Is it possible to induce an effective generalized uncertainty principle (GUP) emerging from geometry and reinterpret the gravitational GUP as the effective uncertainty relation induced by microscopic horizon geometry? More broadly, is it possible to develop a notion of quantum gravity emerging from geometry? We will give a positive answer, but with important caveats.

In conventional lasers, the emitters are typically incoherent, radiating photons independently; in superradiant lasers, many coherent emitters radiate photons collectively, but they essentially do not interact with each other. Here, we present the concept of quantum many-body lasers, in which the emitters interact coherently and radiate collectively. In this proof-of-concept study, we consider a cavity coupled to many pumped spin-1/2 emitters with all-to-all interaction. We find that the squeezing induced by the coherent many-body interaction can be transferred from the spins to photons through superradiant lasing. This work illustrates the concept of using a pumped quantum many-body system to generate bright quantum light with quantum correlations beyond conventional optical coherence, which can facilitate quantum technologies and the study of nonlinear optics in the quantum realm.

Money-back guarantees (MBGs) are features of pooled retirement income products that address bequest concerns by ensuring the initial premium is returned through lifetime payments or, upon early death, as a death benefit to the estate. This paper studies optimal retirement decumulation in an individual tontine account with an MBG overlay under international diversification and systematic longevity risk. The retiree chooses withdrawals and asset allocation dynamically to trade off expected total withdrawals (EW) against the Conditional Value-at-Risk (CVaR) of terminal wealth, subject to realistic investment constraints. The optimization is solved under a plan-to-live convention, while stochastic mortality affects outcomes through its impact on mortality credits at the pool level. We develop a neural-network based computational approach for the resulting high-dimensional, constrained control problem. The MBG is priced ex post under the induced EW--CVaR optimal policy via a simulation-based actuarial rule that combines expected guarantee costs with a prudential tail buffer. Using long-horizon historical return data expressed in real domestic-currency terms, we find that international diversification and longevity pooling jointly deliver the largest improvements in the EW--CVaR trade-off, while stochastic mortality shifts the frontier modestly in the expected direction. The optimal controls use foreign equity primarily as a state-dependent catch-up instrument, and implied MBG loads are driven mainly by tail outcomes (and the chosen prudential buffer) rather than by mean payouts.

Graphene-based systems have emerged as a rich platform for exploring emergent quantum phenomena-including superconductivity, magnetism, and correlated insulating behavior-arising from flat electronic bands that enhance many-body interactions. Realizing such flat bands has thus far relied primarily on moiré graphene superlattices or rhombohedral stacking graphene systems, both of which face challenges in reproducibility and tunability. Here, we introduce an artificial Kagome superlattice in bilayer graphene, engineered via nanopatterning of the dielectric substrate to create a precisely defined and electrostatically tunable periodic potential. Magnetotransport measurements reveal the emergence of a stack of correlated insulating states at moderate superlattice potentials, characteristic of strong electron-electron interactions within Kagome-induced flat bands. As temperature increases, these correlated gaps collapse, signaling the thermal suppression of interaction-driven states. Continuum-model calculations confirm the formation of multiple flat minibands and reproduce the observed evolution of band reconstruction. Our results establish dielectric-patterned graphene superlattices as a robust and controllable architecture for realizing flat-band-induced correlated phenomena beyond moiré systems.

Recent advances in image and signal processing have drawn on geometric function theory, particularly coefficient estimate problems. Motivated by their significance, we introduce a class of starlike functions related to a balloon-shaped domain \[ \mathcal{S}^*_{\mathcal{B}}= \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1}{1-\log(1+z)} := B(z); \; z \in \mathbb{D} \right\}, \] where $B(z)$ maps the unit disk $\mathbb{D}$ onto a balloon-shaped domain. This work establishes bounds for the second order Hankel determinants and second order Toeplitz determinants involving the initial coefficients, the logarithmic coefficients and the logarithmic coefficients of the inverse function for $f \in \mathcal{S}^*_{\mathcal{B}}$

This article defines multi-twisted Goppa (MTG) codes as subfield subcodes of duals of multi-twisted Reed-Solomon (MTRS) codes and examines their properties. We show that if $t$ is the degree of the MTG polynomial defining an MTG code, its minimum distance is at least $t + 1$ under certain conditions. Extending earlier methods limited to single twist at last position, we use the extended Euclidean algorithm to efficiently decode MTG codes with a single twist at any position, correcting up to $\left\lfloor \tfrac{t}{2} \right\rfloor$ errors. This decoding method highlights the practical potential of these codes within the Niederreiter public key cryptosystem (PKC). Furthermore, we establish that the Niederreiter PKC based on MTG codes is secure against partial key recovery attacks. Additionally, we also reduce the public key size by constructing quasi-cyclic MTG codes using a non-trivial automorphism group.

In order to manage electricity transmission and distribution it is now common practice for system operators to offer financial incentives that encourage large consumers to reduce energy usage during designated peak demand periods. For train operators on large rail networks it may be profitable -- with selected individual journeys -- to reduce energy usage during peak times and increase energy usage at other times rather than simply minimizing overall energy consumption. We will use classical methods of constrained optimization to find optimal driving strategies for a fleet of trains subject to limits on total energy consumption during specified intermediate time intervals but with no change to individual journey times. The proposed strategies can be used by a large rail organisation to reduce overall operating costs with only minimal disruption to existing schedules and with no changes to important departure and arrival times.

Notions of ordinal submodularity/supermodularity have been introduced and studied in the literature. We consider several classes of ordinally submodular functions defined on finite Boolean lattices and give characterizations of the set of minimizers of ordinally submodular functions.

Let $K\langle X_d\rangle$ be the free associative algebra of rank $d \geq 2$ over a field $K$. Lane in 1976 and Kharchenko in 1978 proved that the algebra of invariants $K\langle X_d\rangle^G$ is free for any subgroup $G \leq \text{GL}_d(K)$ and any field $K$. Later, Kharchenko introduced an additional action of the symmetric group $\text{Sym}(n)$ on the homogeneous component of degree $n$ of $K\langle X_d\rangle$, given by permuting the positions of the variables. This equips $K\langle X_d\rangle$ with the structure of a $(K\langle X_d\rangle,\circ)$-$S$-algebra. Then Koryukin showed that the algebra of invariants $K\langle X_d\rangle^G$ is finitely generated for every reductive group $G$ with respect to this action. In our paper we study the algebra $K\langle x_1,\ldots,x_d\rangle^{C_d}$ of invariants of the cyclic group $C_d$, $d\geq 2$, where $K$ is an arbitrary field of characteristic 0. We compute the Hilbert series of $K\langle x_1,\ldots,x_d \rangle^{C_d}$. When $K=\mathbb C$ we find a vector space basis of ${\mathbb C}\langle x_1,\ldots,x_d \rangle^{C_d}$ and explicitly describe the generators of ${\mathbb C}\langle x_1,\ldots,x_d \rangle^{C_d}$ as a free algebra. Moreover, we describe a finite generating set for the $S$-algebra $({\mathbb C}\langle x_1,\ldots,x_d \rangle^{C_d},\circ)$. We also transfer the results for $K=\mathbb C$ to the case of an arbitrary field of characteristic 0 for the $S$-algebra $(K\langle x_1,x_2,x_3 \rangle^{C_3},\circ)$ and find a minimal generating set for it as an $S$-algebra.

Let $V$ be a $2m$-dimensional symplectic space over an infinite field $K$. Let $\mathfrak{B}^{(f)}_{n,K}$ be the two-sided ideal of the Birman--Murakami--Wenzl algebra $\mathfrak{B}_{n,K}$ generated by $E_1E_3\cdots E_{2f-1}$ with $1\leq f\leq\left\lfloor \frac n2 \right\rfloor$. In this paper, using the diagram category of framed tangles and canonical basis, we prove that the natural homomorphism from $\mathfrak{B}_{n,K}/\mathfrak{B}^{(f)}_{n,K}$ to $ \mathrm{End}_{U_q(\mathfrak{sp}_{2m})}\left(V^{\otimes n}/\left(V^{\otimes n}\cdot \mathfrak{B}^{(f)}_{n,K}\right)\right)$ is always surjective.

We consider the eigenvalue problem $K x = λx$. Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operator $K$ with Green's kernels. By employing orthogonal and interpolatory projections at $2r+1$ collocation points (which are not necessarily Gauss points) onto an approximating space of piecewise even degree polynomials, we establish the superconvergence of eigenfunctions under iteration. The modified projection methods achieve a faster convergence rates compared to classical projection methods. The enhancement in convergence rate is verified by numerical examples.

Many attempts to introduce fundamental nonlocality into quantum (or classical) field theory are based on the assumption that exponentials of the d'Alembertian are positive-definite, so that these operators can be employed without engendering the Ostrogradskian instability associated with higher derivative Lagrangians. {\bf This assumption is false.} Working in the simple context of a 1-dimensional, point particle $q(t)$, I demonstrate that the equation $\exp[T^2 \tfrac{d^2}{dt^2}] q(t) = 0$ has an infinite number of rapidly oscillating, exponentially rising and falling solutions. This infinite kernel is in one-to-one correspondence with the ability to specify ``initial value data'' {\it arbitrarily} over {\it any} finite interval $t_1 < t < t_2$.

Operational disruptions in retail payments can induce behavioral responses that outlast technical recovery and may amplify liquidity stress. We propose a multi-agent model linking card payment outages to trust dynamics, channel avoidance, and threshold-gated withdrawals. Customers and merchants interact through repeated payment attempts, while customers additionally influence one another on a Watts-Strogatz small-world network. Customers update bounded memory variables capturing accumulated negative experience (scar) and perceived systemic risk (rumor), with merchants contributing persistent broadcast signals that may lag operational recovery. We prove that, under mild conditions on memory persistence and threshold gating, aggregate withdrawal pressure can peak strictly after the outage nadir, including during the recovery phase. Simulations reproduce behavioral hysteresis and confirm delayed peaks of outflows. We further study payment substitution via instant transfer: substitution consistently reduces peak avoidance, yet its effect on cumulative outflows is non-monotonic under realistic merchant broadcast persistence. Robustness experiments across random seeds show stable qualitative behavior. The model highlights why "status green" is not equivalent to risk resolution and motivates incident response strategies that address perception, merchant messaging, and post-recovery communication in addition to technical remediation.

To study the zeros of octonionic polynomials, we generalize the well-known Enestrom-Kakeya Theorem to the case of octonions. In this paper, we first deal with octonionic polynomials with nonnegative and monotonic coefficients, and prove that its zero set is contained within the closed sphere of octonion space. Then, we also consider the octonionic polynomials which the coefficients muduli is monotonic and the real parts of the coefficients is monotonic respectively, and get some results.

Photochromic materials enable dynamic optical modulation through reversible transitions between distinct absorption states, with broad potential for smart windows, adaptive optics, and reconfigurable photonic devices. Micron-scale photochromic hybrid films present a particularly attractive platform for these applications, combining straightforward preparation with substantial optical modulation and scalability for high-volume fabrication. However, rational design of such films remains fundamentally constrained by the absence of well-defined optical constants. Unlike homogeneous thin films, micron-scale hybrid photochromic materials comprise active particles dispersed non-uniformly within polymer matrices. Conventional first-principles electromagnetic simulations face substantial computational costs and discrepancies between simulated and experimental particle distributions. Here, we introduce a data-driven framework that extracts effective optical constants directly from minimal experimental transmittance measurements. Our dual-state effective model approximates the complex inhomogeneous photochromic layer as a compressed homogeneous medium characterized by pseudo-refractive indices and pseudo-extinction coefficients for both pristine and UV-irradiated states. Through systematic optimization against experimental data from tungsten oxide-polyvinylpyrrolidone hybrid films, we determine wavelength-dependent pseudo-optical constants and compression ratios that enable accurate prediction of optical modulation within the tested thickness range. Our methodology establishes a framework for engineering hybrid photochromic systems and demonstrates how data-driven modeling can overcome limitations in characterizing complex nanostructured materials.

When strain-rate sensitivity (SRS) is negative in metallic glasses, the material becomes weaker as the deformation rate increases, leading to accelerated plastic deformation and, eventually, catastrophic fracture. In this study, we elucidate the mechanism underlying the negative SRS using micromechanics-based kinetic Monte Carlo simulations that couple heterogeneous randomized shear transformation zone (STZ) models for metallic glasses. The model accounted for both the thermomechanical structural rejuvenation and relaxation of the energy barrier for thermal activation of STZs, incorporating a Kohlrausch-Williams-Watts (KWW)-type relaxation function. The present simulations systematically reproduce the dependence of flow stresses on strain rate, temperature, and the form of the relaxation function. The SRS tends to decrease at high strain rates and low temperatures in the simulations, and negative SRS appears when a compressed-exponential relaxation function is employed. Shear localization also appears; however, the conditions under which the observed localization emerges do not fully coincide with those leading to the negative SRS, leaving the dominant factor unclear. To clarify the dominant factor, we introduce a simplified theoretical model that reproduces flow stresses consistent with the simulation results. An analytical expression derived from the theoretical model reveals that negative SRS originates primarily from the temporal evolution of the activation barrier. Specifically, negative SRS arises when the timescale of external loading exceeds that of STZ relaxation.

In this study, we investigate the existence of traveling wave solutions for a SIR model on two-dimensional lattice. The existence of traveling waves is established within the framework of upper and lower solutions and the Schauder fixed-point theorem. Moreover, we construct a Lyapunov functional to analyze the asymptotic behavior of the traveling wave solutions. This is a challenging task due to the two-dimensional lattice structure.

If $X$ is a quasi-projective variety over a field $k$ and $ϕ$ a birational endomorphism of $X$ that is injective outside a closed subset of codimension $\geq 2$, we prove that $ϕ$ is an automorphism. This generalizes an old theorem of Ax and proves a conjecture of Miyanishi. A key step in our proof is a finiteness result on class groups, which is of interest in its own right.

Discovering the unknown governing equations of grid-connected inverters from external measurements holds significant attraction for analyzing modern inverter-intensive power systems. However, existing methods struggle to balance the identification of unmodeled nonlinearities with the preservation of physical consistency. To address this, this paper proposes a Physics-Informed Sparse Machine Learning (PISML) framework. The architecture integrates a sparse symbolic backbone to capture dominant model skeletons with a neural residual branch that compensates for complex nonlinear control logic. Meanwhile, a Jacobian-regularized physics-informed training mechanism is introduced to enforce multi-scale consistency including large/small-scale behaviors. Furthermore, by performing symbolic regression on the neural residual branch, PISML achieves a tractable mapping from black-box data to explicit control equations. Experimental results on a high-fidelity Hardware-in-the-Loop platform demonstrate the framework's superior performance. It not only achieves high-resolution identification by reducing error by over 340 times compared to baselines but also realizes the compression of heavy neural networks into compact explicit forms. This restores analytical tractability for rigorous stability analysis and reduces computational complexity by orders of magnitude. It also provides a unified pathway to convert structurally inaccessible devices into explicit mathematical models, enabling stability analysis of power systems with unknown inverter governing equations.

In this paper, we investigate the dynamics of an incompressible viscous Navier-Stokes fluid evolving above a one-dimensional flat surface. The fluid is subject to a uniform gravitational field and capillary forces acting along the free boundary. The interface between the fluid and the surrounding air is a free surface whose motion is driven by gravity, surface tension, and the fluid velocity field. The triple-phase intersections where the fluid, the air above the vessel, and the solid vessel wall meet are referred to as contact points, and the angles formed there are called contact angles. The model under consideration incorporates boundary conditions that allow for full motion of the contact points and dynamic contact angles. Under these conditions, \cite{Yang} established the existence of equilibrium configurations for the model. These equilibria consist of a quiescent fluid occupying a domain whose upper boundary can be represented as the graph of a function in polar coordinates, minimizing a gravity-capillary energy functional subject to a fixed mass constraint. The equilibrium contact angles may take any value in $(0,π)$ depending on the choice of capillary parameters. In the present work, we develop a framework of a priori estimates for this model. We prove that, for initial data sufficiently close to equilibrium, the system admits global solutions that converge exponentially fast to a (horizontally) shifted equilibrium state.

Field studies are irreplaceable but costly, time-consuming, and error-prone, which need careful preparation. Inspired by rapid-prototyping in manufacturing, we propose a fast, low-cost evaluation method using Vision-Language Model (VLM) personas to simulate outcomes comparable to field results. While LLMs show human-like reasoning and language capabilities, autonomous vehicle (AV)-pedestrian interaction requires spatial awareness, emotional empathy, and behavioral generation. This raises our research question: To what extent can VLM personas mimic human responses in field studies? We conducted parallel studies: 1) one real-world study with 20 participants, and 2) one video-study using 20 VLM personas, both on a street-crossing task. We compared their responses and interviewed five HCI researchers on potential applications. Results show that VLM personas mimic human response patterns (e.g., average crossing times of 5.25 s vs. 5.07 s) lack the behavioral variability and depth. They show promise for formative studies, field study preparation, and human data augmentation.

We study the implications of the existence of weak Zero-Knowledge (ZK) protocols for worst-case hard languages. These are protocols that have completeness, soundness, and zero-knowledge errors (denoted $ε_c$, $ε_s$, and $ε_z$, respectively) that might not be negligible. Under the assumption that there are worst-case hard languages in NP, we show the following: 1. If all languages in NP have NIZK proofs or arguments satisfying $ ε_c+ε_s+ ε_z < 1 $, then One-Way Functions (OWFs) exist. This covers all possible non-trivial values for these error rates. It additionally implies that if all languages in NP have such NIZK proofs and $ε_c$ is negligible, then they also have NIZK proofs where all errors are negligible. Previously, these results were known under the more restrictive condition $ ε_c+\sqrt{ε_s}+ε_z < 1 $ [Chakraborty et al., CRYPTO 2025]. 2. If all languages in NP have $k$-round public-coin ZK proofs or arguments satisfying $ ε_c+ε_s+(2k-1).ε_z < 1 $, then OWFs exist. 3. If, for some constant $k$, all languages in NP have $k$-round public-coin ZK proofs or arguments satisfying $ ε_c+ε_s+k.ε_z < 1 $, then infinitely-often OWFs exist.

We consider the single-source shortest paths problem on a directed graph with real-valued (possibly negative) edge weights and solve this problem in $n^{2+o(1)}$ time by refining the shortcutting procedure introduced in Li, Li, Rao, and Zhang (2026).

A string attractor of a string $T[1..|T|]$ is a set of positions $Γ$ of $T$ such that any substring $w$ of $T$ has an occurrence that crosses a position in $Γ$, i.e., there is a position $i$ such that $w = T[i..i+|w|-1]$ and the intersection $[i,i+|w|-1]\cap Γ$ is nonempty. The size of the smallest string attractor of Fibonacci words is known to be $2$. We completely characterize the set of all smallest string attractors of Fibonacci words, and show a recursive formula describing the $2^{n-4} + 2^{\lceil n/2 \rceil - 2}$ distinct position pairs that are the smallest string attractors of the $n$th Fibonacci word for $n \geq 7$. Similarly, the size of the smallest string attractor of period-doubling words is known to be $2$. We also completely characterize the set of all smallest string attractors of period-doubling words, and show a formula describing the two distinct position pairs that are the smallest string attractors of the $n$th period-doubling word for $n\geq 2$. Our results show that strings with the same smallest attractor size can have a drastically different number of distinct smallest attractors.

This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control forcing the solution rest at a time $T>0$, we need to establish the decay property of solutions for the system without control first. We have obtained decay estimates for the $L^\infty$-norm and the $H^1$-norm of solutions to the homogenous quasilinear parabolic equations. Notably, the decay of the $L^\infty$-norm requires no smallness condition on the initial data, whereas the decay of the $H^1$-norm requires that the $L^\infty$-norm remains small. Based on the decay estimates and maximum modulus estimate of solutions to quasilinear parabolic equations, together with the local null controllability of quasilinear parabolic equations under additive controls, we prove the null controllability of the quasilinear parabolic equations via multiplicative controls. As a byproduct, we also obtain the global null controllability for large time to the quasilinear parabolic equations via additive controls. Given that the controllability under multiplicative control is achieved over a long time horizon, we finally investigate the existence of time optimal control.

Probabilistic bits (p-bits) offer an energy-efficient hardware abstraction for stochastic optimization; however, existing p-bit-based simulated annealing accelerators suffer from poor scalability and limited support for fully connected graphs due to fan-out and memory overhead. This paper presents an energy-efficient FPGA architecture for stochastic simulated quantum annealing (SSQA) that addresses these challenges. The proposed design combines a spin-serial and replica-parallel update schedule with a dual-BRAM delay-line architecture, enabling scalable support for fully connected Ising models while eliminating fan-out growth in logic resources. By exploiting SSQA, the architecture achieves fast convergence using only final replica states, significantly reducing memory requirements compared to conventional p-bit-based annealers. Implemented on a Xilinx ZC706 FPGA, the proposed system solves an 800-node MAX-CUT benchmark and achieves up to 50% reduction in energy consumption and over 90\% reduction in logic resources compared with prior FPGA-based p-bit annealing architectures. These results demonstrate the practicality of quantum-inspired, p-bit-based annealing hardware for large-scale combinatorial optimization under strict energy and resource constraints.

This study examines the variability of ionospheric total electron content (VTEC) in response to solar and geomagnetic drivers across solar cycles 23 to 25. While the dominant effect of solar radiation on VTEC is well-known, a comprehensive understanding of how these relationships and their time-lags vary across distinct solar cycle phases and across cycles of differing intensity has been lacking. Using global VTEC data from the Chinese Academy of Sciences Global Ionospheric Maps (CASG) and solar-geophysical indices from NASA's OMNI dataset spanning from 1998 to 2025, this study bridges that gap by quantifying correlation strengths and time-lag relationships between VTEC and parameters such as $F_{10.7}$ solar flux, R sunspot number, Kp, Ap, and Dst indices, and solar wind properties. Results show that solar proxies, particularly $F_{10.7}$ and R sunspot number, exhibit the strongest, most consistent correlations with VTEC, especially during the ascending and descending phases of the solar cycle, with a characteristic $\sim2$-day lag attributed to thermospheric oxygen dynamics and ionospheric recombination processes. In contrast, geomagnetic indices exhibit weaker and phase-dependent correlations, while direct correlations between solar wind parameters and global VTEC are weak, as their influence is primarily mediated by geomagnetic activity and exhibits strong regional and temporal heterogeneity. Phase-resolved analyses further reveal that geomagnetic activity plays a more prominent role during transitional phases, while maximum and minimum periods are dominated by EUV variability and non-solar drivers, respectively. These findings highlight the necessity of incorporating solar phase and time-lag dependencies in ionospheric modelling and forecasting efforts.

What assortments (subsets of items) should be offered, to collect data for estimating a choice model over $n$ total items? We propose a structured, non-adaptive experiment design requiring only $O(\log n)$ distinct assortments, each offered repeatedly, that consistently outperforms randomized and other heuristic designs across an extensive numerical benchmark that estimates multiple different choice models under a variety of (possibly mis-specified) ground truths. We then focus on Nested Logit choice models, which cluster items into "nests" of close substitutes. Whereas existing Nested Logit estimation procedures assume the nests to be known and fixed, we present a new algorithm to identify nests based on collected data, which when used in conjunction with our experiment design, guarantees correct identification of nests under any Nested Logit ground truth. Our experiment design was deployed to collect data from over 70 million users at Dream11, an Indian fantasy sports platform that offers different types of betting contests, with rich substitution patterns between them. We identify nests based on the collected data, which lead to better out-of-sample choice prediction than ex-ante clustering from contest features. Our identified nests are ex-post justifiable to Dream11 management.

Fully bracketed implication terms on $n$ variables are evaluated in Gödel $m$-valued logic on a finite chain, and we enumerate truth-table rows by output value across all Catalan bracketings. Using the Catalan decomposition, we derive a finite system of generating functions for these value counts and introduce a root-split refinement that records the ordered pair of truth values at the top implication, yielding $m^2$ pair classes. We prove that the associated generating functions share a common dominant square-root singularity, which implies a universal $n^{-3/2}$ asymptotic form with exponential growth rate $(4m)^n$ and a limiting output distribution as $n\to\infty$. The root-split refinement yields matching uniform asymptotics for the pair classes and gives a transparent factorization of the original counts.

We present the first detection of the 3-Point Correlation Function (3PCF) Baryon Acoustic Oscillation (BAO) signal from the DESI Data Release 1 (DR1) sample of Luminous Red Galaxies (LRGs), which contains over 2.1 million galaxies. Our analysis is based on a tree-level redshift-space bispectrum template, which is then transformed to position space using the Fast Fourier Transform on Logarithmic scales (FFTLog) algorithm. We detect the BAO feature with a significance of approximately $8.1σ$ using the EZmock covariance matrix and $8.5σ$ using the analytical covariance matrix, for the full LRG redshift range ($0.4<z<1.1$), denoted as the $z_{\rm full}$ sample. We use the Abacus altMTL mocks, the most precise DESI DR1 mock catalogs currently available, to validate our model. We find that our model fits the mocks well, with a small offset of $0.6\%$ in the recovered BAO scale, which we treat as a systematic error due to modeling. We measure the angle-averaged distance, $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.88 \pm 0.27$ ($1.72\%$ precision) when using the covariance matrix estimated from EZmocks and $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.72 \pm 0.18$ ($1.12\%$ precision) when using the analytical Gaussian covariance matrix. Our results show excellent agreement with the DESI DR1 2PCF BAO measurements as well. We also explore several other ways to estimate the error and find between $1.7$--$2.2\%$ precision on the BAO scale from the EZmock covariance matrix and between $1.1$--$1.5\%$ precision from the analytical covariance matrix. This work represents the first detection of the BAO feature in the DESI 3PCF, establishing its ability to probe the expansion history of the Universe with future DESI 3PCF measurements.