponential screening of the pair interaction recovered.
• A Fast Ability Transform for Correlated Fields — experiment complete, note in preparation. Code and figures in exp06_fast_correlated_transform. Factor-conditioned quadrature: $\Sigma \approx VV^\top + D$ by factor analysis, the multiplicative cavity applied conditionally at Gauss–Hermite / Sobol nodes. Exact given the factor model; error tracks the factor residual (7.5e-4 at k=8 on a kinked kernel); the single-deletion ensemble comes from one pass to 1e-16; the correlated-race counterfactual of experiment 3 reproduced deterministically. Documents two traps: eigen-truncation invents correlation, and geodesic squared-exponentials are not PSD on the circle.
• Race-Likelihood Watermark Detection — queued (spec and config in watermark_races). Does weighting token selections by the competitiveness of the underlying next-token race improve LLM watermark detection over green-token counting, particularly for short texts, weak watermarks, and misspecified proxy models?

Planned

• Softmax from Fast Mixing: Green–Kubo Corrections for Counterfactual Races — the flagship (Q7); central formula machine-verified on finite-state chains in experiment 7 (convergence slopes 0.99/1.99; one $(\bar\lambda, K)$ corrects every blocked subset; common mode = exact Luce at all $\varepsilon$). Common-clock proportional-hazard normal form; the killed-resolvent representation; softmax as the homogenized choice law of fast hidden kinetics; the Green–Kubo first correction, uniform over blocked subsets; finite-state exact examples; low-rank compression.
• The Runner-Up Principle for Counterfactual Races — the fastest rigorous paper (Q3); empirical half complete in experiment 8 (the Markov substitution resolvent, from pairs data alone, matches full-prefix accuracy on singleton, pair, and triple blocks). Winner-only nonidentifiability and the sharp partial-identification polytope; top-$(k{+}1)$ sufficiency for $k$-deletion counterfactuals; the Markov substitution resolvent; the ranked narrow-escape experiment.
• Harmonic Cavity Screening for Relaxed Defects — the physical cavity paper (Q1/Q4). True bond and vacancy perturbations (Woodbury, not pinning); vector elasticity; anharmonic relaxation benchmarks; top-K recall and saved relaxation calls as the metrics.

Related lineage

• Cotton, P. (2024). Schur Complementary Allocation. arXiv:2411.05807. The same Schur-complement object in portfolio construction; this project's sibling site is schur.microprediction.org.