This note is a tutorial on the deterministic version of the Kalman filter (state estimator), which is formulated as finding the state trajectory consistent with the system's equations with the minimal amount of $L^2$ process and measurement uncertainty. As stated, this is an input signal design problem with linear dynamics and an objective that is affine-quadratic in the state and inputs. The first step is to convert this problem to one with a purely quadratic objective by embedding in a larger system using ``homogeneous coordinates''. This converts the problem to a purely quadratic (i.e. an LQR) problem, but with non-standard initial or final state constraints. This latter problem can then be solved using a version of the matrix Differential Riccati Equation (DRE) for the larger LQR problem. The second step is a partitioning of this larger problem, which then yields the optimal dynamic observer and the DRE of the traditional Kalman filter. For comparison, the solution of the traditional LQ-tracking (Servomechanism) problem is also treated using a similar construction.

Renormalization group (RG) fixed points are commonly associated with scale invariance and a divergent correlation length. We show that this connection can fail in the tricritical $O(N)$ model in three dimensions in the limit $N\to\infty$. Revisiting the line of fixed points identified by Bardeen, Moshe, and Bander, we use the functional renormalization group to clarify the mechanism leading to mass generation at its singular endpoint (the BMB fixed point). We demonstrate that the generated mass is nonuniversal and originates from the nonanalytic structure of the effective potential. We show that the critical exponent $\nu$ which takes the value $\nu = 1/2$ along the regular part of the BMB line, that is, for $0 \leq \lambda < \lambda_{\rm BMB}$, jumps to $\nu = 1/3$ on the singular part of this line with the BMB FP, corresponding to $\lambda = \lambda_{\rm BMB}$, being the pivotal point between these two regimes. We also show how its singular potential emerges dynamically along the renormalization flow.

The $\eta$ and $\eta^{\prime}$ mesons are nearly unique in the particle universe since they are nearly Goldstone bosons, and their decay dynamics are strongly constrained. While earlier experiments collected samples of order $\sim 10^{9}$ $\eta$, the proposed REDTOP (Rare Eta Decays To Observe Physics Beyond the Standard Model) facility targets $\mathcal{O}(10^{14})$ $\eta$ and $\mathcal{O}(10^{12})$ $\eta'$, enabling broad searches for physics beyond the Standard Model. In this work, we present studies evaluating REDTOP sensitivity to processes that couple the Standard Model to New Physics through four portals: the Vector (dark photon), the Scalar (Higgs-mixing), the Axion-like, and the Heavy Lepton. In parallel, the proposed statistics allow precise tests of $CP$ and $T$ invariance and lepton universality and improve determinations of the $\eta/\eta'$ transition form factors, which are crucial inputs to the hadronic light-by-light contribution to the muon anomalous magnetic moment $(g-2)_\mu$.

We present a one-month-ahead conditional probabilistic framework for wind-power forecasting at ten-minute resolution. Monthly Weibull shape and scale parameters are estimated from serially dependent SCADA wind-speed data, corrected through a Godambe covariance, and forecast by a heteroskedastic Kalman filter on a bivariate VAR(1) state-space model. Conditional on the MMSE forecasted Weibull invariant law, we construct and compare three positive wind-speed SDE models: an Ornstein-Uhlenbeck-Weibull transform, a Fokker-Planck drift-first diffusion, and a Fokker-Planck diffusion-first model. The simulated wind-speed ensembles are mapped to power through a calibrated XGBoost power curve. Applied to January 2021 data from a Senvion MM92 turbine at Kelmarsh Wind Farm, the three SDE formulations are statistically indistinguishable in probabilistic accuracy, with mean CRPS values between 1.569 and 1.575 m/s. The diffusion-first model is therefore preferred on computational grounds, reducing runtime by about a factor of seven relative to the OU-Weibull model. In the power domain, the Wasserstein distance between simulated and observed distributions is 26.1-27.6 kW, below $1.4\%$ of rated capacity, while the monthly energy-yield bias is about $-7.3\%$ for the examined month. Exceedance-probability errors remain below 1.6 percentage points over the 0-1500 kW range and about 2.2 percentage points near rated power. These quantities provide decision-relevant probabilistic inputs for downstream operational problems, rather than completed reserve, storage, market, or fatigue-optimization decisions. Full marginalisation over the Kalman predictive law of the Weibull parameters is left as a natural extension.

Witten recently proposed a background-independent algebraic framework for quantum gravity, wherein an observer endowed with a Hamiltonian defines a diffeomorphism invariant worldline algebra manifested by the modified Hamiltonian constraint. In the semiclassical limit, this construction admits a lift to a von Neumann algebra acting on a Hilbert space defined by geodesic in a fixed background. Motivated by this, we revisit quantization of certain class of deformed CFT Hamiltonian on a cylinder to capture non-perturbative aspects of black holes. We construct a type-I Von-Neuman algebra by imposing conformal boundary conditions on cut-offs near fixed points of Hamiltonian flow, acting on a GNS Hilbert space built from highest-weight representation of `emergent modular Virasoro algebra'. Upon identifying the Hamiltonian with the modular Hamiltonian of a sharp subregion associated to a fixed reference KMS (vacuum) state, the algebra changes to type-III$_{1}$ factor. We also discuss the structure of emergent Hilbert spaces using `open-closed string' duality after incorporating an emergent non-trivial center made out of scalars at fixed points. We further employ this modular quantization of a single holographic CFT to demonstrate how the boundary limit of exact Hartle-Hawking correlator of smooth BTZ background emerge in the strict semiclassical limit in an alternative dual description, while at finite $G_{N}$, the corresponding description is intrinsically non-smooth, featuring both a stretched horizon and a boundary cutoff. The exact correlator has also been precisely reproduced from the vacuum correlators in modular quantization. We further discuss the effect of incorporating gravity by including the center via AdS/CFT on boundary correlators, for which the description of a smooth horizon is replaced by a (stretched) horizon containing explicit microstructures embedded within it.

In this paper we develop a combinatorial algorithm to compute the Gelfand--Kirillov (GK) dimension of simple highest weight modules for basic classical Lie superalgebras. Building upon the results for classical Lie algebras via Lusztig's {\bf a}-function and the Robinson--Schensted (RS) insertion algorithm, we extend these techniques to the super setting, providing explicit formulas for types $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(2|2n)$. Our results show that the GK dimension of a simple highest weight module is determined entirely by the even part of the Lie superalgebras.

Exact results using dual-unitarity largely rely on nearest-neighbor structures, while finite-range interactions typically lead to complications. Going beyond the usual nearest-neighbor setting, we introduce an analytically tractable family of finite-range kicked Ising models that admit exact closed-form entanglement dynamics. The construction is based on a staggered structure in which dual-unitarity is present on sublattices that are then coupled to each other. The central observation is that these inter-sublattice couplings do not obstruct the dual-unitarity of the resulting model. For the minimal interaction range of $r= 2$, we derive exact expressions for all the $n-$Rényi entanglement entropies at all times and show that the result is the sum of the two coupled sublattice contributions. Our framework extends naturally to larger finite interaction ranges and to systems with heterogeneous local Hilbert spaces, without additional assumptions. It thus provides a controlled setting for studying exact entanglement growth beyond strictly nearest-neighbor dual-unitary models.

This work proposes a new terrestrial probe for millicharged particles (mCPs) and demonstrates promising discovery prospects. mCPs can be copiously produced in core-collapse supernovae (SNe), and a fraction may escape, travel to Earth and yield distinct signals. The mCP mass induces a time-of-flight (ToF) delay relative to the SN neutrino burst, opening a clean search window after the neutrino signal has passed. We compute the mCP-induced electron-recoil signals at XENONnT, JUNO, DUNE, and Hyper-Kamiokande for benchmark SN scenarios, and find that for $\varepsilon = 10^{-9}$ and sub-MeV to MeV-scale masses, more than 10 events per year can be detected. This search can improve upon existing SN cooling bound on $\varepsilon$ by up to an order of magnitude.

Multipartite entanglement is a uniquely quantum form of correlation that captures collective properties of a composite quantum state beyond those encoded in its bipartite subsystems. We investigate this phenomenon in the process $e^+e^-\to t\bar tZ$ at a future lepton collider, where the final state spins span the tripartite Hilbert space $\mathscr{H} = \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^3$. Starting from the Standard Model helicity amplitudes, we reconstruct the full $12\times 12$ spin density matrix and characterise its entanglement structure through one-to-one negativities, one-to-other negativities, and the genuine multipartite negativity, evaluated at three increasingly inclusive levels of phase space integration. Pairwise entanglement is generally suppressed relative to the collective (one-to-other) and the genuine multipartite entanglement, and all measures decrease as more kinematic information is integrated out. Assuming quantum tomography in the fully leptonic decay channel at $\sqrt{s}=1$ TeV, we find that collective entanglement should be accessible at a realistic high-luminosity polarised lepton collider. By contrast, certifying genuine multipartite entanglement is more challenging, with only limited sensitivity projected for a specific polarisation benchmark within the expected ILC luminosity. The study establishes $e^+e^-\to t \bar{t}Z$ as an attractive laboratory for probing multipartite entanglement in high-energy collisions and provides a general mixed state framework that applies to any tripartite spin system.

Multimodal large language models (MLLMs) have recently shown strong potential as point-wise rerankers by directly modeling query--document relevance through next-token prediction. However, point-wise reranking suffers from substantial repeated computation across query--document pairs, while the causal structure of transformers allows only prefix segments to be reused via pre-caching. To address the misalignment of existing query-first and document-first formats with both VQA-style prompting and computation-aware reuse, we propose a $\textit{vision-first}$ formulation that improves both cache reuse efficiency and reranking performance. However, the remaining cost is still considerable and stems from three main sources: (1) $\textit{model depth}$, for which we reduce active parameters via early exit; (2) $\textit{cross-segment attention}$, which we restrict to a narrow interaction band across a few layers; and (3) $\textit{visual tokens}$, where we reduce the number of tokens via embedder-guided pruning. Together, these designs form miniReranker, which reduces reranking runtime to <1% of the dense implementation under high-reuse settings for a single query, while preserving >96% of the dense model performance.

As the capabilities of LLM-based code agents continue to advance, their expected role is expanding beyond localized bug fixing in existing codebases toward architecting and implementing complete software repositories from high-level specifications. However, training agents for such long-horizon software engineering tasks remains difficult due to the scarcity of large-scale, verifiable whole-repository generation data. In this paper, we introduce \textbf{DeNovoSWE}, a large-scale dataset for whole-repository generation. DeNovoSWE comprises 4,818 high-quality instances, where each instance requires generating a complete repository from documentation. Our dataset is automatically constructed through a carefully designed sandboxed agentic workflow, enabling scalable curation without human annotation. DeNovoSWE is constructed with "divide and conquer" and critic-repair philosophy. To balance data quality and diversity, we further introduce a difficulty-aware trajectory filtering strategy. Fine-tuning Qwen3-30B-A3B on DeNovoSWE substantially improves long-horizon SWE performance, raising its score on the challenging BeyondSWE-Doc2Repo benchmark from 5.8% to 47.2%.

We formulate a semiclassical stress tensor deformation dictionary in the context of the dS/CFT correspondence. Using the metric-flow formulation, we propose that stress tensor deformations of the putative boundary theory are encoded holographically as mixed boundary conditions for the bulk metric at future infinity. The coupled flow equations determine the deformed boundary metric and stress tensor, thereby specifying the source--response relation of the deformed boundary theory. We test the proposal in Kerr-dS$_3$/CFT$_2$, where the conserved charges constructed from the holographic boundary stress tensor agree exactly with the boundary spectrum obtained from the field-theoretic flow equation, providing a nontrivial consistency check of the dictionary. As an application, we compute the holographic pseudo entropy of boundary intervals from complexified geodesic saddles in the deformed Kerr-dS$_3$ geometry, and present explicit results for the $T\bar{T}$ and root-$T\bar{T}$ deformations.

In bilayer WSe$_2$, interlayer coupling reduces the K--$\Gamma$ valley splitting to $\Delta_{K\Gamma} \approx k_BT$ at room temperature, placing two hole-transport channels of markedly different effective mass in near-thermal equilibrium. We combine density functional theory (DFT) with spin--orbit coupling and an analytical two-valley device model to quantify how this near-degeneracy governs hole transport in gate-all-around (GAA) field-effect transistors. Three main results are obtained: (i)~the subthreshold swing is protected near $60$~mV~dec$^{-1}$ by quantum-capacitance screening independently of layer number; (ii)~the effective mobility is set by the K-to-$\Gamma$ valley occupation ratio and decreases monotonically with layer number; and (iii)~in the bilayer, compressive biaxial strain \emph{simultaneously} enhances the on-current, suppresses the off-current, and improves the on/off ratio from ${\approx}69$ to ${\approx}156$, while the subthreshold swing remains near the thermionic limit. This decoupling of on-state performance from switching slope is inaccessible through conventional mobility engineering and establishes a concrete design principle: \emph{valley-engineering sensitivity is maximized when $\Delta_{K\Gamma} \approx k_BT$}, the condition most naturally satisfied by bilayer WSe$_2$ at room temperature and zero strain, making it the optimal channel for valley-engineered GAA transistors.

The frequency dependence of opacity is crucial for determining the thermal structure of protoplanetary disks, which in turn influences disk dynamics and planet formation. Yet many disk models adopt simplified thermodynamics, and common radiation-hydrodynamic approaches often use gray opacities, ignore scattering, and yield inaccurate results in regions with intermediate optical depth. We present a comprehensive framework that models stellar irradiation with frequency-dependent absorption and scattering across all optical depths using the Athena++ finite-volume code, extended with multigroup radiation transport and newly implemented radial rays to more accurately represent the stellar flux. To calibrate this framework, we focus exclusively on hydrostatic disk models, allowing us to isolate radiative effects and evaluate the method without additional dynamical complexity. Because dust opacity increases strongly with frequency, ultraviolet stellar irradiation heats the tenuous disk atmosphere while the optically thick midplane remains cooler. This vertical temperature gradient is captured more accurately when more frequency bands are used or when scattering is included. Our hydrostatic models achieve equilibrium temperatures that differ from Monte Carlo radiative-transfer benchmarks on average by 2--5% with 64 frequency bands and 7--11% with 3 bands. Reducing the number of bands lowers computational cost by at least an order of magnitude while increasing the maximum possible temperature deviation only from 8% to 19%. This calibration demonstrates the accuracy and efficiency of the framework and provides a solid foundation for future self-consistent studies of irradiated protoplanetary disks, including fully dynamical simulations and applications involving chemical processes and time-dependent stellar luminosity.

Operations research and management science models support decisions that affect patients, workers, citizens, and public institutions. Decision-makers, such as clinicians approving surgical schedules, planners allocating disaster relief resources, or managers designing workforce rotations, increasingly require clear and actionable justifications that bridge the gap between mathematical optimization outputs and the intuitive reasoning stakeholders need to trust, contest, and implement recommended decisions. Yet the field has traditionally evaluated optimization models through computational criteria such as feasibility, optimality, scalability, and solution time, while treating explanation as a secondary concern. Mathematical transparency, provided through access to objectives, constraints, shadow prices, or sensitivity reports, does not automatically offer the forms of justification that stakeholders need to understand, trust, contest, or implement optimization-based decisions. This paper calls for the development of explainable optimization (XOpt) as a distinct interdisciplinary area that moves beyond algorithmic efficiency and incorporates behavioral, cognitive, and pragmatic perspectives to address this explanatory deficit.

We propose the linear combination of the anomalous magnetic moments of the muon and electron, $a_{\mu-e} \equiv a_\mu - (m_\mu/m_e)^2 a_e$, as a natural low-energy window quantity that may directly probe the current discrepancy between the data-driven and lattice-QCD evaluations of hadronic contributions. The rescaling ensures an exact cancellation of the short-range effects, thereby improving the UV behavior and bypassing a number of issues that arise in $a_\mu$ or $a_e$ separately. The hadronic-vacuum-polarization effect in $a^{\rm HVP}_{\mu-e}$, together with its uncertainty, is reduced as compared to $a^{\rm HVP}_{\mu}$ by $\sim 85\%$. This is promising for tests of New Physics, conditional to significant improvements in experimental measurements of $a_e$ and $\alpha$. One can foresee the improvements in tests of New Physics with some degree of flavor non-universality, as well as for the flavor-universal sub-GeV states.

The large number of existing nuclear species and the long list of their possible different exotic properties, such as presence of a halo (A), Borromean structure (B), clusterisation (C) and others, calls for a classification scheme that is universal, concise, categorical, informative, accessible and easily extensible. We provide here a first reasoned attempt to fill this gap with an abridged naming scheme, called $ABC$, based on definitions and properties that characterise modern nuclear physics. We limit our chart to light isotopes with $Z\le 10$ where most of these features appear presently.

We address two open questions in the rough volatility literature. First, we prove finite positive moments for the rough Bergomi price process, and for a wider class of Gaussian Volterra Bergomi models, in the whole subcritical range under negative correlation. More precisely, if \(\rho\in[-1,0)\), then \(\E[S_T^p]<\infty\) for every \(0<p<p_\rho\), where \(p_{-1}=\infty\) and \(p_\rho=(1-\rho^2)^{-1}\) for \(-1<\rho<0\). For the fractional rough Bergomi kernel, this gives the finite side of the sharp critical moment threshold, complementing the known explosion result above the threshold. Second, we prove that the rough Heston variance process, equivalently the scalar Volterra square-root process with fractional kernel \(K_\alpha(t)=t^{\alpha-1}/\Gamma(\alpha)\) and \(\alpha\in(1/2,1)\), has a positive atom at zero at every positive time. Consequently, zero is hit with positive probability before every positive time horizon. This rules out any Feller-type condition making the zero boundary inaccessible in the fractional rough Heston model.

We present a simple, rule-based filter for SETI target selection that flags stars unlikely to host complex life and produces an audit-ready exclusion catalog. Using seven stellar parameters, including age, metallicity, and multiplicity, the model excludes roughly half of a 1.74 million-star Gaia DR3 sample, retaining 777,835 high-priority targets, mainly G and K dwarfs. Age and metallicity dominate the rejections. Importantly, using Gaia's age upper bounds instead of point estimates saves 355,086 stars from exclusion. A comparison of empirical and synthetic proxies shows that while the overall exclusion rate is robust, individual target assignments change significantly; for instance, the commonly used RUWE indicator flags 2.7x more binaries than Gaia's own non-single-star flag. Cross-matching with the Breakthrough Listen target list reveals a 56.5% exclusion rate, highlighting the complementary nature of habitability-driven and proximity-driven surveys. The catalog, pipeline, and a generalized community tool are publicly available.

We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve mathematically represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-information and its regularized Doeblin information. This endows these information measures with a novel operational interpretation. Furthermore, our characterization can be generalized beyond quantum channels to all completely positive maps. This imposes information-theoretic limits on transmitting messages via postselected-teleportation-like mechanisms with arbitrary initial- and final-state boundary conditions, including those considered in various black-hole final-state models.

Binary endpoints are common in clinical trials and conditional odds ratios have traditionally been used to assess treatment effects. However, the interpretation of odds ratios is difficult, they are non-collapsible and rely on strong assumptions in order to be a relevant overall summary measure for the trial. As an alternative, risk differences have gained increasing prominence as a more interpretable, clinically meaningful and assumption-lean measure of treatment effects. This shift has also been motivated by new regulatory guidance, which emphasizes the relevance of marginal estimands and encourages covariate adjustment. Yet, covariate-adjusted inference for risk differences, particularly in smaller samples, has methodological subtleties and lacks well-established best practices. We conduct a simulation study comparing methods for estimating and testing risk differences in small-sample ($N \leq 150$) randomized clinical trials with prognostic categorical baseline covariates, focusing on exact unconditional tests, Mantel-Haenszel methods, and $g$-computation (standardization) approaches. We find that several $g$-computation approaches exhibit inflated Type-I error in very small samples when standard Wald-type inference is applied, whereas robust or penalized variants improve error control at the expense of power. Classical methods such as the Mantel-Haenszel and Suissa-Shuster tests remain robust but may forgo efficiency gains from covariate adjustment. Overall, our results indicate that much of the observed Type-I error inflation reflects misalignment between estimand and variance estimation rather than small sample size alone. Based on these results, we provide practical recommendations to guide method selection that align the estimand, variance estimation, and inferential target.

It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$ goes to infinity and $np$ converges to some $\lambda$. In this note we use instead the coupling technique to show a much more general result. Moreover, we only use elementary results from probability.

We investigate gauge-invariant nonlinear electrodynamics in the Plebański first-order Hamiltonian formulation, taking the single-invariant potential $\hat V(P)$ as the primary object. Our focus is on the existence of stable Lorentz-violating magnetic vacua. For three explicit two-parameter models -- rational asymmetric, logarithmic, and exponential -- we determine the regions of parameter space in which nontrivial constant electromagnetic vacua are compatible with an effective Hamiltonian bounded from below and a positive-semidefinite Hessian. In all three cases, physically admissible Lorentz-violating vacua are realized in the magnetic branch. We further discuss the electric branch and several additional one-parameter models, illustrating that Hamiltonian boundedness by itself does not ensure spontaneous Lorentz symmetry breaking. We also comment on how the symmetry-breaking conditions are related to known strong-field causality criteria.

We explore a modification of QCD sum rules where, instead of Borel transforms of current correlators, one considers the correlators in coordinate space as functions of Euclidean time. Taking the nucleon channel as an example, we derive such Euclidean time sum rules and compare them with the traditional Borel sum rules. We show that a rough estimate of nucleon mass and residue is also possible working in coordinate space, but such sum rules are much more affected by the uncertainties in power corrections and continuum contribution than the Borel ones: the fiducial interval is practically absent.

Observing non-Gaussianities in the timing residuals of Pulsar Timing Arrays (PTAs) has recently attracted attention as a potential discriminator between astrophysical and cosmological origins of the observed Gravitational Wave (GW) signal. In this work, we show that even in an idealized signal-dominated setup, after decorrelating the data to avoid spurious detections, statistical tests applied to PTA data cannot distinguish between a Gaussian and a non-Gaussian amplitude distribution of the GWB in a model-agnostic way. In particular, without making strong assumptions on the GW spectrum or the properties of the population, the sensitivity to any distinctive non-Gaussian feature is washed out.

We present a self-consistent tidal evolution framework that couples binary evolution from MESA to the full linear tidal response from GYRE-tides. Applying this framework to TOI-5882, a subgiant hosting a short-period brown dwarf, we show that interior radiative damping dominates the system's tidal evolution, with the classical equilibrium tidal model significantly underestimating the star's angular momentum evolution by several orders of magnitude. Consequently, our combined framework predicts a 2-6 fold reduction in the engulfment timescale, accelerating the companion's inspiral by roughly 25-110 Myr. By modeling angular momentum transport through the star as it evolves, we demonstrate that the early inspiral is driven by the non-resonant dissipation of internal gravity waves, before transitioning into a regime dominated by resonance crossings as the system approaches Roche-lobe overflow. We highlight the necessity of reframing the historical dichotomy between equilibrium and dynamical tides and instead propose categorizing tidal interactions around their dissipation mechanisms: radiatively damped tides, driven by radiative diffusion, and viscously damped tides, driven by turbulent viscosity. Our framework is broadly applicable to the tidal modeling of a wide class of star-companion systems, from binary stars to hot Jupiters, in a self-consistent and computationally feasible manner.

We show that every derivation of a simple and rational vertex operator algebra of CFT type is an inner derivation.

We employ a holographic model with a modified background that incorporates effective descriptions of key QCD features, including linear confinement and gluon condensation, to study the pion's internal structure, encompassing its mass spectrum as well as electromagnetic and gravitational form factors. This model is capable of simultaneously describing these diverse observables and reaches reasonable agreement with both experimental measurements and lattice QCD results. Our findings indicate that the model captures essential aspects of the pion. The description of multiple structure observables supports its potential as a useful tool for further investigations of pion properties.

We consider cosmological $R^2$ gravity models with radiation. We find the general solution to the trace equation $\Box R=0$ in the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. We analyze possible evolution of the Hubble parameter depending on the sign of the radiation energy density and find conditions for the existence of a bounce solution. A scalar field Lagrangian with the induced gravity term and the fourth-order monomial potential can play a role of radiation. In this case, we also obtain the general solution to the field equation. Therefore, the resulting $R^2$ gravity model with a scalar field is integrable in the spatially flat FLRW metric. Using a conformal metric transformation, we obtain a two-field chiral cosmological model that is also integrable in the spatially flat FLRW metric.

Context: Predicting which source lines will be deleted - and when - matters for maintenance, technical debt, and review prioritization. Existing MSR approaches work at file or method granularity, masking individual-statement risk. Objective: We introduce Code Lifespan Survival Analysis (CLSA), the first framework to model code survival at individual-line granularity. CLSA treats each line as a right-censored subject and estimates deletion risk from structural, contextual, and temporal covariates; its strongest predictors are computable statically from one file (AST structure plus line entropy), without version history or bug data. Method: We mine 32.5 million line birth events from 120 open-source TypeScript repositories. A 5-stage bipartite matching pipeline separates true deletions from refactoring noise (migrations and rewrites), preventing 8.3 million false deaths. We fit a Cox Proportional Hazards model with 15 covariates and check robustness via Weibull/Log-Logistic AFT, gamma frailty, and time-stratified landmark models. Results: More than half of all lines are never deleted (Kaplan-Meier median not reached); among deleted lines the median lifespan is 95.7 days. Covariate effects are strongly time-varying, forming three regimes. Line Shannon entropy is moderately protective for new code (HR=0.84, 0-90 days) and strongly protective for mature code (HR=0.36, 365+ days), explaining its proportional-hazards violation. Lines in conditional branches reverse: protective at birth (HR=0.97), a risk factor after 90 days (HR=1.21). Repository identity is the largest factor: a gamma frailty model (variance theta=1.449) raises concordance from 0.586 to 0.666, outweighing every structural covariate. Conclusion: Line-level survival modeling is tractable, yielding interpretable, mostly static risk signals and a calibration recipe for time-conditional risk scoring in IDEs and code review.