Department of Earth, Planetary, and Space Sciences

Preface

Let a(n,k) be the number of 1324-avoiding permutations of length n with k inversions. Linusson and Verkama proved a(n,k) <= a(n+1,k) for k <= 2n-7. We study the obstruction beyond that line: the indecomposable, non-almost-decomposable residuals at fixed defect. Contracting maximal increasing consecutive runs reduces residuality to a quadratic equation on a finite family of skeletons. For every fixed defect, the eventual residual count is quadratic in n. We determine the leading coefficient uniformly by a generating function, prove inversion monotonicity through k <= 2n+6, and obtain regions whose width grows with n. Complete catalogue and rational-sum certificates for defects 11, 12, and 13 are supplied in the archival supplement. The unrestricted Claesson--Jelinek--Steingrimsson conjecture, the full residual polynomials, and the sharp global base-length bound remain open.

A Leech tree of order n is a tree on n vertices with positive integer edge weights whose n(n-1)/2 pairwise path-weights are exactly 1,2,...,n(n-1)/2. Leech (1975) found five, of orders 2,3,4,4,6; Taylor (1977) showed that the order must be a square or a square plus two; earlier searches excluded the admissible orders 9, 11 and 16, leaving 18 as the smallest open order. We prove that there is no Leech tree on 18 vertices, by an exhaustive generation of forced forests over all 123,867 trees of that order. The search visits 59,779,854,336 nodes and returns no survivor; its per-level counts were reproduced by independent runs and by a clean-room implementation written from the algorithm description alone. The same conclusion was reached independently and concurrently by Ghodsi, through a different reduction and a different trusted base. We also prove that no spider of order n>=5 is a Leech tree, by a finite exact analysis of the largest distances together with independently implemented checks. For the next admissible order n=25 we prove a structural bound rather than a non-existence result: deleting a leaf forces a block of consecutive rooted depths whose pairs are too crowded for the block to be long, so that diam(T-l)>=281 for every leaf, unconditionally. Four finite certified searches raise this to 285, reducing order 25 to fourteen values of one explicit finite normal form; we make no claim that order 25 is settled. Variants of the same engines settle neighbouring questions: M(11)=60 and M(12)=77 for the minimal distinct-distance trees of Calhoun et al., each with exactly two minimal trees; there is no modular Leech tree of order 9 or 11, while order 5 does admit them, contrary to a statement in the literature; and there are exactly six leaf-Leech trees with six leaves.

Magnetic field generation in giant planets and rapidly rotating stars produces a diverse range of field geometries, from large-scale dipole-dominated configurations to complex, small-scale multipolar structures. Earlier dynamo studies have suggested that multipolar solutions tend to arise when rotational effects become less dominant. We investigate the strength of nondipolar magnetic fields generated in systems dominated by rotation. 40 three-dimensional, spherical-shell dynamo simulations were carried out using the MagIC code, primarily made up of bistable pairs—simulations with the same control parameters that can settle in both a dipolar and nondipolar steady state regime. We use this suite of models to test how their magnetic field strength scales with heat flux and velocity. Our dynamo simulations produce magnetic fields with morphologies that fall on the two distinct branches, dipolar and nondipolar, yet have very similar convective velocities. The strength of the dipole component differs by an order of magnitude between the two regimes, when scaled as a function of driving power. However, their nondipolar magnetic field strengths are very similar. We conclude that when attempting to predict the magnetic field strength of rapidly rotating planets and stars, one cannot assume that it will have a dipole-dominated geometry. In particular, the amplitude of the dipole component is expected to be an order of magnitude smaller in the nondipolar regime.

The role of active faults in driving rock uplift is well known, but their influence on rock damage and erosional efficiency remains unclear globally. Using 1744 beryllium-10 (¹⁰Be)-derived erosion rates, we show that erosional efficiency is elevated on average within ~15 kilometers of a fault trace and decreases with distance, up to ~100 kilometers. Reverse faults and those longer than 140 kilometers show the strongest effects. This length scale of decay suggests that tectonic damage extends beyond fault-core pulverization on primary faults, possibly including fracturing or grain-to-grain contact weakening due to seismic shaking and distributed deformation on complex fault networks. Machine learning identified fault proximity as a dominant control on erosional efficiency, exceeding precipitation and lithology, particularly when a measure of seismic shaking is included. These findings indicate that active tectonics are associated with erosion not only through uplift but also by enhancing erosional efficiency through long-range rock damage.

We report on the observation and measurement of astrometry, photometry, morphology, and activity of the interstellar object 3I/ATLAS, also designated C/2025 N1 (ATLAS) with the NSF-DOE Vera C. Rubin Observatory. Comet 3I/ATLAS, the third known interstellar object, was discovered on UT 2025 July 1. Rubin Observatory had coincidentally collected images of the object’s region of the sky during routine commissioning. Facilitated by Rubin’s high resolution and large aperture, we successfully recovered object detections from Rubin observations spanning UT 2025 June 21 (10 days before discovery, when 3I/ATLAS was 4.5 au from the Sun) through the date of discovery, and we acquired additional images through UT 2025 July 20 as part of commissioning. We measure on-sky locations of 3I/ATLAS in Rubin ugrizy bands, with a typical precision of ∼70 mas, and briefly describe the reason this is coarser than our measured static source astrometric precision of ∼3 mas in Rubin images. We measure grizy magnitudes of 3I/ATLAS photometry at ∼0.01 mag precision, detecting no short-term photometric variability above 0.01 mag. We derive an estimated near-nucleus dust-to-nucleus scattering cross-sectional ratio of η ≳ 13 on UT 2025 July 2 based on Rubin photometry and an upper limit nucleus size computed from Hubble Space Telescope observations. We find Rubin colors of g − r = (0.657 ± 0.013) mag, r − i = (0.235 ± 0.018) mag, i − z = (0.147 ± 0.042) mag, and z − y = (0.047 ± 0.052) mag. These data represent the earliest observations of this object by a large (≳8 m class) telescope and illustrate the type of measurements (and discoveries) Rubin’s Legacy Survey of Space and Time will provide after it begins in early 2026.

Abstract High‐pressure rocks from subduction complexes are key records of the physical and chemical processes that operate on the subduction interface, but interpretation of these records requires accurate structural understanding of where they formed in the subduction zone and the mechanisms by which they were exhumed. We present new geologic mapping, outcrop‐scale observations, and geochronology from subduction‐zone assemblages at Punta Prieta Ridge on Cedros Island, Baja California (Mexico), to investigate the history of subduction, exhumation, and structural assembly of these rocks. The rocks of Punta Prieta Ridge are exposed in the footwalls of high‐ and low‐angle normal faults that carry Cretaceous forearc basin strata and attenuated mantle sections of the Cedros Island Ophiolite in their hangingwalls. The footwall rocks are subduction‐zone assemblages organized into distinct nappes that decrease in metamorphic grade and degree of strain structurally downward. Garnet‐amphibolite and blueschist blocks within the subduction complex yield 40 Ar/ 39 Ar cooling ages between 172 and 144 Ma and are hosted in siliciclastic rocks which yield detrital zircon maximum depositional ages between 92 and 72 Ma. Based on field evidence and age relationships, we interpret the occurrence of older higher‐grade blocks in younger clastic matrix to be depositional rather than the result of tectonic mixing. We then present a model for their exhumation and assembly via multiple cycles of extensional unroofing of the subduction complex and sedimentary recycling of high‐pressure rocks back into the subduction trench. We conclude by comparing the record of subduction on Cedros Island to other parts of the Cordillera. Key Points Subduction complex rocks are exhumed in the footwalls of normal faults beneath forearc basin strata and attenuated mantle High‐pressure blocks record 40 Ar/ 39 Ar ages from 172 to 144 Ma and are hosted in much younger siliciclastic matrix (ca. 92 to 72 Ma) Blocks were assembled via multiple cycles of extension and sedimentary recycling back into the subduction trench

Improved understanding of hydroclimatic drivers in water-stressed regions enables more accurate forecasting of future climate change impacts. Lake Bonneville was the largest Pleistocene lake in western North America, with a maximum surface area of ~52,000 km², before shrinking markedly to become the modern Great Salt Lake. After more than a century of study, the balance between enhanced precipitation and reduced evaporation as drivers of lake growth continues to be debated. Multiple studies identify precipitation as the main factor associated with the highest lake levels, but most proxies provide an estimate of net evaporation and cannot independently resolve precipitation from evaporation. Therefore, factors associated with lake size, growth, and retreat remain uncertain. This study uses the thermodynamically based carbonate clumped isotope geothermometer to estimate temperature, evaporation, and precipitation at Lake Bonneville from 23 to 16 thousand years ago (ka). Clumped isotope derived constraints on hydroclimate are also applied to assess the accuracy of regional climate model outputs. During transgressive and open phases of the lake, we find that regional and large-scale precipitation delivery were the driving factors of lake expansion. In contrast, at its maximum extent (~17.5 ka), Lake Bonneville was maintained via suppressed evaporation rates at 50% relative to modern while precipitation rates were similar to modern levels.