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Oxygen is the most abundant terrestrial element and is found in a variety of materials, but still wanting is a universal theory for the stability and structural organization it confers. Herein, a computational molecular orbital analysis elucidates the structure, stability, and cooperative bonding of α-quartz silica (SiO 2 ). Despite geminal oxygen-oxygen distances of 2.61–2.64 Å, silica model complexes exhibit anomalously large O-O bond orders (Mulliken, Wiberg, Mayer) that increase with increasing cluster size—as the silicon-oxygen bond orders decrease. The average O-O bond order in bulk silica computes to 0.47 while that for Si-O computes to 0.64. Thereby, for each silicate tetrahedron, the six O-O bonds employ 52% (5.61 electrons) of the valence electrons, while the four Si-O bonds employ 48% (5.12 electrons), rendering the O-O bond the most abundant bond in the Earth’s crust. The isodesmic deconstruction of silica clusters reveals cooperative O-O bonding with an O-O bond dissociation energy of 4.4 kcal/mol. These unorthodox, long covalent bonds are rationalized by an excess of O 2 p –O 2 p bonding versus anti-bonding interactions within the valence molecular orbitals of the SiO 4 unit (48 vs. 24) and the Si 6 O 6 ring (90 vs. 18). Within quartz silica, oxygen 2 p orbitals contort and organize to avoid molecular orbital nodes, inducing the chirality of silica and resulting in Möbius aromatic Si 6 O 6 rings, the most prevalent form of aromaticity on Earth. This long covalent bond theory (LCBT) relocates one-third of Earth’s valence electrons and indicates that non-canonical O-O bonds play a subtle, but crucial role in the structure and stability of Earth’s most abundant material. 

Direct observations of the oceans acquired on oceanographic research ships operated across the international community support fundamental research into the many disciplines of ocean science and provide essential information for monitoring the health of the oceans. A comprehensive knowledge base is needed to support the responsible stewardship of the oceans with easy access to all data acquired globally. In the United States, the multidisciplinary shipboard sensor data routinely acquired each year on the fleet of coastal, regional and global ranging vessels supporting academic marine research are managed by the Rolling Deck to Repository (R2R, rvdata.us) program. With over a decade of operations, the R2R program has developed a robust routinized system to transform diverse data contributions from different marine data providers into a standardized and comprehensive collection of global-ranging observations of marine atmosphere, ocean, seafloor and subseafloor properties that is openly available to the international research community. In this article we describe the elements and framework of the R2R program and the services provided. To manage all expeditions conducted annually, a fleet-wide approach has been developed using data distributions submitted from marine operators with a data management workflow designed to maximize automation of data curation. Other design goals are to improve the completeness and consistency of the data and metadata archived, to support data citability, provenance tracking and interoperable data access aligned with FAIR (findable, accessible, interoperable, reusable) recommendations, and to facilitate delivery of data from the fleet for global data syntheses. Findings from a collection-level review of changes in data acquisition practices and quality over the past decade are presented. Lessons learned from R2R operations are also discussed including the benefits of designing data curation around the routine practices of data providers, approaches for ensuring preservation of a more complete data collection with a high level of FAIRness, and the opportunities for homogenization of datasets from the fleet so that they can support the broadest re-use of data across a diverse user community. 

Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in GL(n,Z). We compare the strengths of various methods to sample random elements of GL(n,Z), finding some are stronger than others with respect to the problem of recognizing rotations of the Zn lattice. In particular, the standard algorithm of multiplying unipotent generators together (as implemented in Magma’s RandomSLnZ command) generates instances of this last problem which can be efficiently broken, even in dimensions nearing 1,500. Likewise, we find that the random basis generation method in one of the NIST Post-Quantum Cryptography competition submissions (DRS) generates instances which can be efficiently broken, even at its 256-bit security settings. Other random basis generation algorithms (some older, some newer) are described which appear to be much stronger. 

It is well-known that there are automorphic eigenfunctions on SL(2,Z)∖SL(2,R)/SO(2,R)—such as the classical j-function—that have exponential growth and have exponentially growing Fourier coefficients (e.g., negative powers of q=e2πiz, or an I-Bessel function). We show that this phenomenon does not occur on the quotient SL(3,Z)∖SL(3,R)/SO(3,R) and eigenvalues in general position (a removable technical assumption). More precisely, if such an automorphic eigenfunction has at most exponential growth, it cannot have non-decaying Whittaker functions in its Fourier expansion. This confirms part of a conjecture of Miatello and Wallach, who assert all automorphic eigenfunctions on this quotient (among other rank ≥2 examples) always have moderate growth. We additionally confirm their conjecture under certain natural hypotheses, such as the absolute convergence of the eigenfunction’s Fourier expansion.