Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show that appending linearly independent rows to a check matrix of a stabilizer code can reduce the search space for a valid degenerate solution. Motivated by this, we extend the recently proposed affine subcode ensemble decoding technique from the classical to the quantum setting. Moreover, we employ overcomplete matrices for each decoding path. Monte-Carlo simulations on toric and generalized bicycle codes demonstrate improved convergence and reduced logical error rate.

Given a global equivariant ultracommutative ring spectrum $E$ and inclusion $H\hookrightarrow G$ of finite groups, one may apply geometric fixed points to the norm $N_H^G E_H \to E_G$ to obtain what we call a \emph{geometric norm} $Φ^H E \to Φ^G E$. We prove that, together with inflations, these assemble into a functor $Φ\colon\mathrm{UCom}_{\mathrm{fin}} \to \mathrm{Fun}(\mathrm{Span}(\mathcal{G},\mathcal{E},\mathcal{O}),\mathrm{CAlg})$, where $\mathrm{Span}(\mathcal{G},\mathcal{E},\mathcal{O})$ is the span category of finite connected groupoids with full backwards maps and faithful forwards maps, and that $Φ$ restricts to an equivalence between full subcategories of rational objects. Central to our construction is a refinement of geometric fixed points to a natural transformation $Φ\colon \mathrm{Sp}_\bullet\to\mathrm{Fun}(\mathrm{Orb}_\bullet^\simeq,\mathrm{Sp})$ which is compatible with restrictions and norms, and which restricts to an equivalence on full subcategories of rational objects. We explain how this may also be used to recover theorems of Barrero--Barthel--Pol--Strickland--Williamson and Wimmer on algebraic models for rational global spectra and normed $G$-commutative ring spectra respectively.

We study the state estimation problem for linear control systems with quadratic outputs which are locally unobservable at the equilibrium. We show that, despite this inherent lack of observability, an adversary with sensor read and write capability can induce observability by injecting an appropriate signal into the measurement channel. Taking the role of an adversary, we characterize when an injected signal can or cannot induce observability and, in the successful case, construct an observer that achieves local exponential convergence of state estimates to the true states of the system. A simulation study demonstrates our results.

A graph $G$ is called $H$-good if $R(G,H)=(|G|-1)(χ(H)-1)+σ(H)$, where $σ(H)$ denotes the size of the smallest color class in a $χ(H)$-coloring of $H$. In Ramsey theory, it is an interesting problem to study whether a graph $G$ is $H$-good or not. In this article, we study the Ramsey goodness of the pair $(K_{2,n},C_m)$, which naturally lies between the classical star-cycle and book-cycle problems. We prove that \begin{equation*} R(K_{2,n},C_{\{m,m+1\}})=m+1. \end{equation*} for all $m\ge 2n+1$, and consequently establish that \begin{equation*} R(K_{2,n},C_{m})=m+1. \end{equation*} for all $m\ge 3n+4$. This proves that $C_m$ is $K_{2,n}$-good in this range and improves a particular case of a result on the Ramsey goodness by Pokrovskiy and Sudakov. Further, we provide a construction of a graph that disproves the $C_{m}$-goodness of $K_{2,n}$ for all even $m$ satisfying $n\geq m+2$.

Ingestible electronic systems enable non-invasive, in situ sensing within the gastrointestinal (GI) tract, yet clinical translation has been limited by uncontrolled transit, short operational lifetimes, and unreliable wireless communication that prevent continuous monitoring. Here, we present a gastric-resident ingestible robotic platform that achieves week-long operation through integration of a bioinspired, electrically triggered release mechanism with a kirigami-enabled electronic architecture. A kirigami-patterned flexible printed circuit board spans the capsule body and deployable superelastic arms, enabling high-density integration of sensing, power management, and wireless modules within a constrained volume while tolerating large mechanical deformation during gastric residence. Stable retention and on-demand disassembly are achieved using thermally responsive polycaprolactone joints that transition from rigid to compliant states under electrical activation, avoiding dependence on variable chemical triggers. Reliable telemetry in the highly attenuating gastric environment is maintained using a dual-band Bluetooth Low Energy and sub-gigahertz module with RSSI- and throughput-aware adaptive transmission, balancing link robustness and energy consumption. We demonstrate long-term, continuous monitoring of gastric radiation exposure, enabling early detection of dose accumulation and providing a promising in vivo alternative to wearable or handheld dosimeters. Swine studies confirm stable gastric residence, sustained real-time telemetry, and safe gastrointestinal passage following triggered disassembly. This work establishes kirigami-enabled integration as a scalable strategy for long-term gastric-resident robotic systems.

The institutional separation between local energy communities and public electric vehicle (EV) charging limits the efficient use of locally generated renewable energy. This paper introduces the concept of community-to-vehicle (C2V) as an institutional design mechanism to bridge this gap by enabling EV charging within the community boundary, where locally generated photovoltaic (PV) surplus is preferentially allocated and offered to external users at a community charging price. Building on the recently introduced local electricity community framework in Switzerland, we design scenarios that capture the transition from full separation to coordinated EV charging and evaluate their impacts on EV users and the community. The results show that C2V significantly improves local PV utilization and enhances economic performance, reducing EV charging costs relative to commercial alternatives while generating additional revenue streams for the community. These findings highlight the potential of C2V as a practical, implementable mechanism for integrating EV charging into local energy communities, providing a clear pathway for adopting coordinated community-EV interaction within existing regulatory frameworks.

We study the asymptotic power means of the coefficients associated with the Schneider continued fraction map on $p\mathbb{Z}_p$. Using tools from thermodynamic formalism, we compute the Hausdorff dimension of the corresponding level sets and obtain explicit formulas for the associated multifractal spectra. The locally constant nature of the geometric potential enables a precise description in terms of polylogarithm functions, in sharp contrast with the classical real setting.

Effective disaster management requires rapid access to information distributed across structured operational records, unstructured institutional documents, and dynamic external sources. However, most existing disaster information systems and retrieval-augmented generation frameworks remain organized around a single access pathway, limiting their ability to support heterogeneous, time-sensitive, and context-dependent information needs. This study presents DisastRAG, a disaster-aware information integration and access system that combines large language models with retrieval-augmented access to structured, unstructured, and contextual disaster information. The framework is built around a multi-path architecture that supports document retrieval over a curated hazard corpus, structured access over relational disaster records, and external web fallback for out-of-corpus requests, while also incorporating query understanding, strategy routing, response generation, and contextual memory within a unified system. We evaluated the document retrieval performance using four open-source large language models across multiple retrieval configurations on multiple-choice and open-ended disaster information tasks. Retrieval augmentation consistently improves performance over no-retrieval baselines, yielding multiple-choice gains of 12-23 percentage points and open-ended keypoint coverage gains of up to 10.5 percentage points. Results show that larger candidate pools are most helpful for weaker models, while stronger models are more sensitive to retrieval noise. Hybrid retrieval performs best for open-ended coverage, whereas vector retrieval and shallower reranking more often favor closed-form factual selection. Case studies further show that structured access and web fallback extend the framework beyond document-only RAG.

Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of oscillations. The origin of this behavior is geometric: phase averaging over the emergent periodic attractor eliminates odd powers of the oscillation amplitude, while the squared amplitude varies smoothly with the distance from the bifurcation. Consequently, the excess of any smooth time-averaged observable admits an integer-power expansion; observables remain finite but display discontinuities in finite-order derivatives. This yields an Ehrenfest-like hierarchy of Hopf singularities, in which the first nonanalytic derivative is determined by the lowest-order coupling between the observable and the limit-cycle waveform that survives phase averaging. Generic observables therefore exhibit kink singularities, while symmetry or geometric cancellations can suppress lower-order couplings and shift nonanalyticity to higher derivatives. We demonstrate this mechanism in chemical, electronic, and climate oscillators. Our results identify supercritical Hopf bifurcations as a universal mechanism for nonanalytic observable behavior, where singular features arise without any underlying singular stationary state. They thus provide a generic setting for singular behavior without divergence.

A C library for random number generation, Randompack, is presented. The library implements several modern random number generators (engines), including xoshiro256, PCG64, Philox, ranlux++, and sfc64; 14 continuous distributions including uniform, normal, exponential, gamma, beta, and multivariate normal; raw bit streams, bounded integers, permutations, and sampling without replacement. The engine and the distribution layers are separated so any engine can be used with any distribution. Benchmarks show that Randompack is faster overall than competing libraries, with speedup factors ranging from about 1 to 15 depending on engine, distribution, interface, and platform. A distinguishing feature is reproducibility: with the same seeds Randompack gives compatible results across programming languages, computers, CPU architectures, and compilers. The library includes comprehensive support for parallel simulation. It is accompanied by a comprehensive test suite, benchmarking programs, and example programs. Interfaces to Fortran, Python, Julia, and R have been implemented; their benchmark results are included, although their design and implementation are otherwise outside the scope of the article. Unlike other available C libraries with comparable scope, Randompack is permissively licensed under the MIT license, and it is open source and publicly available through GitHub and conda-forge.

With the addition of large numbers of distributed energy resources (DERs) to distribution networks comes the increasing risk that their operation may violate the safety constraints of these networks. The problem considered in this paper is that of combined siting, sizing and dispatch of these DERs, also known as distributed energy system (DES) design, to help meet electrical and heat loads within the network. Here, the operation of these DERs is modelled, along with the unbalanced three-phase alternating current (AC) power flow in the network. When this network power flow is considered, this admits a non-convex mixed-integer nonlinear program (MINLP) model formulation which scales poorly with network size in terms of solve time. To address this, the problem is decomposed into a series of algorithmic steps, starting with a mixed-integer linear program (MILP) formulation that does not consider network constraints, then fixing binary variables, adding power flow constraints and solving as a nonlinear program (NLP) and finally removing operational binary variables and replacing them with a complementarity reformulation. As the main contributors to the overall solve time, the NLP and Complementarity steps are solved using a hybrid spatial/temporal decomposition strategy and the alternating direction method of multipliers (ADMM) distributed optimisation method. Results are presented for networks based on the European low voltage test feeder with up to 55 loads and 120 timepoints, with the ADMM approach showing speed-ups of up to 13x when considering parallel computation of the subproblems, for a maximum observed optimality gap of 0.61%.

Very low-yield nuclear tests pose a major verification challenge for the zero-yield standard of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). The zero-yield standard prohibits any explosive experiment that produces a self-sustaining fission chain reaction while allowing subcritical experiments. Previous research shows that on-site gamma spectroscopy of post-test debris provides useful insight into the criticality level, although it remains heavily dependent on knowledge of certain experimental settings. Here, we adopt a new approach whereby machine learning models are trained on simulated gamma spectroscopy data to infer the fission yield of a nuclear very low-yield test. Using high-fidelity 3D Monte Carlo particle transport simulations, we generated gamma spectra measured outside containment vessels after very low-yield tests for 66 million representative scenarios. From these spectra, we extracted 82 fission-product-to-plutonium-239 peak ratios, then trained ML models for two tasks: (1) binary classification of whether a test exceeded a chosen yield threshold, and (2) regression to estimate the actual yield. We find that XGBoost performs best on the classification task across the most policy-relevant yield range. The classifier achieves high accuracy even for yields near the chosen threshold (e.g., >95% for yields +-100 g around a threshold at 1 kg TNT), and the regressor presents a mean absolute relative error of 12.4% for measurements taken a month to a year after the test. These results demonstrate that using machine learning to infer the yield of a past very low-yield nuclear test from gamma spectroscopy data is feasible and accurate. This approach can support efforts to establish a robust verification protocol for the zero-yield standard and could pave the way for a future yield threshold-based verification regime that is both technically feasible and politically viable.

We show that it is consistent relative to the existence of suitable large cardinals that for any countable-to-one coloring $c: [ω_2]^2\to ω_2$, there exists a closed subset $A\subseteq ω_2$ of order type $ω_1$ such that $c\restriction [A]^2$ is injective. This theorem simultaneously strengthens two theorems, one by Abraham, Cummings and Smyth and another one by Garti and Zhang, as well as answers a question raised by Garti and Zhang. New combinatorial principles involving towers of countable elementary submodels, games concerning regressive functions and variants of strong Chang's conjecture, which are key elements of the proof, are investigated.

We derive a physics-based, closed-form model linking antenna directivity to the root-mean-square (RMS) delay spread and mean excess delay in large reverberant indoor environments. Starting from the Rician K-factor-the ratio of line-of-sight (LOS) to scattered power we show that K scales with the total transmit-plus-receive (Tx+Rx) antenna gain through a single reverberance factor that quantifies scatter anisotropy. For an arbitrary scatter power delay profile (PDP), we derive a general identity connecting sigma, tau, and K; the exponential scatter model is the physically motivated special case. Ray-tracing simulations over 100 random link placements in a 57300 m3 industrial hall at 75 GHz validate the model. Compact design rules map target delay-spread values to the minimum required antenna gain, enabling wideband mmWave industrial links.

In this work we construct non-holomorphic, complete and minimal submanifolds of the odd-dimensional complex projective spaces $\cn P^{2n-1}$ and their dual complex hyperbolic spaces $\cn H^{2n-1}$. We then provide complete minimal submanifolds of the quaternionic projective spaces $\hn P^{n-1}$ and their dual quaternionic hyperbolic spaces $\hn H^{n-1}$. All the constructed minimal submanifolds are of codimension two. Our main tools are complex-valued harmonic morphisms from the above mentioned ambient spaces.

This short note explores the maximum-entropy walk on the unit interval that is a median-martingale. That is, the median of its next state is equal to its current state. The stationary distribution of this walk is the arcsine distribution, and we provide a proof that elucidates the connection to two classical arcsine laws for Brownian motion. The notion of a martingale is further generalized, and a larger class of walks is considered and similarly characterized.

Artificial intelligence (AI) is increasingly central to understanding how the brain processes information. However, the integration of neuroscience and modern AI is bottlenecked by a fragmented software ecosystem. Current tools are siloed by recording modality and optimized for small-scale, in-memory workflows, limiting the use of massive, naturalistic datasets. Here, we introduce NeuralSet, a Python framework that efficiently unifies the processing of diverse neural recordings (including fMRI, M/EEG, and spikes) and complex experimental stimuli (such as text, audio, and video). By decoupling experimental metadata from lazy, memory-efficient data extraction, NeuralSet harmonizes standard neuroscientific preprocessing pipelines with pretrained deep learning embeddings. This approach provides a single PyTorch-ready interface that scales seamlessly from local prototyping to high-performance cluster execution. By eliminating manual data wrangling and ensuring full computational provenance, NeuralSet establishes a scalable, unified infrastructure for the next generation of neuro-AI research.

We establish an expansion theory for $\text{SL}_2(\mathbb Z/q\mathbb Z)$. Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.

Universal scaling near phase transitions is one of the central ideas of physics, linking the growth of spatial correlations to the slowing down of dynamics. So far, direct experimental access to this critical behavior has remained largely confined to equilibrium many-body systems, and especially to static critical behavior. Here we probe how universality emerges in a driven quantum fluid of light formed by exciton--polaritons in a semiconductor microcavity. By probing the fluctuation-dominated disordered phase below the condensation threshold, we directly measure both the static growth of the correlation length $ξ$ and the dynamical slowing down of the relaxation time $τ$. We find that these quantities obey the universal relation $τ\propto ξ^{z}$ with dynamical exponent $z \approx 2$, revealing diffusive dynamics of a non-conserved order parameter. Our results extend the physics of critical dynamics from equilibrium matter to driven optical systems, bridging quantum condensates and lasers.

Semantic communication (SemCom) has emerged as a promising paradigm for next-generation networks. However, its typical end-to-end joint source--channel coding (JSCC) architecture also raises serious privacy concerns. To guide future secure SemCom design, it is important to understand how serious such leakage can be. Nevertheless, existing eavesdropping attacks mainly rely on fixed-configuration solvers and often require instantaneous wiretap channel state information (CSI) to achieve effective privacy inference. This may lead future secure SemCom designs to overlook potentially severe risks. To address this, we propose a large language model (LLM)-orchestrated agentic eavesdropper. Specifically, the proposed eavesdropper forms a closed-loop workflow with three functional agents. The optimization agent adaptively performs joint semantic-and-channel inversion to recover private information from the intercepted signal without requiring wiretap CSI. The perception agent evaluates the effectiveness of the optimization agent and assesses whether the recovered private semantics are reasonable, providing feedback to the optimization agent. The refinement agent further analyzes the recovered content and uses a generative prior to refine promising candidates into more realistic and complete private reconstructions while preserving consistency with the intercepted signal. Simulation results over a MIMO Rayleigh fading channel show that the proposed eavesdropper achieves more than $75\%$ eavesdropping success rate at $\mathrm{SNR}\geq 5$~dB even without wiretap CSI, highlighting a severe privacy threat that future secure SemCom systems must address.

In this paper we consider the subnormality of block Toeplitz operators $T_Φ$, where $Φ$ is an $n\times n$ matrix-valued function on the unit circle $\mathbb T$ of the form $$ Φ=QΦ^* \quad \hbox{($Q$ is a finite Blaschke--Potapov product).} $$ This is related to a matrix-valued version of Halmos's Problem 5 and Nakazi-Takahashi Theorem. We ask whether $T_Φ$ is either normal or analytic if $T_Φ$ is subnormal, where $Φ$ is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when $Φ^*$ is not of bounded type.

The pursuit of dissipationless spin supercurrents is a central theme in superconducting spintronics. We propose a field-free Josephson junction using an inhomogeneous altermagnetic interlayer with in-plane Néel vectors. We show that the current-phase relation and the critical Josephson current are highly sensitive to the misorientation angle between the altermagnetic layers' Néel vectors. Specifically, at a $π$ misorientation with equal layer thicknesses the spatial oscillations of the superconducting pair amplitude, governed by the center-of-mass momentum, undergo mutual cancellation. This compensation suppresses individual layer pair-breaking, significantly enhancing the critical current and eliminating $0$-$π$ transitions. Furthermore, the non-collinear alignment of the Néel vectors facilitates the emergence of a net spin-polarized Josephson current. This spin current serves as a distinct signature of spin-triplet pair correlations, generated by the spin-dependent momentum shifts inherent to the altermagnetic exchange field. Our results establish a highly tunable, field-free platform for the realization of dissipationless spintronic devices.

The transport experiments reveal that the low-temperature resistivity in the normal-state of cuprate superconductors is quadratic in temperature (T-quadratic) in the underdoped pseudogap phase, while it is linear in temperature (T-linear) in the overdoped strange-metal phase, however, the full understanding of these different behaviours is still a challenging issue. Here starting from the microscopic electronic structure of cuprate superconductors, the low-temperature resistivity in the normal-state is investigated from the underdoped pseudogap phase to the overdoped strange-metal phase. It is shown that the mechanism requires both the impurity scattering and the umklapp scattering: the impurity scattering is needed to restrict the modification of the distribution function to at around the antinodal region,while the impurity-scattering assisted umklapp scattering from a spin excitation is at the heart of the behaviour in the low-temperature resistivity, where the doping dependence of the temperature scale exists, and presents a similar behavior of the antinodal spin pseudogap crossover temperature. In the low-temperature region above the temperature scale in the overdoped strange-metal phase, the resistivity is T-linear, however, in the low-temperature region below the temperature scale in the underdoped pseudogap phase, the opening of the spin pseudogap lowers the spin excitation density of states at around the antinodal region, which reduces the strength of the electron umklapp scattering from a spin excitation associated with the antinode, and thus leads to a T-quadratic behaviour of the resistivity.

We present a systematic study of the transverse momentum ($p_{\rm T}$) spectra of charmonium (J/$ψ$, $ψ(2S)$) and bottomonium ($Υ(nS)$) states in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV within an analytical relativistic hydrodynamics framework. The medium evolution is described assuming cylindrical symmetry with boost-invariant longitudinal expansion and Hubble-like transverse flow. Quarkonium spectra are evaluated using the Cooper-Frye formalism on a constant-temperature freeze-out hypersurface, supplemented by a core--corona approach to include both thermal and non-thermal contributions. The model describes the measurements from ALICE and CMS over a broad $p_{\rm T}$ range. For charmonium, both the spectra and the $ψ(2S)$/J/$ψ$ ratio are well reproduced, while deviations at high $p_{\rm T}$ for J/$ψ$ indicate additional hard production mechanisms. In the bottomonium sector, the $Υ(nS)$ spectra and their yield ratios are successfully described, consistent with the expected sequential suppression pattern. These results demonstrate that an analytical hydrodynamic approach combined with a core-corona framework provides a unified and transparent description of quarkonium production in heavy--ion collisions at LHC energies.

The problem of characterizing graphs with a prescribed number of main eigenvalues is a long-standing problem in spectral graph theory. Although some constructions are known, only a few produce infinite families of simple connected graphs with exactly $s \ge 2$ main eigenvalues. Zero-divisor graphs form a well-structured class of algebraic graphs whose spectra can be described explicitly using equitable partitions, making them a convenient setting to study main eigenvalues. In this paper, we prove that the zero-divisor graphs of reduced rings provide an infinite family of simple connected graphs with exactly $s$ main eigenvalues, and that certain induced bipartite subgraphs also have exactly $s$ main eigenvalues for any positive integer $s$.

We show that the leading bubble test suffers severe size distortion when fundamentals incorporate general-purpose technology adoption. Embedding a hump-shaped technology shock in the Campbell-Shiller present-value model, we prove that the fundamental price becomes locally explosive during adoption, contaminating the test's limit distribution with a non-centrality parameter proportional to the shock's peak. We propose a fundamental-versus-speculative decomposition that projects prices onto observable technology proxies and applies the test to the residual. Empirically, the decomposition eliminates evidence of speculation in the 2020-2025 AI rally while confirming a speculative peak confined to December 1999-March 2000 in the dot-com episode.

Artificial intelligent language-model based coding agents have significantly changed the way we interact with computers in our day-to-day, as it is common to use them to create, improve, and run programming scripts only using natural language. Agent code updates can be better guided when such programs can be executed and scored automatically rather than judged by human preference. In quantum computing and classical quantum simulation settings, ground-state preparation has a parallel structure: candidate protocols can be ranked by estimated energies and other proxies indicating proper quantum-state convergence. In this work, we study how autoresearch, a code optimization strategy based on coding agents, can be used to optimize hyperparameter choices of different ground-state preparation and sampling protocols, including the variational quantum eigensolver (VQE), density matrix renormalization group (DMRG), and auxiliary-field quantum Monte Carlo (AFQMC). We validate the viability and capacity of this method on simple spin models and molecular Hamiltonians. Across all three settings, the agent mutates simple baselines into complex protocols with improved energy proxies while operating under constrained space-time computational budgets. We conclude with discussions of other quantum routines that support executable scalar scoring, enabling evolutionary coding agents to automate a substantial portion of the protocol-tuning work that would otherwise be required manually.

We prove that a factorial tracially complete C*-algebra with CPoU has real rank zero and stable rank one. This leads to an essentially complete description of the Cuntz semigroup of these algebras. In particular, the results of this paper hold for the uniform tracial completions of $\mathcal{Z}$-stable C*-algebras.

M-theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ has recently been proposed to yield, via quotients, ten-dimensional non-supersymmetric string theories. We revisit the construction that leads to the heterotic theories, finding a consistent set of rules that reproduces the light spectra and gauge groups, including indications of their global structure. Our approach uses the gauge enhancement mechanism of type I' string theory, applied to a setting in which the type I' interval is curled onto itself, with its two boundaries separated by a branch cut. Using these tools, we reproduce the ten-dimensional heterotic theories and provide some evidence for junctions among them.

Unsigned distance functions offer a powerful and flexible implicit surface representation that, unlike their signed counterparts, allow for surfaces that are open, non-orientable, or non-manifold. We consider the problem of reconstructing arbitrary surfaces from a finite set of samples of unsigned distance data. Existing methods for mesh reconstruction from distance data rely on sign information, accurate gradients, a corresponding continuous distance function, or extensive data-dependent training. However, they fail when applied to input that is both discrete and unsigned. Inspired by this challenge, we study the power diagram generated by the distance samples and propose a novel theoretical concept, the superpower contour, which we prove converges to the true surface in the limit of sampling density. We use this superpower contour as an initial surface proxy and design an algorithm that leverages it to produce a polygonal mesh approximating the unknown true geometry. Our method vastly outperforms other conceivable strategies for the discrete unsigned distance reconstruction task, and sets the stage for future work on this mathematically rich problem.