September 2026

We prove the classical Lonely Runner assertion for an infinite family of fifteen-runner configurations. If the integer speeds, in a suitable labeling, form a fifteen-term arithmetic progression modulo an integer m >= 900 with invertible common difference, every runner is at some time at least 1/15 from all the others....

Evaluation systems often screen candidates before the conditions in which those candidates will succeed are known. When screening and downstream matching are separated, channel-marginal scoring can reject candidates whose value would become high after later information reveals where they fit. This paper studies the design of such staged systems. Blackwell’s...

We formulate a residual-and-information framework for continuous quantum measurement in which non-Markovian record history is represented by an exact anchored accumulation and conditional measurement ambiguity is represented by a residual whose zero set is the extremal record manifold. The construction is deliberately layered on established quantum instruments, nondemolition filtering, and...