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1. Exact null octagon

   https://doi.org/10.1007/JHEP05(2020)070  

   Belitsky, A.V.; Korchemsky, G.P. (May 2020, Journal of High Energy Physics)
2. Quantitative null-cobordism

   https://doi.org/10.1090/jams/903  

   Chambers, Gregory R.; Dotterrer, Dominic; Manin, Fedor; Weinberger, Shmuel (October 2018, Journal of the American Mathematical Society)
3. Bridging time across null horizons

   https://doi.org/10.1007/s10714-025-03410-4  

   Zenginoğlu, Anıl (April 2025, General Relativity and Gravitation)

   Abstract General relativity, as a diffeomorphism-invariant theory, allows the description of physical phenomena in a wide variety of coordinate systems. In the presence of boundaries, such as event horizons and null infinity, time coordinates must be carefully adapted to the global causal structure of spacetime to ensure a computationally efficient description. Horizon-penetrating time is used to describe the dynamics of infalling matter and radiation across the event horizon, while hyperboloidal time is used to study the propagation of radiation toward the idealized observer at null infinity. In this paper, we explore the historical and mathematical connection between horizon-penetrating and hyperboloidal time coordinates, arguing that both classes of coordinates are simply regular choices of time across null horizons. We review the height-function formalism in stationary spacetimes, providing examples that may be useful in computations, such as source-adapted foliations or Fefferman–Graham–Bondi coordinates near null infinity. We discuss bridges connecting the boundaries of spacetime through a time hypersurface across null horizons, including the event horizon, null infinity, and the cosmological horizon. 

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4. Randomisation inference beyond the sharp null: bounded null hypotheses and quantiles of individual treatment effects

   https://doi.org/10.1093/jrsssb/qkad080  

   Caughey, Devin; Dafoe, Allan; Li, Xinran; Miratrix, Luke (August 2023, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract Randomisation inference (RI) is typically interpreted as testing Fisher’s ‘sharp’ null hypothesis that all unit-level effects are exactly zero. This hypothesis is often criticised as restrictive and implausible, making its rejection scientifically uninteresting. We show, however, that many randomisation tests are also valid for a ‘bounded’ null hypothesis under which the unit-level effects are all non-positive (or all non-negative) but are otherwise heterogeneous. In addition to being more plausible a priori, bounded nulls are closely related to substantively important concepts such as monotonicity and Pareto efficiency. Reinterpreting RI in this way expands the range of inferences possible in this framework. We show that exact confidence intervals for the maximum (or minimum) unit-level effect can be obtained by inverting tests for a sequence of bounded nulls. We also generalise RI to cover inference for quantiles of the individual effect distribution as well as for the proportion of individual effects larger (or smaller) than a given threshold. The proposed confidence intervals for all effect quantiles are simultaneously valid, in the sense that no correction for multiple analyses is required. In sum, our reinterpretation and generalisation provide a broader justification for randomisation tests and a basis for exact non-parametric inference for effect quantiles. 

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5. Null-homotopic knots have Property R

   https://doi.org/10.1017/S0305004123000129  

   NI, YI (July 2023, Mathematical Proceedings of the Cambridge Philosophical Society)

   Abstract We prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that $Y-K$ does not have an $$S^1\times S^2$$ summand, then the zero surgery on K does not have an $$S^1\times S^2$$ summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere. 

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