arXiv preprints from January 1, 2026 through September 22, 2026 — 02:40:14 EST
Fang and Huang proved that every cancellative pair $(\mathcal{A},\mathcal{B})$ of families of subsets of $[n]$ satisfies $|\mathcal{A}|\cdot|\mathcal{B}|\leq(\frac{9}{4})^n$. Their proof uses entropy. We give a Fourier-analytic proof based on Lifshitz's one-sided noise operator $\mathrm{T}^{1/4\to1/2}$. The main tool is a near-$L^1$...
Searches for parity violation (PV) in the Universe's large-scale structure have recently been carried out using parity-odd modes of the galaxy 4-Point Correlation Function (4PCF). Here, we introduce a new estimator for a 3-Point Correlation Function (3PCF) that is sensitive to PV. The construction exploits the handedness of triangles...
We derive the two-loop anomalous dimension relevant for the resummation of subleading non-global and, for the first time, also clustering logarithms within the framework of effective field theory. Special emphasis is put on the choice of the renormalization scheme. We show that the modified minimal subtraction scheme is problematic...
We establish quantitative Parisi formulas and fluctuation bounds for the Sherrington-Kirkpatrick model at zero external field. In particular, using that the Parisi measure is supported on an interval, we show that for every fixed inverse temperature greater than one, the variance of the logarithmic partition function lies between...
Reconstructing the initial conditions (ICs) of the matter field for an observed volume gives a complete picture of that region's temporal evolution. IC reconstruction is common at low redshifts but largely unexplored during the epoch of reionization (EoR; $z\gtrsim 5$), partly due to difficulties modeling inhomogeneous cosmic...
We prove the Trudinger inequality with exponent $\frac{s}{s-1}$ for $M^{1,s}$ Sobolev spaces on metric measure spaces under the sole measure growth assumption $μ(B(x,r))\ge br^s$. This improves the previously known exponential integrability with power one. Our argument also yields sharp asymptotic bounds for the Sobolev constants as...
Synchronisation by noise for McKean--Vlasov stochastic differential equations is investigated. A transfer principle is introduced by which synchronisation by noise and diagonal mixing can be transferred from an associated limiting frozen-diffusion SDE to a genuinely law-dependent McKean--Vlasov SDE. The usefulness of this principle is...
Curriculum learning is governed by several coupled design choices---how difficulty is defined, how examples are ordered, how much exposure each level receives, and how quickly training moves across levels---making it hard to isolate what actually helps. We present Wasserstein curriculum paths, a simple transport-based framework that...
This is the first part of a program to construct hyperholomorphic families of boundary conditions for the Kapustin--Witten B-twist of the Langlands QFT, otherwise known as \textit{(BBB)-branes}. We define the category of quasi-algebraic sheaves over the Deligne moduli stack, which serves as an analog of the twistor space of Hitchin's...
The realization of the superconducting diode effect (SDE), characterized by non-reciprocal supercurrent, is a major step towards dissipationless logic circuits. A polarity-tunable superconducting diode with high diode efficiency primarily consists of Josephson-junction architectures that couple two superconducting regions via a weak...
We provide a pathwise proof of global-in-time well-posedness for the generalised KPZ equation in the full subcritical regime by an adaptation of the strategy recently applied to the generalised Parabolic Anderson Model in [ES26]. Since this strategy relies crucially on the assumption that control of the supremum norm is sufficient to...
FP8 Ozaki II emulates FP64 matrix multiplication by tensor-core products over a CRT residue system; converting the operands into residue planes (the deconstruction term in the Tensor-Memory Equilibrium model of the companion paper "FP8 is All You Need, Part 1") costs integer-pipe and memory resources before tensor instructions issue....
Combining search with function approximation has driven major advances in game-playing programs, making self-play algorithms more competitive than ever. Still, the computational overhead of the most popular methods, based on Monte Carlo Tree Search (MCTS), can be substantial. In this work, we investigate whether simpler methods remain...
Jones described how the Ising and Potts models from statistical mechanics give rise, with appropriate choices of Boltzmann weights, to invariants of an oriented link. The Boltzmann weights that Jones proposed, however, work only with a correction factor that he does not mention. We fill in the missing details in two different ways. We...
Extending standardized urban microcell (UMi) path loss (PL) models from the upper mid-band (FR3) to sub-terahertz (sub-THz) frequencies requires measurement-based comparisons spanning a wide spectral range within a unified framework. In this paper, we derive single- and multi-frequency omnidirectional PL models for UMi environments...
We show that one-way one-round quantum LOCAL algorithms cannot $4$-color directed cycles with high probability, even with unbounded local computation and quantum message length. This is the first lower bound in the high-probability quantum LOCAL setting that goes beyond the non-signaling and bounded-dependence models, exploiting the...
Large language models (LLMs) may abandon correct positions when users push back, exhibiting a failure mode known as sycophancy. Existing evaluations typically use short, pre-specified conversations and may therefore miss failures that emerge under sustained, adaptive disagreement. We introduce SPINE, a benchmark in which an LLM proxy...
We estimate optimal transport maps on an infinite-dimensional Hilbert space with a Gaussian reference measure, from noisy paired observations. A source draw is seen together with a noisy evaluation of its image, rather than through independent unpaired samples. The estimator is a cylindrical sieve of Cameron--Martin gradient maps,...
We present NRHJSur3dq8, a family of numerical-relativity (NR) surrogates for non-eccentric aligned-spin binary-black-hole waveforms inspired by an action-angle parameterization. The model provides both the dynamics: the Hamiltonian values, azimuthal action $J_φ(Φ)$, the orbital clock $τ(Φ)$ as functions of its phasing, and the...
As Large Language Model (LLM) agents increasingly automate offensive operations across the cyber kill chain, their efficacy in complex local post-exploitation tasks remains inadequately quantified. Among these, Linux privilege escalation is a key step between initial access and full system compromise. However, existing evaluations for...
Gravitational-wave searches do more than identify individual sources - they provide a way to infer the underlying astrophysical populations that produce them. Currently, Pulsar Timing Arrays (PTAs) constrain the supermassive black-hole binary (SMBHB) merger-rate density through both the stochastic gravitational-wave background (SGWB)...
Large Language Models (LLMs) often exhibit "Attention Sink" (AS) and the accompanying "Massive Activations" (MAs) at the initial position of a sequence. These phenomena frequently co-occur, and MAs can pose challenges for low-bit quantization. In this study, we analyze the factors underlying AS and MAs that emerge at the initial...
In recent years, smart contracts have become the backbone of decentralized applications (DApps), and off-chain systems such as bridges, wallets, and indexers rely heavily on event logs to track contract execution and state changes. However, the Ethereum Virtual Machine (EVM) does not validate or enforce event semantics, so logs can...
In this paper, we prove that for two cyclically ordered sequences of complex numbers of unit modulus $(ξ_j)_{j=1}^{n}$ and $(ζ_j)_{j=1}^{n}$ the inequality: $$\bigg|\sum_{m=1}^{n}(ξ_{m+1}-ξ_m)ζ_m\bigg|^2+ \bigg|\sum_{m=1}^{n}(ξ_{m+1}-ξ_m)ζ_m^{-1}\bigg|^2\leqslant 4n^2\sin^2\fracπ{n}$$ holds for $n\geqslant 4$. As a consequence, for...
The submillimeter band offers a complementary route to identifying electromagnetic counterparts of high-energy neutrinos, tracing relativistic transients and persistent dust-obscured galaxies. We present a pilot search combining JCMT/SCUBA-2 follow-up of IceCube events with catalog searches for bright high-redshift dusty systems....