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The magnesium-to-calcium ratio measured on benthic foraminiferal species (Mg/Cabf) is a commonly used proxy for reconstructing deep-ocean temperatures. However, its application over the geological record can be challenging, mostly due to non-thermal effects that influence Mg2+ incorporation into the calcite lattice. Previous work showed that the deep-sea carbonate chemistry, such as the carbonate ion saturation ([CO32-]) or the calcite saturation state (Ωcalcite), can reduce the Mg/Cabf sensitivity to temperature. In addition, interspecies element/Ca offsets complicate the use of multiple benthic foraminiferal species in the same samples. In this study, we present downcore measurements of Mg/Cabf and Sr-B-Li/Cabf to reconstruct temperature and carbonate chemistry from ~23 to ~76 Ma. We analyzed element/Ca ratios (89 samples) in multiple benthic foraminiferal species (Cibicidoides hyphalus, C. mundulus, C. praemundulus, C. proprius, C. pseudoperlucidus, C. velascoensis, Nuttallides umbonifera, N. truempyi, O. umbonatus, P. costata, P. renzi, S. beccariiformis) in samples located at different paleodepths in the Atlantic Ocean and spanning the Late Cretaceous and Paleogene. Benthic foraminiferal element/Ca data were collected using Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). Test preservation and contamination were assessed by measuring test Al-Mn-Si-Fe/Ca. Selected specimens were also analyzed using a Scanning Electron Microscope. The statistical treatment of our data shows that the correlation between Mg/Cabf and B/Cabf is very weak (Spearman’s ρ=0.01), whereas Mg/Ca and Sr/Ca show a moderate correlation (ρ=0.4). The strongest relationship is observed between Mg/Ca and Li/Ca (ρ= 0.7). Linear regression analysis demonstrates that C. hyphalus, C. praemundulus, N. truempyi, and S. beccariiformis present statistically significant correlations (p-value <0.05) with O. umbonatus, with R2 values ranging from 0.56 (S. beccariiformis) to 0.76 (C. hyphalus). The element/Ca variability among species exhibits a paleodepth gradient, with sites located at 3000-3500 m showing lower element/Ca compared to sites at 2300–2400 m and 1000–1400 m within time slices. The moderate correlation between Mg/Cabf and Sr-Li/Cabf, alongside the observed paleodepth element/Ca gradient, indicates that interspecies element/Ca variability is likely influenced by the depth-related variation in Ωcalcite. Overall, the data collected in this study will improve our ability to reconstruct deep-sea temperature and Ωcalcite in the Late Cretaceous and Paleogene. In addition, we show that the application of species-specific correction factors can result in trace element records that can be evaluated using coretop O. umbonatus calibrations, thus providing a method of reconstructing deep ocean temperature and saturation state in the absence of extant species. 

Benthic foraminiferal Mg/Ca and Mg/Li are often used to reconstruct deep-sea temperatures, whereas Sr/Ca and B/Ca are proxies used to estimate past seawater carbonate chemistry. Thus, these geochemical proxies are essential to investigating past oceanic environmental conditions. However, their interpretation remains challenging because the influence of additional variables on element/Ca of the benthic foraminiferal calcite is still not fully understood. To address this gap, we compiled published and unpublished element/Ca coretop datasets for multiple benthic foraminiferal species (Cibicidoides mundulus, C. pachyderma, Lobatula wuellerstorfi, Oridorsalis umbonatus, Nuttallides umbonifera and Uvigerina spp.). We reanalyzed these datasets to determine the sensitivity of each species’ Mg/Ca, Mg/Li, Sr/Ca, and B/Ca to in situ temperature and calcite saturation state (Ωcalcite), simultaneously using a multivariate linear regression analysis. Although we also explored models including dissolved inorganic carbon (DIC) and salinity, these parameters did not improve the explained variance in the element/Ca dataset and were therefore not included in the linear regression analysis. Overall, our results indicate that, compared to previous studies, the Mg/Ca sensitivity to temperature is reduced when the Ωcalcite is included in the regression analysis, whereas Mg/Li yields more precise and accurate temperature reconstruction with no significant influence from Ωcalcite. In addition, Sr/Ca and B/Ca are primarily controlled by Ωcalcite across species, although C. pachyderma Sr/Ca also exhibits a temperature influence. We further demonstrate that, based on the coretop analysis, the accuracy and precision of temperature and carbonate chemistry reconstructions depend on the species-specific calibrations. Finally, based on our multivariate regression results, we developed a user-friendly processing software (ElCarBenthic) that can be used to reconstruct deep-sea temperatures and the carbonate chemistry by combining benthic foraminiferal Mg/Ca or Mg/Li with Sr/Ca or B/Ca measurements, while fully propagating reconstruction uncertainties. 

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Abstract We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the$$E_{8}$$ $E_8$subfactor on a noncommutative 3-torus, and of$$\text {PSU}(2)_{15}$$ $\text{PSU}{\left(2\right)}_{15}$on a noncommutative 4-torus. 

Though Large Language Models (LLMs) have demonstrated remarkable capabilities, they are still prone to outputting falsehoods using seemingly persuasive language. Many recent works attempt to address this problem by using LLMs in a framework where a single seed prompt results in a series of interactions involving augmented prompts with an otherwise unchanged LLM, and the results are aggregated with a goal of producing a more reliable output. We consider the replicability and generalizability of evaluations of inference-time methods intended to improve the reliability of responses from a base LLMs. We survey how methods have been evaluated in the literature and find a great variety of benchmarks and models in use. Motivated by this, we conduct our own evaluation to evaluate the effectiveness of a few methods across a range of benchmarks and models. Our evaluation reveals that while these techniques show promise in improving reliability, there is still significant variability in performance across different domains and tasks, and methods that show substantial improvements on weaker base models often do not improve reliability for better base models. 

Initial release 

The Mg/Ca ratio of benthic foraminifera (Mg/Cabf) is a widely used proxy for deep ocean temperature. However, previous work has shown that the seawater carbonate ion saturation (D[CO32-]) can also influence the Mg/Cabf signal in some species. To test this hypothesis, we measured Mg/Cabf and Li-B-Sr/Cabf as a proxy for D[CO32-]. We analyzed element/Ca ratios in multiple benthic foraminiferal species (Cibicidoides mundulus, C. pachyderma, C. praemundulus, C. wuellerstorfi, Nuttallides umbonifera, Oridorsalis umbonatus, and Planulina renzi) across a Neogene paleodepth transect (~1000-3500 m) in the Atlantic Ocean. Benthic foraminiferal element/Ca data were collected using a Laser Ablation Inductively Coupled Plasma Mass Spectrometer (LA-ICP-MS), with preservation and potential surface contamination assessed via Al-Mn-Si-Fe/Ca data and via Scanning Electron Microscopy (SEM) on selected specimens. The data allow us to assess interspecies offsets in Mg- Li-B-Sr/Cabf and to calculate correction factors that can be applied to normalize Neogene data to Cibicidoides spp., with the aim of developing an overall record of paleotemperature change that does not require the presence of a single species throughout the record. Element/Ca ratios show distinct patterns with paleodepth and age. Specifically, Mg/Cabf, Li/Cabf, and B/Cabf co-vary in Neogene samples, whereas Sr/Cabf varies independently of the other data. A multivariate model will be used to reconstruct temperature and D[CO32-] in the Neogene Atlantic Ocean using the data collected (normalized to Cibicidoides spp.).