Papers

Programmable microcavities support grand-canonical photon gases. We show that bosonic state counting creates an entropic staircase of most-probable total occupations. For detuning density continuous and nonzero at the chemical-potential threshold, the active-cell fraction is asymptotically linear at low temperature and the conditional law has a universal limit; for uniform disorder the law is exact over a finite temperature interval. For two modes it is the Gauss–Kuzmin distribution, linking photonic thermodynamics and metric number theory. We outline finite-array and dye-microcavity tests.

For Gamow's liquid drop model, we improve the nonexistence bound of Frank-Killip-Nam from 8 to 7.5. The key additional input is a geometric perimeter inequality arising from the capillarity problem. This yields a quantitative gain in the averaged slicing argument and shows that the variational problem admits no minimizer for $A\geq 7.5$.

In this paper, we study the equation which we call Manton's exotic vortex equation. The equation arose in Manton's study of a deformation of the classical vortex equation [Ma]. We first investigate the existence problem for Manton's exotic vortex equation and establish existence results. We then construct the moduli space of solutions. Finally, we establish a dimensional reduction for Manton's exotic vortex equation. More precisely, we establish a correspondence between solutions of Manton's exotic vortex equation and pseudo-Hermitian-Yang–Mills connections with pseudo-Hermitian metrics of signature (1,1).

Recent work of Colbrook and Stepaniants produced the first counterexamples to the planar Pompeiu and Schiffer conjectures and introduced the conformal fixed-disc, disk-polynomial, and validated-tail machinery used here. By adapting this framework to the complementary Dirichlet endpoint, we disprove the unrestricted planar Berenstein conjecture. Specifically, we construct a bounded simply connected domain $\Omega$ with real-analytic Jordan boundary, which is not a disc and for which there exist $k\in(27.4381178838,27.4381198839)$ and a nonzero real-valued function $u\in C^\omega(\overline\Omega)$ satisfying $(\Delta+k^2)u=0$ in $\Omega$, with $u=0, \partial_\nu u=\text{constant}\ne0$ on $\partial\Omega$. Thus the overdetermined Dirichlet–Neumann data do not characterize the disc without an additional sign assumption on $u$. The domain has dihedral symmetry of order $26$, but is neither a disc nor centrally symmetric, and the corresponding eigenfunction changes sign. Equivalently, its boundary arclength measure satisfies $\widehat{\sigma_{\partial\Omega}}(k\omega)=0$ for $\omega\in\mathbb S^1$. After conformally transferring to the unit disc, exact support identities and quantitative disk-polynomial estimates yield rigorous control of the infinite-dimensional tail. A Newton–Kantorovich argument then reduces existence to finitely many explicit inequalities, which are certified using interval arithmetic. The extension from the Pompeiu–Schiffer problem is not formal. The earlier construction absorbs both boundary conditions into a single inverse-Laplacian equation. At the Dirichlet endpoint considered here, the nonzero Neumann datum forces the harmonic source modes to remain, producing a coupled interior–boundary system involving the full zero-Dirichlet inverse and its Neumann trace, together with a separate sign-recovery problem.

Building on prior results [1], we introduce vector-valued modular resurgent series, whose components exhibit a single infinite tower of singularities in the Borel plane, trivial secondary resurgent series, and Stokes constants given by linear combinations of the coefficients of a vector of $L$-functions. We extend the paradigm of modular resurgence to this setting, emphasizing the role of the Stokes constants and the interplay between the associated vectors of $q$-series and Dirichlet series, and describing the resulting symmetry relating canonical pairs of vector-valued modular resurgent series. Moreover, we conjecture that certain vectors of $q$-series with modular resurgent asymptotics are vector-valued quantum modular forms and can be reconstructed via median resummation. Finally, we show that vectors of $q$-Pochhammer symbols, previously considered in [2], and Eichler integrals of vector-valued modular forms of weight $1/2$ and $3/2$ can be studied within the framework of vector-valued modular resurgence. While the first case amounts to a convenient repackaging of scalar modular resurgence, the second involves a non-trivial representation of the modular group and therefore illustrates the necessity of the vector-valued framework; we establish its modular resurgent structure in general, and work it out in full detail for the unary theta series, whose Eichler integrals are the false theta functions of quantum topology.

Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.

A differential calculus for causal variational principles is developed, which generalizes the exterior calculus of differential forms and some of the associated differential topological structures to non-smooth spaces. Our calculus includes the exterior derivative, de Rham cohomology, glueing constructions (restrictions and extensions of differential forms, Mayer-Vietoris sequence), a Künneth formula and Poincaré's lemma. Moreover, we prove versions of Stokes' theorem and the Gauß divergence theorem. The constructions and results are illustrated by several examples.

A class of elliptic solutions to the matrix CKP equation is studied. Equations of motion for their poles and matrix coefficients at the poles are obtained. As in the scalar case, they are of the first order, in contrast to what takes place in the KP and BKP hierarchies, where the equations of motion are of the second order.

We present a systematic study of finite, non-split 2-group symmetries with a non-trivial Postnikov class, focusing on the simplest example with a $\mathbb{Z}_2$ 0-form symmetry and a $\mathbb{Z}_2$ 1-form symmetry, intertwined together by the non-trivial Postnikov class in $H^3(B\mathbb{Z}_2;\mathbb{Z}_2)\cong\mathbb{Z}_2$, denoted by $\mathcal{G}$. We classify the anomalies of this 2-group symmetry for physical theories in $d$-dimensional spacetime, by computing the oriented bordism groups $\Omega_{d+1}^{\rm SO}(B\mathcal{G})$ and the spin bordism groups $\Omega_{d+1}^{\rm Spin}(B\mathcal{G})$ for $d\leq 5$. For the case of $d=3$, we investigate the Symmetry TFT/TO of the 2-group symmetry $\mathcal{G}$ using the language of fusion 2-categories, as well as (3+1)D TQFT actions, for the cases without or with the 2-group anomaly classified by $\operatorname{Hom}\left(\widetilde{\Omega}_4^{\rm SO}(B\mathcal{G}),U(1)\right) \cong H^4(B\mathcal{G};U(1))\cong\mathbb{Z}_2$. We classify the minimal topological and physical boundary conditions of the Symmetry TFTs, and carry out the categorical Landau paradigm for such a non-split finite 2-group.

We study the distribution of the two-replica overlap $R_{1,2}$ in the Ising and spherical Sherrington-Kirkpatrick models at the critical inverse temperature $\beta = 1$. Our main result shows that in both models, $R_{1,2}$ has scale $N^{-1/3}$, and the quenched distribution of $N^{1/3} R_{1,2}$ converges to an explicit random probability measure defined in terms of the reflected $\mathrm{Airy}_1$ point process. As a consequence, we characterize the limiting value of $N^{2/3} \mathbb{E} \langle R_{1,2}^2 \rangle$, answering a question of Talagrand \cite{talagrand2011mean2}. For the spherical SK model, we obtain the limit by representing the Gibbs measure as an anisotropic Gaussian on $\mathbb{R}^N$ conditioned to have norm $\sqrt{N}$, and then passing to the $\mathrm{Airy}_1$ scaling limit at the GOE spectral edge. For the Ising SK model, the proof is based on a sphere-to-cube comparison principle showing that the quenched distributions of $N^{1/3} R_{1,2}$ under the spherical and Ising Gibbs measures asymptotically coincide. This paper is a companion to \cite{du2026fluctuations}, where we introduced a related comparison principle to identify the limiting fluctuations of the SK free energy. Most of the arguments in this paper were generated using GPT-5.6 Pro, with the aim of exploring further consequences of the ideas developed in that work.

We present a new avenue to the usual Schwinger effect via the open string pair production for a system of two Dp branes with $1 \le p \le 6$ in Type II superstrings. The two Dp are placed parallel at a separation with one of them carrying the most general constant electromagnetic background allowed for the pair production. By taking the so-called field theory limit, we obtain systematically, from the open string pair production rate, the respective explicit Lorentz invariant QED pair production rate in diverse dimensions for a pair of charged/anti-charged massive particles, which can be scalars, spinors or vectors.

In this Brief Communication, we establish the notion of critical damping for generic two-degree-of-freedom system. For given set of masses and stiffnesses, the critical damping corresponds to the real eigenvalue with maximal multiplicity, equal to minus geometrical mean of the eigenfrequencies. This case corresponds to the fastest possible asymptotic decay rate for generic initial conditions. The damping matrix for the critical case is unique up to reflection of one modal coordinate and, generically, non-diagonal. Quite surprisingly, for large difference of the eigenfrequencies, it is also not positive definite. Therefore, physical realization of the critical case will require active elements that provide negative effective damping.

The random-cluster model with cluster weight $0<q<1$ is expected to exhibit negative dependence, but without FKG even pairwise negative correlation remains open on general graphs. We study the model on the infinite $\Delta$-regular tree with wired boundary conditions. Write $\widehat p:=p/(p+q(1-p))$ and $p_{\mathsf c}:=q/(\Delta+q-2)$. Classical results identify the product wired state for $p\le p_{\mathsf c}$ and construct a percolative all-wired limit for $p>p_{\mathsf c}$. We prove that the supercritical wired DLR specification has a unique Gibbs measure, namely this all-wired limit. Consequently, the wired DLR phase diagram is complete: the unique measure is Bernoulli bond percolation with parameter $\widehat p$ for $p\le p_{\mathsf c}$, while it percolates for $p>p_{\mathsf c}$. We also establish negative dependence across wired branches. On a finite wired tree, the vector of branch-connectivity indicators satisfies conditional negative association under positive external fields (CNA+). Hence bounded increasing observables supported on disjoint collections of branches incident to a common vertex have nonpositive covariance. The same inequality holds in the unique infinite-volume wired measure for every $p$, with equality for $p\le p_{\mathsf c}$.

We study annealed current fluctuations in the two-dimensional symmetric simple exclusion process (SSEP) across a circular passive counting boundary. The initial average density is $\rho_1$ inside a disk of radius $R$ and $\rho_2$ outside, and the observable is the net decrease of the particle number in the disk over a finite time. Using convexity of the macroscopic fluctuation theory action and rotational averaging, we show that the minimizer of the full two-dimensional variational problem may be chosen radially symmetric. For the resulting radial problem, a suitable change of variables leads to a nonisospectral formulation on the half-line. Combining the associated scattering construction with a scalar factorization, we obtain a closed expression for the scaled cumulant generating function and hence the annealed large-deviation statistics of the current.

In this paper, we analyze global minimizers of the Landau–de Gennes functional in 3-dimensional domains in the Lyuksyutov regime. We prove smooth convergence to an $\mathbb{S}^4$-valued limit and obtain an $O(\mu^{-1})$ estimate for the distance to $\mathbb{S}^4$ as $\mu \to +\infty$, thereby extending the convergence results of Dipasquale et al.[Arch. Ration. Mech. Anal. 239: 599–678, 2021].

In this paper, we investigate the monic orthogonal polynomials $P_{n}(x;T_{m};\lambda)$ and the Hankel determinants $D_{n}(T_{m}; \lambda)$ associated with the generalized Freud weight \[w(x;T_{m};\lambda) = |x|^{2\lambda+1}\exp\biggl(-\sum_{k=1}^m t_k x^{2k}\biggr),\quad m \in \mathbb{Z}^+,\; t_{k} \in \mathbb{R} , x\in\mathbb{R}\setminus\{0\},\] where \(T_{m}=\{t_{1},t_{2},\cdots, t_{m}\}\), $t_{m}>0$ and \(\lambda>-1\).By employing ladder operators and compatibility conditions, we find that all members of the discrete Painlevé I hierarchy have a unified structure and the recurrence coefficient \(\beta_n\) of $P_{n}(x;T_{m};\lambda)$ satisfies the $m$-th member of the discrete Painlevé I hierarchy. Besides, we derive the second-order differential equation satisfied by $P_{n}(x;T_{m};\lambda)$, the partial derivatives of the recurrence coefficients \(\beta_n\) with respect to parameters \(t_1, t_2, \dots, t_{m-1}\) and the corresponding differential identities for $D_{n}(T_{m}; \lambda)$. Based on the discrete Painlevé I hierarchy and the above differential identities, we obtain new partial differential equations satisfied by $\ln\beta_n$ and $\ln D_{n}(T_{m}; \lambda)$.Using the discrete Painlevé I hierarchy and the asymptotic theory of linear difference equations, we derive the full asymptotic expansions of the recurrence coefficient $\beta_n$, the nontrivial leading coefficient $\mathrm{p}(n; T_m; \lambda)$, and the Hankel determinant $D_n(T_m; \lambda)$ as $n\to\infty$, for general $T_m$ and $\lambda>-1$. Notably, while the logarithmic term $\ln n$ appears in the leading-order contributions, it is absent from the remainder terms in these expansions.We illustrate our results under the specific decic Freud weight $w(x;t_1,t_2;\lambda)=|x|^{2\lambda+1} \exp\bigl(-x^{10}-t_2x^4-t_1x^2\bigr)$.

We study the role of generalized symmetry in massless renormalization group flows or Higgs transitions. In particular, we revisit the massless renormalization group flows in unitary minimal models, $\mathbf{M}(p,p+1) \rightarrow \overline{\mathbf{M}(p-1,p)}$ preserving the fusion ring symmetry $\text{FR} (SU(2)_{p-2})\subset \mathbf{M}(p,p+1)$ where $p$ is an integer satisfying $p>3$. In this series of flows, we demonstrate that the unbroken fusion ring symmetry $\text{FR} (SU(2)_{p-2})$ eliminates all relevant perturbations in the $\overline{\mathbf{M}(p-1,p)}$ model. Hence, the infrared theory $\overline{\mathbf{M}(p-1,p)}$ is stable at the level of the scaling analysis and can be interpreted as a (weak-)symmetry-enforced gapless phase in contemporary theoretical physics. Phenomenologically, by the folding trick, the unbroken fusion ring symmetry corresponds to a (half-)integer spin nonsimple current, a variant of the Cooper pair involving nonabelian anyons generated from the coset or level-rank duality structures. Moreover, we demonstrate that the structure of (half-)integer spin nonsimple current plays a fundamental role in causing the resonance effect of relevant and dangerously irrelevant perturbations. This resonance effect may result in the cascade of phase transitions (or the system flows to unexplored fixed points), and the symmetry can be a stopper of such unconventional flows.

These are detailed expository notes on the staggered optical-lattice hard-core Bose gas of Aizenman, Lieb, Seiringer, Solovej and Yngvason. They restate and expand the arguments and their principal inputs in a common notation, and describe the central and orbitwise decompositions of thermodynamic-limit equilibrium states. The purpose is to make compressed or delegated steps explicit, not to introduce a new method, strengthen the estimates, or otherwise improve the cited results.

In this article we consider polynomials orthogonal with respect to the inner product $$\langle P,Q \rangle_S = \int_{\mathbb{R}}P(x)Q(x) \mathrm{e}^{-V(x)} \, \mathrm{d}x + \lambda\int_{\mathbb{R}}P^\prime(x)Q^\prime(x) \mathrm{e}^{-V(x)} \, \mathrm{d}x$$ where $V$ is a polynomial of even degree (at least four) and positive leading coefficient, and $\lambda > 0$ a constant. The above inner product is a special case of the so-called Sobolev inner product. We show how one can represent the associated Sobolev orthogonal polynomials as a species of Type I multiple-orthogonal polynomial. This correspondence makes use of the WKB asymptotics of a certain second order ODE. From this we may write a Riemann–Hilbert problem for the Sobolev orthogonal polynomials, from which one can deduce a Christoffel–Darboux-type formula for the projection kernel.

We investigate the analyticity of the free energy of the Ising model in the presence of a non-zero external magnetic field, at high temperature, and at low temperature. Using the Fernandez–Procacci convergence criterion for cluster expansions, together with generating-function techniques and graph-theoretical methods, we derive improved convergence conditions in all three regimes. In particular, the generating-function approach yields sharper estimates for polymers and contours in the strong-field and low-temperature regimes, while a new high-temperature expansion based on Veblen's theorem provides a substantially larger analyticity region than the classical results in the literature.

Non-Hermitian degeneracies are usually discussed through spectral coalescence, whereas entanglement is a property of eigenvectors and need not be fixed by the eigenvalues alone. We formulate a compact bipartite model that separates these two notions. A Hermitian operator with a degenerate eigenspace is transformed by an invertible non-unitary similarity map. The resulting Hamiltonian is non-Hermitian and retains a non-defective degeneracy at every finite value of the non-Hermiticity parameter. For an exactly solvable two-qubit realization, the right eigenstates evolve continuously from product states to maximally entangled states although the spectrum is unchanged. We distinguish the positive right-state reduced density matrix from the generally non-positive biorthogonal reduction, for which entropy may become complex. The same two-qubit solution gives a closed partial-transpose negativity and a Schmidt-gauged non-local magic. Entanglement grows monotonically with the non-Hermiticity parameter, whereas the non-local magic vanishes for both the product and maximally entangled limits and is largest at an intermediate coupling. In larger bipartite spaces, the Page entropy and Haar-averaged purity provide reference values for eigenstate typicality. These diagnostics separate non-defective degeneracy, exceptional-point sensitivity, Haar-typical entanglement, and non-stabilizer correlations without relying on a proliferation of basis-dependent spectral quantities.

A new recursive implementation of the equivariant moving frame method for infinite-dimensional Lie pseudo-group actions is presented. It allows pseudo-group normalizations to be performed before the prolonged action is computed, thereby avoiding the introduction of unnecessarily complicated intermediate expressions. Several examples are provided to illustrate the algorithm.

We develop a perturbative framework for time-dependent point interactions in quantum systems with purely discrete unperturbed spectrum. In two and three dimensions the point interaction is described through the renormalized resolvent obtained from heat-kernel regularization, while in one dimension the diagonal Green function is finite and no renormalization is required. Time dependence is introduced either through the interaction parameter or through the motion of the support point. In both cases we expand the non-autonomous Hamiltonian in the spectral basis of the corresponding static point-interaction problem and derive the first- and second-order pole shifts, projection corrections, and transition amplitudes. We also describe how finite degeneracies are treated by separating the coupled point-interaction direction from the unaffected orthogonal subspace in each degenerate eigenspace. The method is illustrated by explicit examples: point interactions with time-dependent coupling, harmonic oscillators perturbed by moving point interactions, and a particle on a sphere with a moving interaction center. We also discuss the one-dimensional harmonic oscillator with a moving delta potential, showing that in the non-renormalized case the present formulation reduces to the standard time-dependent perturbation theory. Finally, an exactly solvable delta center moving with constant velocity on a circle is used as a discrete-spectrum example for the local moving-center expansion and its velocity-dependent dynamical corrections.

Given a spherical finite tensor category C, not necessarily semisimple, and a two-sided modified trace on its projective ideal, we define an open-closed three-dimensional topological field theory with values in vector spaces. The bordism category has as morphisms three-dimensional bordisms with corners, whose boundary is partitioned into the gluing boundary, parametrised by source and target surface, and the unparametrised free boundary. The free boundary is equipped with an embedded C-coloured graph satisfying an admissibility condition. Our construction starts from a new three-manifold invariant based on the multi-handlebody invariant of [arXiv:1809.07991] and the chromatic maps of [arXiv:2302.04509]. The open-closed topological field theory is then obtained via the universal construction.

We present several representations of the Schwarzschild spacetime. Some of these are classical, such as the embedding, Tortoise, and Kruskal representations. The latter two motivate the introduction of pulsating coordinates (or the Diamond representation), a compact approach recently proposed for spherically symmetric static metrics. We then introduce the Golden representation for the Schwarzschild spacetime, where what we call the Fibonacci metric, and the golden ratio, become ubiquitous. We conclude by offering some visual and physical interpretations of this approach.

The Lambert $W$ (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model to observational data, in order to estimate the model's parameters. That paper exhibits a formula for the logarithm of the relative Hubble factor at redshift $z$, $\ln(H(z)/H_0)$, which is based upon a numerical integration. That integral can be evaluated analytically, and we present the details in this working paper. The resulting analytic expression for $H(z)/H_0$ may be convenient for exploration of the LW model. We present two approximation formulas for the Lambert $W$ function, highly accurate for redshifts $z$ between 0 and 3, which may be useful for researchers who do not have ready access to a function library with the Lambert $W$ function. We also present a simplified proof of the analytic formula for another logarithmic integral which may be useful for exploring some variants of the LW model.

A coarse description of a dynamical system generally fails to evolve autonomously: evolving and coarse-graining in different orders gives different predictions, and the compressed propagator fails the semigroup law. We show that this path dependence is the observable boundary of missing state. For a finite continuous-time Markov chain with generator $L$, coarse channel $C$, and stochastic section $R$ satisfying $CR=I$, define $P=RC$, $Q=I-P$, and $K=CLR$. The exact coarse propagator $T_t=C\mathrm{e}^{tL}R$ obeys a Volterra equation with memory kernel $\mathcal{M}(t)=CLQ\,\mathrm{e}^{tQLQ}\,QLR$. Every memory jet $\mathcal{M}^{(k)}(0)$ is recursively recoverable from the short-time derivatives of $T_t$ alone. The rank of the block Hankel operator $\mathbb{H}_{\infty}=(\mathcal{M}^{(i+j)}(0))_{i,j\geq 0}$ is exactly the smallest number of auxiliary linear state variables required to turn the coarse dynamics into an exact autonomous, time-homogeneous system. A minimal completion is constructible by Ho–Kalman factorization and is unique up to similarity. If $d=\min\{k:\mathcal{M}^{(k)}(0)\neq 0\}$, then every smooth classical $f$-divergence generically scales as $t^{2d+4}$. Exact Markov examples realize exponents $4,6,8$ and closure ranks $1,2,3$. We also derive finite-sample singular-value certificates for hidden predictive coordinates, including a matrix-Bernstein bound with intrinsic-variance control. Finally, histories are identified when they induce the same future law under every admissible intervention, yielding the minimal counterfactual predictive state. The results turn coarse-graining into a constructive state-completion problem and separate ordinary linear realization from the harder requirement of a positive or Markov realization.

We disprove the conjectural converse to Kato's positivity criterion for commutators of functions of the canonical position and momentum operators $Q$ and $P$ by showing that the operator \[ i\,[\,\arctan(P),\,\arctan(Q)\,] \] is nonnegative and nonzero.

We give a Lefschetz thimble definition of the Chern–Simons–Kodama wavefunctional in Lorentzian self-dual gravity with positive cosmological constant. By complexifying the connection and choosing the Lefschetz thimble attached to the self-dual de~Sitter saddle, Witten's analytic continuation of Chern–Simons theory replaces the real contour, on which the defining integral is at best conditionally convergent, by an absolutely convergent integration cycle and yields a controlled semiclassical expansion. The relevant integrand is the full holomorphic exponential $e^{I}$, with $I=\kappa Y_{\rm CS}+(\text{source})$, and the steepest descent flow is governed by the Morse function $h=\operatorname{Re} I$. In the homogeneous isotropic de Sitter reduction, the construction reproduces the Hartle–Hawking Airy wavefunction. In the Bianchi~IX truncation, we take the Lefschetz thimble attached to the expanding de~Sitter saddle (the contracting branch defines a conjugate Lefschetz thimble); within this sector, the symmetric configuration is the only critical point for $\Lambda>0$. The corresponding Lefschetz thimble contains one trace direction with the FRW Airy structure and two anisotropic shear directions that are real-Gaussian damped at leading quadratic order. This gives a finite Bianchi~IX wavefunction which, to leading order, is the FRW Airy factor multiplied by a real anisotropy Gaussian. Thus, the Airy behavior is not an artifact of the one-dimensional minisuperspace reduction, but the leading form of the wavefunction on the Lefschetz thimble. We also discuss how the Lefschetz thimble prescription interfaces with Lorentzian reality conditions.

We develop a one-dimensional theory of dispersive elasticity within Rational Extended Thermodynamics, taking local first-order balance laws rather than higher spatial gradients as the fundamental description. A supplementary mechanical-energy law and the Ruggeri–Strumia main-field principle determine the admissible stress, internal fluxes and production. A canonical two-field hierarchy is symmetric hyperbolic under explicit convexity conditions and contains nonlinear elasticity and a generalized-stress theory as principal subsystems. For the reversible linear singular two-field class, elimination of the fast stress mode yields the Love–Rosenau equation exactly, together with a necessary and sufficient realizability condition. Nonlinear elastic stresses and non-quadratic higher-field energies are compatible with the same RET architecture; for the exact nonlinear Love–Rosenau reduction we retain quadratic higher-field inertia while allowing nonlinear elastic stress. The reduced equation admits a travelling-wave first integral. For the leading cubic elastic correction we obtain an exact parametric smooth solitary pulse in a supersonic velocity window, while the truncated-cosine compacton is excluded. Direct simulations of the hyperbolic parent system show finite-time pulse persistence in the reversible regime and slow decay under weak dissipation. The local parent energy flux is kept distinct from interstitial working in the reduced theory.