Retrieval shapes how language models access and ground knowledge in retrieval-augmented generation (RAG). In historical research, the target is often not an arbitrary relevant passage, but the exact record for a specific regnal month, where temporal consistency matters as much as topical relevance. This is especially challenging for Classical Chinese annals, where time is expressed through terse, implicit, non-Gregorian reign phrases that must be interpreted from surrounding context, so semantically plausible evidence can still be temporally invalid. We introduce \textbf{ChunQiuTR}, a time-keyed retrieval benchmark built from the \textit{Spring and Autumn Annals} and its exegetical tradition. ChunQiuTR organizes records by month-level reign keys and includes chrono-near confounders that mirror realistic retrieval failures. We further propose \textbf{CTD} (Calendrical Temporal Dual-encoder), a time-aware dual-encoder that combines Fourier-based absolute calendrical context with relative offset biasing. Experiments show consistent gains over strong semantic dual-encoder baselines under time-keyed evaluation, supporting retrieval-time temporal consistency as a key prerequisite for fai
We study non-Birkhoff periodic orbits in symmetric convex planar billiards. Our main result provides a quantitative criterion for the existence of such orbits with prescribed minimal period, rotation number, and spatiotemporal symmetry. We exploit this criterion to find sufficient conditions for a symmetric billiard to possess infinitely many non-Birkhoff periodic orbits. It follows that arbitrarily small analytical perturbations of the circular billiard have non-Birkhoff periodic orbits of any rational rotation number and with arbitrarily long periods. We also generalize a known result for elliptical billiards to other $\mathbb{D}_2$-symmetric billiards. Lastly, we provide Matlab codes which can be used to numerically compute and visualize the non-Birkhoff periodic orbits whose existence we prove analytically.
Inspired by the Movshev-Mason-Skinner Cauchy-Riemann (CR) ambitwistor approach, we provide a rigorous yet elementary construction of a twisted CR holomorphic Chern-Simons action on CR ambitwistor space for maximally supersymmetric Yang-Mills theory on four-dimensional Euclidean space. The key ingredient in our discussion is the homotopy algebraic perspective on perturbative quantum field theory. Using this technology, we show that both theories are semi-classically equivalent, that is, we construct a quasi-isomorphism between the cyclic $L_\infty$-algebras governing both field theories. This confirms a conjecture from the literature. Furthermore, we also show that the Yang-Mills action is obtained by integrating out an infinite tower of auxiliary fields in the Chern-Simons action, that is, the two theories are related by homotopy transfer. Given its simplicity, this Chern-Simons action should form a fruitful starting point for analysing perturbative properties of Yang-Mills theory.
In this note we focus on the defect of singular plane curve that was recently introduced by Dimca. Roughly speaking, the defect of a reduced plane curve measures the discrepancy from the property of being a free curve. We find some lower-bound on the defect for certain classes of irreducible plane curves admitting nodes, ordinary cusps and ordinary triple points. The main result of the note tells us that reduced simply singular plane curves with sufficiently high Arnold exponents are never free.
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert spaces, and little is known about its variant on real Hilbert spaces. In this article we study positive maps acting on a full matrix algebra over the reals, pointing out a number of fundamental differences with the complex case and discussing their implications in quantum information. We provide a necessary and sufficient condition for a real map to admit a positive complexification, and connect the existence of positive maps with non-positive complexification with the existence of mixed states that are entangled in real Hilbert space quantum mechanics, but separable in the complex version, providing explicit examples both for the maps and for the states. Finally, we discuss entanglement breaking and PPT maps, and we show that a straightforward real version of the PPT-squared conjecture is false even in dimension 2. Nevertheless, we show that the original PPT-squared conjecture implies a different conjecture for real maps, in which the PPT property is
From quantum mechanical first principles only, we rigorously study the time-evolution of a $N$-level atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at thermal equilibrium (reservoir). In particular, we establish the relation between the full dynamics of the compound system and the effective dynamics for the $N$-level atom, which is studied in detail in [Bru-de Siqueira Pedra-Westrich, Annales Henri Poincaré, 13(6):1305-1370, 2012]. Together with [Bru-de Siqueira Pedra-Westrich, Annales Henri Poincaré, 13(6):1305-1370, 2012] the present paper yields a purely microscopic theory of optical pumping in laser physics. The model we consider is general enough to describe gauge invariant atom-reservoir interactions.
A historical record of a seismic tsunami is identified in the Irish annals for October 720 (all dates herein CE). It is contained in the earliest stratum of the annals, which survives in the form of a handful of iterated scribal copies of the foundational text of the tradition. This was compiled by the contemporary observation of noteworthy events for the years c. 563-740 at the monastery of Iona in the Scottish Hebrides. The 720 event is close outside the 2$σ$ radiocarbon terminus ante quem date ranges for tsunami deposits identified at Dury Voe (530-660) and Basta Voe (430-650) in the Shetland Isles, and is identified as a candidate progenitor. The possibility of the existence of associated tsunami deposits in Scotland or on the north coast of Ireland is highlighted.
Pre-print of a publication in "Annales mathématiques du Qu{é}bec". Let $k$ be a totally real number field and let $k_\infty$ be its cyclotomic $\mathbb{Z}_p$-extension for $p$ totally split in $k$. This text completes our article entitled: "Approche $p$-adique de la conjecture de Greenberg pour les corps totalement réels" (Annales Mathématiques Blaise Pascal 2017), by means of heuristics on the $p$-adic behavior of the norms, in $k_n/k$, of the ideals in $k_\infty$ ; indeed, this conjecture (on the nullity of the invariants $λ$ et $μ$ of Iwasawa) depends of images in the torsion group ${\mathcal T}_k$ of the Galois group of the maximal abelian $p$-ramified pro-$p$-extension of $k$, thus of Artin symbols in a finite extension $F/k$ obtained by Galois descent of ${\mathcal T}_k$. An assumption of distribution of these norms implies $λ=μ=0$. Several statistics and numerical examples in the quadratic case confirm the probable exactness of such properties which constitute the fundamental obstruction for a proof of Greenberg's conjecture in the sole context of Iwasawa's theory.
This paper deals with several issues concerning the algebraic quantization of the real Proca field in a globally hyperbolic spacetime and the definition and existence of Hadamard states for that field. In particular, extending previous work, we construct the so-called Møller $*$-isomorphism between the algebras of Proca observables on paracausally related spacetimes, proving that the pullback of these isomorphisms preserves the Hadamard property of corresponding quasifree states defined on the two spacetimes. Then, we pull-back a natural Hadamard state constructed on ultrastatic spacetimes of bounded geometry, along this $*$-isomorphism, to obtain a Hadamard state on a general globally hyperbolic spacetime. We conclude the paper, by comparing the definition of a Hadamard state, here given in terms of wavefront set, with the one proposed by Fewster and Pfenning, which makes use of a supplementary Klein-Gordon Hadamard form. We establish an (almost) complete equivalence of the two definitions.
Astronomers may have witnessed one of the rarest and most dramatic cosmic events ever seen: a long-sought intermediate-mass black hole ripping apart a dense white dwarf star and devouring it。 The Einstein Probe space telescope caught the explosion in its earliest moments, revealing an unusual sequence of intense X-ray flashes unlike anything seen i
A surprisingly simple fuel modification could help tackle one of diesel engines’ biggest problems: pollution。 Researchers reviewing studies from around the world found that mixing small amounts of water into diesel fuel can dramatically reduce harmful emissions, including nitrogen oxides and soot, while maintaining or even improving engine efficien
Researchers have created quantum control techniques that can make a system appear to run backward in time。 By precisely managing quantum measurements, they can reshape the system's arrow of time and even harvest energy from the measurement process itself。 The breakthrough could lead to more powerful quantum computers, quantum batteries, and other a
The race to build data centers in space is gaining momentum as AI drives unprecedented demand for computing power。 Orbital facilities could tap into abundant solar energy and avoid many of the environmental challenges faced on Earth。 Yet space remains a harsh and expensive place to operate, with major hurdles including cooling, maintenance, radiati
A major breakthrough in quantum technology has turned magnons, tiny magnetic waves once considered too short-lived for practical use, into promising carriers of quantum information。 Researchers extended their lifetime by nearly 100 times, reaching up to 18 microseconds, and discovered that the main limitation is not a law of physics but the purity
NASA’s Lucy spacecraft discovered that asteroid Donaldjohanson is a wobbling, peanut-shaped relic born from a violent collision and slowly reshaped by the subtle force of sunlight。 It also carries traces of ancient water, making it an important clue to the solar system’s mysterious past
Scientists have found that staple-shaped particles can tangle together to create a material that is both strong and flexible。 Unlike conventional materials, these particles can be locked into a sturdy structure or rapidly unraveled using vibrations。 The unusual behavior could open the door to recyclable buildings, reconfigurable structures, and eve
Researchers have shown that ultracold atoms can be driven into a strange new quantum state called a fractional Fermi sea, where particles organize themselves in unexpected ways。 The discovery points to a new phase of matter that goes beyond established quantum theories and could expand the possibilities of quantum simulation
A newly proposed quantum sensing technique could make it much easier to identify one of physics’ newest and most intriguing classes of magnets: altermagnets。 These unusual materials, discovered only a few years ago, appear to combine the speed and efficiency of antiferromagnets with some of the useful electronic properties of traditional magnets, m