Formalization of mathematics is a major topic, that includes in particular numerical analysis, towards proofs of scientific computing programs. The present study is about the finite element method, a popular method to numerically solve partial differential equations. In the long-term goal of proving its correctness, we focus here on the formal definition of what is a finite element. Mathematically, a finite element describes what happens in a cell of a mesh. It notably includes the geometry of the cell, the polynomial approximation space, and a finite set of linear forms that computationally characterizes the polynomials. Formally, we design a finite element as a record in the Rocq proof assistant with both values (such as the vertices of the cell) and proofs of validity (such as the dimension of the approximation space). The decisive validity proof is unisolvence, that makes the previous characterization unique. We then instantiate this record with the most popular and useful, the simplicial Lagrange finite elements for evenly distributed nodes, for any dimension and any polynomial degree, including the difficult unisolvence proof. These proofs require many results (definitions, lemmas, canonical structures) about finite families, affine spaces, multivariate polynomials, in the context of finite or infinite-dimensional spaces.

The core-Sérsic model is the standard tool for describing partially depleted stellar cores in massive early-type galaxies, yet its physical admissibility has rarely been examined. Using numerical deprojections, we show that many formally allowed parameter combinations cannot represent realistic stellar systems: sharp transitions between the inner power-law core and the outer Sérsic profile (large $α$) always generate non-monotonic intrinsic density profiles. We identify, for each set of structural parameters $(γ, m, R_{\text{e}}/R_{\text{b}})$, a critical transition parameter, $α_{\text{crit}}$, above which monotonicity is violated. This threshold systematically depends on the core slope and Sérsic index, implying that a fraction of the commonly used parameter space, including the widely adopted sharp-transition limit $α\rightarrow\infty$, is physically ruled out. These constraints have important consequences for measuring core sizes and mass deficits in massive ellipticals, for constructing dynamical models, and for comparing observations with simulations of supermassive black hole binary evolution.

In this paper, motivated by study on universal inequalities for eigenvalues of the Dirichlet Laplacian, we prove some new inequalities for eigenvalues of the Dirichlet Laplacian on the hyperbolic space. In particular, we verify Cheng's conjecture (Adv. Lect. Math. 37, 2017) up to loss of $ε$ for two special kinds of bounded domains in the hyperbolic space.

This paper presents e112, a context-aware mobile emergency response application designed to strengthen communication between citizens and authorities during disasters. Building on the ubiquity of smartphones, the system provides SOS requests, incident reporting, customized alerts, evacuation guidance, and moderated community interaction, supported by a cloud-based back end and an operator dashboard for situational awareness. A user-centered design approach guided our development, ensuring clarity and usability under stressful conditions. Evaluation through usability studies and technical audits demonstrated high user satisfaction, robust performance, and accessibility. The results show that a simple, well-designed mobile application can significantly enhance emergency preparedness and response, reducing risks to human life during climate change--driven emergencies.

Ditlevsen and Ditlevsen [Nature Communications, 2023] (DD23 hereafter) propose a statistical framework to estimate the timing of a potential collapse of the Atlantic Meridional Overturning Circulation (AMOC) based on extrapolating information from observed sea-surface temperature (SST) variability. By fitting a stochastic one-dimensional fold-bifurcation model to an SST-based fingerprint of the AMOC using Maximum Likelihood Estimation (MLE), they conclude that a collapse is most likely to occur in the middle of the 21st century, with a reported 95% confidence interval covering the time span from 2037 to 2109. Given the profound implications of such a claim for both climate and society, it is essential to thoroughly test the robustness of this result, to critically assess the underlying assumptions and uncertainties, and to estimate the extent to which the reported confidence interval reflects the true limits of current knowledge. Here we examine the sensitivity of DD23's results and argue that four types of uncertainty are insufficiently explored in their analysis: (i) structural uncertainty associated with the assumed low-order bifurcation model, (ii) statistical uncertainty in their model fit, (iii) uncertainty in the representativeness of SST-based fingerprints as proxies for the high-dimensional AMOC dynamics, and (iv) uncertainty in the underlying data, arising from non-stationary observational coverage and dataset preprocessing. Using synthetic experiments and a systematic analysis of alternative fingerprints and observational products, we show that the tipping times estimated by DD23 are highly sensitive to the uncertainties listed above, and extend several millennia into the future when these uncertainties are thoroughly propagated.

We derive a robust sum rule among the branching fractions of $Λ_b \to Λν\barν$ and $B \to K^{(\ast)} ν\barν$, assuming that right-handed neutrinos are decoupled. Despite the presence of 18 independent Wilson coefficients in the effective Hamiltonian, this relation remains exact. Remarkably, it is found that the coefficients of this baryon-meson sum rule are numerically identical to those of the $b\to c$ semileptonic sum rule among the branching fractions of $Λ_b \to Λ_c τ\barν$ and $B \to D^{(\ast)}τ\barν$. Once the decay rate of $B \to K^{\ast} ν\barν$ is measured, the decay rate of $Λ_b \to Λν\barν$ can be determined in a model-independent manner for new-physics scenarios involving only left-handed neutrino interactions. This clearly demonstrates that observables in baryonic and mesonic $b \to s ν\barν$ transitions will serve as a powerful probe for discriminating among new-physics scenarios.

We study a two-layer one-dimensional energy balance model, which allows for vertical energy exchanges between a surface layer and the atmosphere, as well as meridional energy transport across latitudes via a diffusion law. The evolution equations of the surface temperature and the atmospheric temperature are coupled by exchange of infrared radiation as well as other non-radiative energy exchanges. The energy enters the system as solar radiation, which is partially absorbed and partially reflected by the two layers. The system is then composed of two degenerate parabolic equations coupled by nonlinear terms, the growth of these terms being crucial for the choice of the functional setting. An essential parameter is the absorptivity of the atmosphere, denoted $\varepsilon _a$, whose value depends critically on greenhouse gases. We prove that blow up in finite time occurs if $\varepsilon _a >2$, while global existence of solutions and the existence of a global attractor hold when $\varepsilon _a \in (0,2)$. Proofs are based on comparison principles that derive from the cooperative structure of the problem, and that provide invariant rectangles for smooth initial conditions, and on regularity properties.

Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant challenge due to the combinatorial complexity. We introduce a novel graph formulation to model the physical and logical structure of repeaterless quantum networks, enabling the systematic optimization of switching strategies. The problem is posed as a linear program and solved using a column generation approach. This method enables scalable computation despite the exponential number of possible network configurations. Our results not only provide a formal foundation but also a practical algorithm for the optimization of switching. Empirical tests confirm the solver's scalability with network size, demonstrating the framework's effectiveness and laying the groundwork for future optimization of quantum network control.

Despite recent progress in identifying the exotic random singlet (RS) state in disordered frustrated magnets as a distinct correlated phase, three-dimensional (3D) realizations remain scarce. Sr$_3$CuNb$_2$O$_9$ was proposed to be one of such 3D frustrated systems with magnetic site disorder hosting an RS ground state. Here, we report a detailed microscopic investigation of Sr$_3$CuNb$_2$O$_9$ employing muon spin relaxation ($μ$SR) and $^{93}$Nb nuclear magnetic resonance (NMR) techniques. The $μ$SR zero-field relaxation rate reveals a power-law divergence of the relaxation rate as a function of temperature. Also, a power-law divergence is present in the relaxation rate as a function of applied longitudinal field, consistent with the formation of an RS phase. The $^{93}$Nb NMR spectra unambiguously resolve two components with distinct local magnetic environments, whose nature is further elucidated through spin-lattice relaxation measurements analyzed via an inverse Laplace transform (ILT) of the nuclear magnetization recovery. The relaxation-rate distribution obtained from ILT reveals two well-separated channels: a fast component, $(1/T_1)_{\mathrm{fast}}$, and a slow component, $(1/T_1)_{\mathrm{slow}}$. Both components follow distinct power-law temperature dependences ($T^α$), with $α= 0.6$ and $1.1$ for the fast and slow channels, respectively. The combined spectral and relaxation data demonstrate that the fast channel qualitatively represents an RS-like state, whereas the slow channel exhibits quantum spin liquid (QSL) like behavior, thereby establishing the microscopic coexistence of RS and QSL-like phases in Sr$_3$CuNb$_2$O$_9$.

We study a class of quantum dynamical maps for d-level systems that interpolate between positive, Schwarz, and completely positive evolutions. Our approach is based on a geometric analysis of the parameter space, which reveals the structure of regions corresponding to different positivity classes and their boundaries. We show that dynamical trajectories naturally move across these regions, providing a clear geometric interpretation of transitions between Markovian and non-Markovian regimes. It is shown that within presented class the evolution becomes eventually entanglement breaking. This analysis highlights the role of divisibility and eternally non-Markovian evolution.

The advent of NMT has expanded the scope of translation beyond isolated sentences, enabling context to be preserved across paragraphs and documents. However, current evaluation metrics largely remain restricted to the sentence level and typically depend on reference translations. Without references, existing metrics cannot provide a clear basis for their quality assessments. To address these limitations, we propose an evaluation framework that independently extracts and compares latent topic structures within source and translated texts. This framework utilises various topic modelling techniques, including LSA, LDA and BERTopic, to achieve this. Our methodology captures statistical frequency information and semantic context, providing a comprehensive evaluation of the entire document. It aligns key topic tokens across languages using a bilingual dictionary and quantifies thematic consistency via cosine similarity. This allows us to evaluate how faithfully the translation maintains the thematic integrity of the source text, even in the absence of reference translations. To this end, we used a large scale dataset of 9.38 million Korean to English sentence pairs from AI Hub, which includes pre evaluated BLEU scores. We also calculated CometKiwi, a state of the art, reference free metric for this dataset, in order to conduct a comparative analysis with our proposed, topic based framework. Through this analysis, we confirmed that, unlike existing metrics, our framework evaluates the differentiated attribute of document level thematic units. Furthermore, visualising the key tokens that underpin the quantitative evaluation score provides clear insight into translation quality. Consequently, this study contributes to effectively complementing the existing translation evaluation system by proposing a new metric that intuitively identifies whether the document's theme has been preserved.

Let $ξ$ be a value, at an algebraic point, of a Siegel $E$-function. As a special case of a very general interpolation result, we prove that there exists an $E$-function $f$ such that $f(1)=ξ$, and such that 1 is not a singularity of the minimal differential equation satisfied by $f$. We prove that the same property does not hold at the point $0$, when $ξ$ is the value at a non-zero algebraic number of the Bessel function. This answers an analogue of a question asked by Yves Andr{é} for $G$-functions.

We study composition operators acting on the weighted Bergman spaces on the bidisc, i.e. $C_Φ:A^2_β(\mathbb{D}^2)\to A^2_β(\mathbb{D}^2)$ where $Φ$ is induced by rational inner functions (RIFs) or a RIF and a smooth function (mixed case). Our approach is geometric. Our main result is a uniform criterion for all $β\in(-1,0]$ that can be summarized as follows: Boundedness of the composition operator is equivalent to transversal intersection of the level sets for non-smooth symbols, under the assumption that if any tangential intersection occurs on the singularity it must be of high order. This extends the characterization of Bayart-Kosiński to the non-smooth self maps of the bidisc. To reach our conclusions, we utilize results obtained by Anderson, Bergqvist, Bickel, Cima and Sola on Clark measures associated to RIFs and Puiseux factorizations.

Let $X_t = B_t + μt$, $t \geq 0$, be planar Brownian motion with nonzero drift, and let $K_t^r = \{x \in \mathbb{R}^2 : {\rm dist}(x, X[0,t]) \leq r\}$ be the radius-$r$ Wiener sausage up to time $t$. For a bounded Borel function $ψ$ supported in a compact interval $[r_0, r_1] \subset (0,\infty)$, consider the smoothed Betti-curve functional $Φ_ψ(t) := \int_{r_0}^{r_1} β_1^t(r)\,ψ(r)\,dr$, where $β_1^t(r)$ denotes the number of holes of $K_t^r$. In a previous paper, a regeneration scheme along the drift direction was used to prove a law of large numbers for $Φ_ψ(t)$. In the present paper we prove the corresponding central limit theorem. More precisely, there exist a deterministic constant $ρ_ψ$ and a variance $σ_ψ^2 \geq 0$ such that $(Φ_ψ(t) - ρ_ψt)/\sqrt{t} \xrightarrow{d}_{t \to \infty} \mathcal{N}(0, σ_ψ^2)$. We also obtain the finite-dimensional Gaussian limit for finitely many test functions. The proof preserves the regenerative structure of the law of large numbers, but requires a new $L^2$ analysis of the topological interface terms created at regeneration cuts. The key input is a finite-time polynomial moment bound for integrated hole counts of the Wiener sausage. This yields square-integrability of cycle increments, within-cycle oscillations, and the last incomplete-cycle remainder, which in turn allows one to combine a standard central limit theorem for stationary $1$-dependent sequences with a renewal time-change argument.

An image of Lyman-$α$ (Ly$α$) emission from Europa obtained with the Hubble Space Telescope Space Telescope Imaging Spectrograph (HST/STIS) has previously provided the first evidence of localized water vapor (H$_2$O) aurora, potentially originating from outgassing. Subsequent STIS observations have revealed the presence of a global atomic hydrogen (H) exosphere. We present a comprehensive analysis of STIS Ly$α$ observations of Europa acquired in 1999 and between 2012 and 2020 to search for localized auroral emissions and constrain the properties of Europa's H exosphere. We analyze the complete dataset of STIS observations obtained when Europa was sunlit and not transiting Jupiter. A forward model is constructed to account for all known sources of Ly$α$ emission, including resonantly scattered sunlight from Europa's H exosphere. To identify localized anomalies, such as H$_2$O aurora, the modeled Ly$α$ emission is subtracted and the residuals are examined. Emission from Europa's H exosphere is detected at all observing epochs, but is attenuated by absorption in Earth's exosphere when Europa's radial velocity relative to Earth (and thus the Doppler shift) is small. From the velocity dependence of this attenuation, we estimate an H-exosphere temperature of $\sim 1000$ K and derive an upper limit of 5100 K. For the best-constrained epoch in 2014--2015, we infer a vertical H column density of $1.4x10^{12}$ cm$^{-2}$ and an H source rate of $1.1x10^{27}$ s$^{-1}$. No localized emission enhancements are detected in any of the observations, including the image previously interpreted as evidence of H$_2$O aurora near Europa's south pole. The discrepancy with earlier results arises primarily from differences in the assumed position of Europa's disk on the detector, as well as from the inclusion of an H-exosphere signal in the present analysis...

We emphasize that for a stochastic differential equation with isotropic stable additive noise and non Lipschitz drift, when considering an appropriate discretization scheme and the associated weak error, it is somehow natural to consider a test function having the same spatial regularity as the drift involved. We will in particular focus on drifts belonging to Lebsegue, H{ö}lder or Besov spaces with negative regularity index in their spatial variable. Choosing such a test function allows to improve the convergence rate previously obtained on the densities (for Lebesgue or H{ö}lder drifts) or preserve the rate for possibly singular generalized test functions (for Besov spaces with negative regularity).

The zero-inflated logistic regression model accommodates binary responses with excess zeros, which often arise from a latent mixture of susceptible and insusceptible subpopulations or asymmetric misclassification of the response. The model has two components: regression for the binary response and a latent binary indicator for the zero-inflation state. In applied settings, it is common to use the same design matrix for both components if there is no prior knowledge. However, this shared-design specification lacks guaranteed identifiability of the regression parameters, as established in prior works. This paper investigates the theoretical properties of the zero-inflated logistic regression model under the shared-design setting and computational methods for applications. First, to motivate the use of the zero-inflated model, we prove that ignoring the zero-inflation mechanism can lead to a sign flip in the pseudo-true coefficient value relative to the true value. We then establish sufficient conditions for the existence of the maximum likelihood estimate. As a main result, we establish that the model under the shared-design setting is identifiable up to exchange symmetry of the parameters for two components and that the expected log-likelihood has a unique maximizer on the resulting quotient space. The posterior bimodality is examined using a Pólya-Gamma Gibbs sampler with replica exchange. Finally, we propose a simple relabeling rule to select a single ordered parameter pair, and evaluate its performance through simulation studies and an application to self-reported diabetes data.

The Traveling Salesman Problem is a classical NP-hard combinatorial optimization problem that has been extensively studied in operations research. A major challenge in Traveling Salesman Problem formulations is the large number of subtour elimination constraints required to ensure a valid tour. To address this issue, we adopt an iterative approach grounded in well-established operations research techniques, in which subtour elimination constraints are generated dynamically. In addition, we integrate a preprocessing phase to reduce the number of candidate arcs. In this work, we investigate both classical and quantum optimization approaches for solving the problem using the proposed framework. In particular, for quantum optimization we analyze quantum annealing techniques within the D-Wave framework, considering both direct quantum execution on the QPU and hybrid quantum classical solvers. Computational experiments show that the proposed strategies significantly reduce the model size and lead to positive improvements in computational performance across classical, direct quantum, and hybrid optimization approaches.

We show that two non-isometric, smooth, globally hyperbolic Lorentzian metrics can have the same hyperbolic Dirichlet-to-Neumann map on an infinite cylinder with timelike boundary.

We consider saturated fusion systems $\mathcal F$ on a Sylow $2$-subgroup of $Ω^+_8(2)$ with $O_2(\mathcal F) = 1$. Examples for this are the $2$-fusion systems of $Ω^+_8(2)$, $Ω^+_8(2):3$, $PΩ^+_8(3)$ and $PΩ^+_8(3):3$

We consider a superconducting altermagnet heterostructure and demonstrate that the interplay between altermagnetism and a selective filter of transverse momentum channels enables perfect nonreciprocal spin-polarized currents. We demonstrate that this nonreciprocity manifests in both local and nonlocal spin currents, signalling the emergence of directionally selective local and nonlocal spin behaviors. We show that the selective filter of transverse momentum channels is realized by gating a finite normal region between the superconducting altermagnet and the metallic reservoir, which then directionally selects transport channels that match the momentum-dependent spin-split superconducting altermagnetic states, allowing for nonreciprocal spin-polarized currents. We discover that the local and nonlocal spin nonreciprocity features a highly tunable polarity and nearly perfect quality factors, respectively, which is achieved by means of gate voltages and by varying the length of the finite region. Moreover, we find that local and nonlocal charge currents also develop a nonreciprocal behavior, whose quality factors can also reach perfect values. In all cases, the spin and charge currents are sensitive to variations of the altermagnetic field, a functional dependence that can be exploited to identify the type of altermagnetism. Our findings put forward an electrically controllable route towards nonreciprocal superconducting spintronic devices based on altermagnets.

The application of large language models (LLMs) to OdorSpace analysis attracts growing interest. Recent studies have explored the comparison of sensory evaluation spaces derived from LLMs with odor character profiles in the Dravnieks' dataset. In this study, we calculated pairwise distances of odor descriptors using three distance measures and statistically compared these LLM-derived similarities with distances derived from the original data. Next, we extended this approach to odor names (ingredients). Statistical comparison revealed that LLMs can infer odor similarity to some degree, suggesting the potential of odor maps generated from these similarity data. Applying this approach, we generated an odor map of essential oils. It demonstrates that essential oils within the same group are closely located in the odor map, suggesting that the proximity in the odor map corresponds to human evaluation.

We introduce the use of a crossed pair of Multilayer Laue Lenses (MLLs) as an objective in Dark-Field X-ray Microscopy (DFXM). In a demonstration experiment at the ID03 beamline at ESRF, two flat Mo-Si MLLs were used, with a physical aperture of 50 x 50 $\mathrm{μm^2}$ and a focal length of 14.25 mm at 19 keV. Applying a 10 % criterion to the Modulation Transfer Functions (MTFs) acquired, a spatial resolution of 56 nm is obtained in bright-field mode -- more than three times better than with a compound refractive lens (CRL) objective. The dark-field resolution is similar. With an efficiency of 26.7 % the MLL objective expands the science domain of DFXM significantly, both for bulk and near-surface studies. Similar to the CRL case, the reciprocal space resolution is dominated by the numerical aperture (NA) of the objective, with the NA being three times larger in the MLL case. This enables faster orientation mapping and implies improved options for the use of tomographic reconstruction algorithms. Although the MLL objective pupil varies with energy and position, secondary peaks are suppressed, simplifying both interpretation and forward simulations. We present an example DFXM application using the MLL as an objective, imaging a through-silicon via Kelvin device.

We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes that enable a direct measurement of the WF, and establishes the coherent-state basis as a privileged basis for determining when the WF exhibits negative regions. We show that the absence (presence) of coherent superpositions in the coherent-state basis provides direct information about the positivity (negativity) of the WF. In particular, the absence of such superpositions constitutes a sufficient condition for WF positivity. Although a general proof of necessity remains elusive, we demonstrate that this condition is also necessary in two relevant cases: Schrödinger-cat states and higher-order cat states on a circle. More precisely, for Schrödinger-cat states we establish a necessary and sufficient condition for the positivity of the WF in full generality, whereas for high-order cat states on a circle we derive an analogous condition in the limit of a large number of densely packed coherent states.

Monitoring exercise intensity is critical for safe and effective physical activity, particularly for individuals with cardiovascular disease, where overexertion can pose serious risks. Although physiological measures such as heart rate are widely used for avoiding overexertion, they can be unreliable in certain cases, such as when affected by medication or when wearables are worn too loosely. We introduce AktivTalk, a mobile prototype that digitizes the clinically validated Talk Test to support voice-based, in-the-moment self-assessment of exertion. In a within-subject study with 20 participants, we collected exertion-labeled voice samples and found that AktivTalk was rated as highly usable and preferred over conductor-guided assessment. We further explored automated exertion classification from Talk Test speech. Using MFCC-based features with class balancing and cross-validation, a lightweight neural classifier achieved up to 90% accuracy for detecting high vs.non-high exertion from Talk Test recordings. This work highlights the potential of structured voice interactions for accessible exertion assessment and motivates future passive exertion monitoring from speech.

Surface creasing in swelling polymer gels is commonly attributed to compressive strain or interlayer mismatch, yet its general control remains unclear. Here we show that solvent polymerization degree $N_{\rm s}$ provides an independent control parameter for crease onset in surface-bound polydimethylsiloxane gels swollen by silicone oils. Despite nearly identical swelling kinetics and through-thickness solvent concentration profiles, we observe a transition from creased to stable surfaces with increasing $N_{\rm s}$. A theory coupling swelling thermodynamics and mechanical stability reveals that polymeric solvents reduce the mixing entropy and thereby modify the osmotic pressure, allowing $N_{\rm s}$ to tune separately the equilibrium swelling and the crease threshold. This framework captures the stability boundary across solvent polymerization degree and network elasticity. These results identify polymeric solvents as active thermodynamic-mechanical regulators of swelling-induced surface.

In this paper, with suitable assumptions, we generalize the work of Külshammer and Puig on extensions of nilpotent blocks to inertial blocks.

We focus on the classification of positive solutions to $(-Δ)^s u=\frac{x_n^α}{u^γ}$ in the half space with $γ>0$, subject to the Dirichlet condition. We show that when $-2s<α<(γ-1)s$, all positive solutions exhibit one-dimensional symmetry and are monotone increasing in $x_n$. Moreover, we provide a complete classification of all such one-dimensional solutions via their ``asymptotic $s$-order slope". When $α$ lies outside this range, we demonstrate the nonexistence of global positive solutions.

We characterize the Archimedean lattice-ordered algebras with identity that admit a polynomial growth continuous function calculus. More precisely, for an $n$-tuple $\mathbf{x}=(x_1,\dots,x_n)$ in an Archimedean lattice-ordered algebra $X$ with identity $1_X$, we prove that the existence of a lattice-algebra homomorphism from the algebra $PG_n$ of continuous functions on $\mathbb{R}^n$ of polynomial growth, sending the coordinate projections to $x_1,\dots,x_n$ and the constant function to $1_X$, is equivalent to the existence of $f\ge 1_X\vee |x_1|\vee \cdots \vee |x_n|$ and an $f\!$-subalgebra $Y$ of $X$ such that $1_X,x_1,\ldots ,x_n \in Y$ and, for every $m \in \mathbb{N}$, the norm $\|{\cdot }\|_{f^{m}}$ is complete on $Y\cap I_{f^{m}}$. This result may be viewed as an analogue, for lattice-ordered algebras, of the characterization of positively homogeneous continuous function calculus for Archimedean vector lattices due to Laustsen and Troitsky. As a by-product, we describe the finitely generated free objects in the category of uniformly complete Archimedean $f\!$-algebras and also show that the existence of a nontrivial polynomial growth continuous function calculus on a vector space forces it to be a commutative $f\!$-algebra.

Light scalars generically mediate a fifth force incompatible with local tests of gravity unless their couplings are parametrically suppressed or screening mechanisms are introduced. We demonstrate that such suppression can arise from symmetry. We propose a $Z_2$-symmetric mirror extension of the Standard Model within a bi-conformal gravity construction, where spontaneous breaking of scale invariance produces a light scalaron as a pseudo-Nambu-Goldstone boson. This scalaron couples to the difference of trace anomalies between the Standard Model and mirror sectors. We find a parameter-independent correlation between the fifth-force strength $α$ and the scalaron mass $m_σ$, with the proportionality set by QCD observables and the electroweak scale. The Standard Model predicts $α\sim 10^{-4}$ at meter scales for $m_σ\sim 10^{-7}$ eV, which is directly in the target window of next-generation experiments. In contrast to environmental screening mechanisms, this suppression mechanism follows directly from symmetry rather than nonlinear scalar dynamics.