Research
Research
Research
Research
40,031+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
To couple many independent modes from free space to on chip, the key challenge is not enhancing the many necessary coupling rates (scattering-matrix elements) between targeted mode pairs. Instead, the…
For three-dimensional (3D) magnetic objects with linear size $L$ exceeding a few exchange lengths, the micromagnetic state exhibits pronounced informational sparsity: low-dimensional, high-gradient re…
Primates exhibit a robust deviation from canonical allometric scaling: at fixed body mass, their lifespans exceed those of non-primate mammals by factors of two to three. A rhesus macaque (8 kg) lives…
Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for c…
Lattice reduction smooths the Gram-Schmidt profile, and we use majorization to describe the local swap mechanism behind that smoothing. In this language, each non-degenerate Lov\'asz swap acts as a T-…
Exponential growth in the scale of modern foundation models has led to the widespread adoption of Low-Rank Adaptation (LoRA) as a parameter-efficient fine-tuning technique. However, standard LoRA impl…
Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least $4.1~\mathrm{dB}$ across this range…
Open-source projects often rely on a small group of highly active contributors known as hero developers. Prior work shows that hero developers are common in many OSS and enterprise projects, yet who q…
Crowds have long held a paradoxical place in the human imagination, feared for their destructive potential yet essential for collective expression. This tension was tragically manifested in the 1919 J…
MAX phases (M$_{n+1}$AX$_n$), precursors to MXenes, span a vast compositional space, motivating efficient computational screening for synthesisable candidates. We employ CrystaLLM$-\pi$, a large langu…
Let $k\in\mathbb{N}$. Wigert's divisor function $d^{\left(\frac{1}{k}\right)}(j)$ counts the number of representations of $j$ of the form $m^k+mn$ with $m\geq1 , n\geq0$. Let $\mathcal{F}_k(s)$ denote…
Accurately linking microscopic energy deposition from ionizing radiation to emergent biological outcomes remains a central challenge in radiobiological modelling, particularly when stochastic damage i…
News consumption behavior is shaped by the coupling between temporal dynamics and content selection. This study proposes a multi-scale temporal-content framework and validates it on two large real-wor…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the correspond…
We compute exact finite-rank BPS generating functions for the fermionic matrix model with single-trace supercharge $Q_p=\operatorname{tr}(\Psi^p)$ at $(p,N)=(5,3),(5,4),(5,5),(7,4)$, together with par…
Large-language-models (LLMs) demonstrate enormous utility in long-context tasks which require processing prompts that consist of tens to hundreds of thousands of tokens. However, existing LLM training…
IRAS 13224-3809 is one of the most intensively studied narrow-line Seyfert 1 galaxies, with a rich literature reporting diverse and sometimes contrasting interpretations of its complex X-ray spectra a…
Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential $T$-count scaling in stabilizer-rank approaches, and p…
The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxatio…
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