Papers

The method of types is a fundamental tool in classical information theory, with applications ranging from composite hypothesis testing and universal source coding to the capacity of arbitrarily varying channels. In this work we introduce an empirical operator acting as a quantum analog of the empirical distribution. We show that this empirical operator satisfies combinatorial and large-deviation bounds, which in combination describe a quantum method of types. As an application, we use our method to prove a universal achievability result for composite quantum hypothesis testing.

This work investigates how torsion and nonmetricity modify tidal accelerations in metric-affine gravity. We derive a projected deviation equation that generalizes the standard geodesic deviation equation to metric-affine geometry, and apply it to the relative acceleration of neighboring autoparallels in the weak-field, nonrelativistic limit. In this regime, the tidal acceleration separates into the usual Newtonian contribution and linear post-Riemannian corrections sourced by torsion and non-metricity. By decomposing torsion and nonmetricity into their irreducible Lorentz components, we identify the corresponding signatures in the tidal tensor and discuss to what extent these contributions can be distinguished. We then show how future direct tidal measurements could be translated into benchmark bounds on post-Riemannian tidal contributions, assuming probe dynamics sensitive to the affine connection. Our results suggest that the tidal acceleration may provide a systematic route toward probing post-Riemannian spacetime features in the future.

The morphology of a spectral-line profile contains information beyond scalar summaries of line strength, centroid, width, global asymmetry, or diagnostic line ratios. Broad wings, shoulders, double peaks, secondary components, and composite emission–absorption structures encode how flux is ordered across wavelength but can remain indistinguishable under conventional summaries. We introduce an interpretable geometric representation of line profiles inspired by rough path theory. Each wavelength-sampled profile is mapped to a common systemic rest-frame velocity grid and treated as a trajectory in velocity–flux space, traversed from blue to red. From this path, we define a compact set of low-order descriptors measuring signed velocity–flux area, blue–red imbalance localization, higher-order shape complexity, and emission–absorption ordering. Using synthetic profiles, we show that these descriptors separate morphologies with similar full width at half maximum (FWHM), non-parametric velocity width ($W_{80}$), and low-order moment summaries. We then apply the method to MaNGA integral-field spectroscopy by computing H$\alpha$ descriptors in individual spaxels and clustering them in a low-dimensional feature space. The resulting classes form spatially coherent regions of similar ordered line morphology. Although no external velocity field is supplied to the clustering, stacked spectra within these regions recover coherent large-scale centroid-velocity patterns broadly consistent with the MaNGA reference velocity fields. We release a minimalist MIT-licensed package ${\it spectropath}$, available at \href{https://rafaelsdesouza.com.br/spectropath/}{the project website}.

We prove that a certain representation of the Baumslag-Gersten one-relator group $\mathrm{BG}(1,2)$ by germs of continuous functions is not faithful. This gives a negative answer to a problem of A. Yu. Olshanskii from 2010 (Problem 17.99 in the Kourovka Notebook).

We construct integrals of uniformly bounded ultraweakly measurable functions against positive operator-valued measures (POVMs) in von Neumann algebras, assuming that the integrand algebra has separable predual. The integral lies in the spatial tensor product and is uniquely characterized by its evaluations on product normal states. Integration is unital and completely positive and descends faithfully to the quotient by POVM-null functions. When both preduals are separable, this quotient is a von Neumann algebra and integration is normal, agreeing with the amplification of scalar POVM integration. We establish a dilation factorization, a Leibniz rule and a Fubini theorem, and specify the additional joint-normality hypothesis needed for realization in an ambient algebra. As an application, under the stated separability and joint-normality assumptions, we extend operational quantum reference frame relativization to covariant POVMs on arbitrary measurable spaces carrying a group action. Its domain is the fixed-point von Neumann algebra of system-valued functions modulo null equality. For homogeneous spaces of second countable locally compact Hausdorff groups with closed stabilizers, this domain is identified with the stabilizer-fixed system algebra. For sharp frames, relativization is a normal unital $*$-homomorphism, faithful when ambient multiplication is injective. For localizable frames on metrizable spaces, restriction recovers continuous integrands at supported configurations. On trivial principal bundles, the domain is identified with system-valued fields on the base. These results provide integration machinery for forthcoming applications to relativistic gauge theories.

Investigating the non-perturbative behavior of QCD and the dynamics of strong interaction is crucial for the study of heavy quarkonia and the understanding of exotic fully-heavy tetraquarks. In this work, using the analytical exact iteration method (AEIM), the analytical eigenvalue solutions of the non-relativistic Schrödinger equation are obtained in the presence of topological defects and external magnetic flux. The interactions are modelled using a modified Cornell potential supplemented by harmonic and inverse quadratic terms. We demonstrate that the energy levels are distinctly shifted by the topological defect parameter ($\alpha$). The mass spectra of heavy quarkonia ($c\bar{c}$ and $b\bar{b}$) and fully-heavy tetraquarks ($cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$) across several radial and orbital excitation states are successfully calculated using this approach. The computed masses of bottomonium and charmonium accord well with current theoretical predictions and experimental findings. Our findings for the heavy tetraquarks are in line with previous theoretical investigations that consider tetraquarks as configurations of diquarks and antidiquarks. The numerical results demonstrate that a nontrivial interaction between the confining potential and the background space-time geometry governs the mass hierarchy of these exotic hadronic states, providing high-precision data with excellent agreement with established theoretical models and experimental benchmarks.

We show how the geometric information in the motivic Hall algebra and the correspondence of the moduli stack recovers the Auslander-Reiten sequences and the Auslander-Reiten quiver.

We study the distance between two uniformly chosen points on a uniform random triangulation whose genus g is proportional to the number of faces 2n. We show that the distance rescaled by log(n) converges in probability to a deterministic constant, which answers a conjecture of Budzinski, Chapuy and Louf. The proof relies on the precise study of the volume growth of the ball of radius r for r of order log(n). The main ingredients are the recent local convergence results for uniform triangulations with boundaries and the isoperimetric inequalities obtained by Budzinski and Louf.

Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution. Recent hybrid methods promote physical correctness by targeting the PDE residual via gradient descent or Gauss–Newton steps, but inherit the compute cost and instability of the underlying classical optimizers. We show, theoretically and empirically, that numerically minimizing the PDE residual can be an unreliable proxy for reconstruction accuracy in ill-conditioned systems, explaining why these methods often do not make accurate predictions despite achieving low residuals. We propose error-conditioned Neural Solvers (ENS), built on a different principle: rather than an optimization target, the PDE residual field is passed as a direct input to the network at each iteration, enabling it to read the spatial structure of its own errors and learn an update policy to iteratively correct its predictions. Across four PDE families, ENS attains the highest prediction accuracy in the large majority of settings, with gains reaching $10\times$ on turbulent Kolmogorov flow, while avoiding the expensive compute cost of hybrid methods. ENS's learned correction policy generalizes under distribution shift, including zero-shot parameter changes and cross-equation transfer, where its relative advantage is largest in the ill-conditioned regimes where residual minimization is least reliable. Project website: https://neuralsolver.github.io/.

Given a finite nonempty planar point set $S$, what is the maximum number of congruent copies of $S$ contained in a set of $n$ points in the Euclidean plane? Building on OpenAI's recent breakthrough on the unit distance problem, we construct planar sets consisting of $n$ points that contain $\Omega_S(n^{1+\delta_S})$ congruent copies of $S$, for some positive constant $\delta_S$ depending only on $S$. This answers a question of Brass and Pach in a strong form, and makes progress on questions posed by Erdős and Purdy, and Ábrego and Fernández-Merchant. Our proof uses the number field construction from Sawin's quantitative refinement of OpenAI's result and consequently yields an explicit choice for $\delta_S$ for each fixed $S$.

How different are several probability distributions from one another? For two distributions the standard answer is the family of Rényi divergences, singled out by two natural requirements: processing the data never makes distributions easier to tell apart, and independent repetitions add. Many problems in learning and statistics compare more than two distributions at once, such as testing among several hypotheses or bounding generalization against several priors. The same two requirements leave one kind of building block, built on a coincidence probability: how unlikely it is that independent samples, one from each distribution, all show the same empirical distribution. The logarithm is forced because repetitions add, which is already visible for a single experiment repeated. This characterization is known in greater generality, and this paper is about the meaning of its building blocks. On a finite alphabet, each building block indexed by a rational point of the simplex is the exponential rate of that coincidence as the samples grow in fixed proportions. Each is also the limiting free energy of Bayesian inference over distributions. At any amount of data, the free energy of the posterior is the coincidence measure plus two costs: the expected distance from a posterior draw to the most likely distribution, and the information gained per unit of data. Both costs vanish as data accumulate. When the comparison is conditioned on side information, every kind of building block has a conditional counterpart, and the coincidence ones alone do not suffice.

We introduce coquasi-bialgebroids over a noncommutative base algebra. Using Takeuchi's \(\times_B\)-coalgebra formalism, we require the coproduct to remain an algebra map into the Takeuchi product, while the product is associative only up to an invertible normalized \(3\)-cocycle. This gives a bialgebroid analogue of coquasi-bialgebras and provides a natural framework for cocycle-twisted bialgebroid constructions. We develop the basic theory and prove a twisting theorem by convolution-invertible \(2\)-cochains. As a main class of examples, we construct coquasi Connes–Moscovici-type bialgebroids on \(B\otimes H\otimes B\), where \(H\) is a coquasi-bialgebra measuring an algebra \(B\), with twisting data \(\gamma:H\otimes H\to B\). We also give finite-group examples arising from a subgroup \(G\subseteq X\) and a choice of transversal. Finally, under finite projectivity assumptions, we describe the dual quasi-bialgebroid construction and its relation to Drinfeld-type twisting.

We give an operadic approach to deformation quantization of vertex Poisson algebras, a chiral analogue of the traditional problem of deformation quantization of Poisson algebras. Our main result is an order-by-order deformation-obstruction theory for such quantizations, controlled by the chiral analogue of Poisson cohomology. In the special case of chiral quantizations of affine symplectic varieties, quantizations of the vertex Poisson algebras of functions on their arc spaces, we prove that this deformation-obstruction theory is controlled by their de Rham cohomology. As another application, we prove that the boundary Virasoro minimal models are rigid under deformations.

The Godbillon–Vey class is a secondary characteristic class which is defined for regular foliations and has been studied extensively. In this paper, we fix a Lie algebroid and relatively define the Godbillon–Vey class for its Lie subalgebroids, and study their properties. We also present several examples.

The dynamics of local subsystems in a thermodynamically large quantum many-body system can be understood as effectively open as the system produces its own effective bath. The action of this bath can be characterised in terms of the so-called influence matrices. In generic situations, the complexity of these objects grows unfavourably with time, however, there exist solvable cases where influence matrices can be characterised exactly even in the presence of non-trivial interactions. Here we show that Rule 201, a deterministic version of the Floquet-PXP model, is one of these solvable instances. Indeed, it admits influence matrices given by a finite-dimensional matrix-product operator (MPO) that solves a finite set of algebraic conditions. We provide the solution, and characterise multi-time autocorrelation functions.

We investigate the local and global geometry of almost complex $4$-manifolds admitting non-degenerate torsion bundle. The rigidity of these structures forces a parallelizable $J$-adapted double cover, which imposes severe topological constraints on the underlying manifold. Exploiting this rigidity, we give a complete classification in the homogeneous setting. We show that such a manifold is diffeomorphic either to a $4$-dimensional Lie group carrying an almost complex structure with non-degenerate torsion bundle, or to a product $L(4,1)\times\mathbb R$ or $L(4,1)\times\mathbb T$, where $L(4,1)$ is a lens space. We also determine exactly which real $4$-dimensional Lie algebras admit such a structure. Constructively, we realize every admissible algebra by an explicit invariant structure, thereby closing the existence question in dimension $4$. We also relate these structures to certain Engel structures that we call Nijenhuis–Engel, and answer the resulting existence questions in the homogeneous case.

A flexible forward (FF) is a customized FX hedging instrument that guarantees a fixed exchange rate while letting the holder choose the delivery date within a pre-agreed window. It is therefore an American-style option on timing, and its valuation must respect the volatility skew of the underlying currency pair. We price FF contracts (and, more generally, American options) under a time-inhomogeneous Heston model which captures the forward-skew term structure while preserving analytical tractability through a recursive (matrix) Riccati solution for the joint characteristic function. Extending the integral-equation (decomposition) approach to time-dependent coefficients, we derive a Volterra equation characterizing the early-exercise surface. The expectation in the decomposition formula is evaluated by two complementary spectral methods: a double cosine (COS) expansion of the transition density, and a damped-Sinc (DSINC) local-basis scheme that is more accurate and stays robust when a low Feller ratio or large vol-of-vol induces Gibbs oscillations in the COS series. Benchmarked against a penalty-iteration MCS-ADI finite-difference solver, both methods price a contract in about 1-2 seconds, roughly an order of magnitude faster than the finest finite-difference grid, while DSINC improves median accuracy over COS by about a factor of twelve. The experiments also show that the early-exercise surface is a substantially nonlinear function of the variance, contrary to the linear-in-variance approximation common in earlier work.

We prove a precompactness result for homogeneous Einstein metrics on the set of homogeneous torus bundles over a common base. This set can contain infinite families of compact simply connected homogeneous torus bundles over a common simply connected base with toral fibres of fixed dimension.

For a graph $G$ and a field $\mathbb{F},$ the first clique-homology $H_1(\text{Cl}(G),\mathbb{F})$ vanishes precisely when the cycle space of $G$ over $\mathbb{F}$ is generated by the signed boundaries of the triangles. We develop cycle-surgery methods for establishing this property in arbitrary characteristic and apply them to strongly regular graphs. Combining our results with Neumaier's classification, we show that $H_1(\text{Cl}(G),\mathbb{F}) \ne 0$ can only occur in the Petersen graph, the Shrikhande graph, the complete bipartite graphs, the conference graphs on at most $255$ vertices, the lattice graphs, and the finite exceptional families $E_m$ in Neumaier's classification of strongly regular graphs with smallest adjacency eigenvalue $-m$, for some integer $m \geq 3$. Consequently, if $(G_n)_{n\geq 1}$ is an infinite family of pairwise distinct strongly regular graphs and $(\mathbb{F}_n)_{n\geq 1}$ is a sequence of fields such that $H_1(\text{Cl}(G_n), \mathbb{F}_n)\not=0$ for every $n$, then either $G_n$ is a lattice graph for infinitely many $n$, or $\lim_{n\rightarrow +\infty} \lambda_{\min}(G_n)=-\infty$. For Latin square graphs, we determine the clique homologies over arbitrary fields and show that if $G$ is the strongly regular graph associated with a Latin square $M$ of order $n \geq 5$ and $\mathbb{F}$ is any field, then $H_i(\text{Cl}(G),\mathbb{F})=0$ for $i=1$ or $i \geq 3$, and $\dim H_2(\text{Cl}(G),\mathbb{F})=(n-1)^3-I(M),$ where $I(M)$ is the number of $2 \times 2$ Latin subsquares or intercalates in $M$.

We invariantly define Gelfand-Shilov spaces on classes of non-compact manifolds with a certain “structure at infinity”. We also construct and study a global calculus of pseudodifferential operators on such manifolds, locally defined by symbols satisfying estimates associated with weight sequences. The operators so obtained act naturally on the previously defined Gelfand-Shilov spaces. These generalise analogous functional spaces and operators defined on Euclidean spaces.

This article examines the Kolmogorov equation corresponding to the following stochastic two- and three-dimensional incompressible ($\nabla\cdot\boldsymbol{u}=0$) convective Brinkman-Forchheimer equations, also known as the damped Navier-Stokes equations, driven by Lévy noise on the torus: \begin{align*} \mathrm{d}\boldsymbol{u}+[-\mu\Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}+\nabla p]\mathrm{d} t =\sqrt{\mathrm{Q}}\mathrm{d}\mathrm{W}+\int_{Z}\sigma(t,z)\widetilde{\pi}(\mathrm{d} t,\mathrm{d} z), \end{align*} where $\mu,\alpha,\beta>0$ are physical constants; $\mathrm{Q}$ is a non-negative, trace-class operator; $\mathrm{W}$ is a cylindrical Wiener process on a Hilbert space; $\sigma$ represents the jump-noise coefficient; $(Z,\mathscr{B}(Z))$ is a measurable space; $\pi$ is a time-homogeneous Poisson random measure; and $\widetilde{\pi}$ denotes its compensator. The main contribution of this work is the establishment of the essential $m$-dissipativity of the corresponding Kolmogorov operator, a property that has received limited attention in the existing literature for systems driven by jump-type noise. \emph{Our main innovation is that, in contrast to traditional techniques which crucially depend on exponential moment estimates, we utilize the intrinsic structure of the absorption term $\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}$ to dispense with these requirements. This allows us to establish the essential $m$-dissipativity of the Kolmogorov operator without the need for exponential moments.} We apply the developed framework to an infinite-horizon stochastic optimal control problem, demonstrating the solvability of the associated infinite-dimensional Hamilton-Jacobi-Bellman (integro-differential) equation.

We establish asymptotic formulae for two-piece amplified second and fourth moments of the Riemann zeta function. As applications, we obtain unconditional effective lower bounds for several joint moments of zeta which are in strong agreement with the conjectures of Keating–Wei and Keating–Snaith. In particular, we prove an unconditional lower bound for the sixth moment of zeta $M_3(T)\geq(34.4+o(1))c_3T(\log T)^9$. We further improve some of the lower bounds obtained by Soundararajan, removing the assumption of the Lindelőf Hypothesis, and we obtain effective lower bounds for all joint integer moments of zeta consistent with the predictions of random matrix theory.

We study the weighted fruit Diophantine equation $ax^{d} - c\bigl(m^{2}y^{2}+n^{2}z^{2}\bigr) + xyz - b = 0$, generalising previous work by Majumdar–Sury, Vaishya–Sharma, and Prakash–Chakraborty. Subject to specific hypotheses on the parameters, our main result shows that for any prime $l \equiv 3 \pmod 4$ and $b = a (2 c m n)^{d} - l\, c^{s}t^{2q}$, the above equation has no integer solutions except for certain residue classes of $x$ modulo $4l$. An analogous result also holds when $l$ is replaced by an odd power of $l$ in the definition of $b$. We prove some insolvability results for $l=-1$. By applying the main result to the small values of $l$, such as $l \in \{3, 7, 11, 19\}$, we explicitly determine the exceptional residue classes outside of which the equation has no solutions. In particular, for $l = 3$, this yields complete insolvability, and weakening these hypotheses still yields non-existence results, though with specific coprimality restrictions on any possible solutions. We also consider a more general variant of the above Diophantine equation and provide some insolvability results. Subsequently, we establish bounds for the positive solutions of the aforementioned equation. Finally, by associating a family of hyperelliptic curves with the equation under consideration and applying Grant's analogue of the Nagell–Lutz theorem, we translate these insolvability results into results about their rational torsion points.

Fermionic time-reversal-invariant insulators in two dimensions–class AII in the Kitaev table–come in two topological phases. These phases are characterized by a $\mathbb{Z}_2$-valued invariant, the Fu-Kane-Mele index. We prove a geometric bulk-edge correspondence for curved interfaces: if two such insulators occupy complementary regions separated by a curved boundary, then the $\mathbb{Z}_2$ edge index of the interface system is the product, modulo two, of the difference of the two bulk $\mathbb{Z}_2$ indices and a geometric intersection number associated with the boundary and the measurement region. The argument is a $\mathbb{Z}_2$ analogue of the curved-interface connection formula proved for Hall insulators in \cite{DZ24}.

This article establishes a verification theorem for an optimal control problem governed by the two- and three-dimensional convective Brinkman–Forchheimer equations on the $d$-dimensional torus, $d\in\{2,3\}$: $$\frac{\partial\mathfrak{u}}{\partial t} -\mu\Delta\mathfrak{u} +(\mathfrak{u}\cdot\nabla)\mathfrak{u} +\alpha\mathfrak{u} +\beta|\mathfrak{u}|^{r-1}\mathfrak{u} +\nabla\mathfrak{p} =\boldsymbol{f}, \qquad \nabla\cdot\mathfrak{u}=0,$$ where $\mu,\alpha,\beta>0$ and $r\in[1,\infty)$. We derive the Pontryagin maximum principle and develop a verification framework for the associated control problem, a topic that has received comparatively little attention for fluid models of Navier–Stokes type. A major challenge in establishing the verification theorem and the corresponding feedback characterization for the CBF system is that the analysis requires a substantially different regularity framework from that used for the two-dimensional Navier–Stokes equations. In particular, the present approach relies on strong solution theory, a delicate treatment of the nonlinear absorption term, novel estimates in negative-order Sobolev spaces, and continuous dependence estimates in stronger topologies, especially in the three-dimensional setting. A distinctive feature of the present work is that the verification framework is developed not only in two dimensions, but also in the three-dimensional supercritical regime, corresponding to $r\in(3,5]$, and in the critical case $r=3$ under the condition $2\beta\mu\geq1$. Consequently, the feedback characterization and verification arguments can be rigorously justified in both two and three dimensions.

Let $X\subseteq \mathbb{P}^{3}$ be a very general element of the Noether-Lefschetz divisor that parametrizing smooth quartic surfaces containing a line. Let $L\subseteq X$ denote the corresponding line. We study the curves contained in $X$ and analyze their behavior in the Hilbert scheme. We first determine which linear systems contain smooth irreducible curves. For most classes, we verify that the general member is a smooth point of the expected Hilbert scheme. Finally we compute the Rao function of any curve on $X$.

As the study of temporal and spatial discretization schemes continues to advance, recent work has focused on the use of Galerkin-in-time discretization schemes that enable broader structure-preservation than is known for Runge-Kutta integrators. While the promise of such discretizations is immense, their realization has, until now, generally relied on bespoke implementations that have limited their wider use. In this work, we present automation in Irksome for both discontinuous Galerkin and continuous Petrov-Galerkin time stepping of semidiscrete variational problems. The implementation supports auxiliary variables, flexible temporal quadrature, and monolithic algebraic solvers, and it enables switching between Runge-Kutta and Galerkin-in-time formulations with minimal changes to user code. Numerical examples illustrate accuracy, solver performance, and structure preservation across representative PDE systems.

We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace. Lee, Mehrotra and Zampetakis (FOCS'24) recently obtained the first polynomial time algorithm for this problem, but their resulting sample and time complexity bounds are not optimal. Under non-trivial truncation, for any target accuracy $\varepsilon > 0$ and dimension $d$ we give an efficient algorithm that uses $n = \tilde{O}(d^2/\varepsilon^2)$ samples and learns the underlying Gaussian to error $\varepsilon$ in total variation distance. Our algorithm is also fast: its runtime is dominated by the cost of computing the empirical covariance matrix. Both our sample and time complexity are optimal in terms of $d$ and $\varepsilon$ even without truncation: in this regard, we can learn a Gaussian under halfspace truncation for free. The key ingredient behind our result is a novel reinterpretation of the low-degree moments of the truncated Gaussian in terms of a relative truncation parameter. This relative truncation parameter uniquely determines the parameters of the untruncated Gaussian and enables direct parameter recovery. This reinterpretation allows us to circumvent the time intensive projected stochastic gradient descent procedure that is widely used in learning under truncation.

Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning, yet the theoretical conditions under which a ground-truth ODE can be uniquely and stably identified from multiple solution observations remain largely undeveloped, and no quantitative analysis of the sample complexity of such learning tasks exists in the literature. To address this gap, we introduce the Hausdorff distance on solution sets as the natural metric for comparing differential equations, since it captures the worst-case separation between two equations over all admissible initial conditions and thus encodes the minimax structure of the identification problem. We establish identifiability bounds for governing ODEs across a wide class of structure equations–ranging from linear ODEs to nonlinear classes with Lipschitz (Hölder)-continuous vector fields–characterizing precisely when two distinct equations can be distinguished from solution data. Using this metric, we derive metric entropy estimates for the relevant ODE classes and analyze sample complexity bounds, quantifying how many solution observations are needed to reliably recover the governing equation.

This paper is devoted to the analysis of a quasi-variational–hemivariational inequality associated with the convective Brinkman–Forchheimer extended Darcy (CBFeD) equations for Bingham fluids in both two and three spatial dimensions. The considered model describes incompressible fluid flow through porous media while incorporating convection, nonlinear damping effects, and Forchheimer-type resistance, together with non-smooth and non-convex slip boundary conditions. We first derive an appropriate weak formulation of the problem, which leads naturally to a Bingham-type quasi-variational–hemivariational inequality with a velocity-dependent constraint set. By employing the Kakutani–Ky Fan fixed point theorem, we establish the existence of weak solutions for the resulting multivalued quasi-variational inequality formulation of the CBFeD system. Furthermore, we prove that every weak solution of the associated quasi-variational inequality is also a solution of the corresponding quasi-variational–hemivariational inequality. The analysis presented in this work provides a rigorous mathematical framework for CBFeD models with Bingham fluids under non-monotone and non-smooth boundary interactions.