Papers

The expected signature uniquely determines the law of a random rough path under a moment-growth condition, yet finite-sample bounds for estimating its truncations from a single long dependent trajectory remain unavailable. We study a strictly stationary stochastic process equipped with a geometric rough-path lift, observed in non-overlapping blocks of equally-spaced samples, and prove a non-asymptotic mean-squared error (MSE) bound for the block-averaging estimator of its truncated expected signature. Under moment and stationarity assumptions together with a direct covariance-decay condition on block signatures – strictly weaker than $\alpha$-mixing and applicable to long-range-dependent processes – the error separates into a discretization term and a fluctuation term, with rates determined respectively by path regularity and dependence strength. A levelwise rough-factorial variance analysis keeps finite-truncation constants explicit and yields an optimal allocation rule under a fixed observation budget. We verify the assumptions for independent-coordinate fractional Ornstein–Uhlenbeck processes in three regimes: short-range (Hurst $1/4<H<1/2$), semimartingale ($H=1/2$), and long-range ($H>1/2$); in all three, the block-signature covariance is summable, so the fluctuation term decays at the same rate as in the independent-block case, even under long memory at $H>1/2$. Monte Carlo experiments show empirical slopes steeper than the guaranteed upper-bound rates.

Cylindric Schur functions are a family of symmetric functions that generalize skew Schur functions. We give a short proof that skew cylindric Schur functions expand positively in terms of non-skew cylindric Schur functions. In particular, we show that the expansion coefficients are fusion coefficients.

Flexible coupler antenna systems have recently received significant research interest due to their capability to intelligently reconfigure wireless channels by controlling coupler positions and/or rotations and dynamically exploiting mutual coupling. In this paper, we investigate a new type of flexible coupler antenna, termed rotatable coupler antenna (RCA), for enabling spectrum and energy efficient wireless communication cost-effectively. Specifically, an RCA consists of one fixed active antenna and multiple low-cost passive couplers, each of which can independently rotate in three-dimensional (3D) space, so as to collaboratively achieve mechanical beamforming without requiring additional radio-frequency (RF) chains for the couplers. We study an RCA-enhanced point-to-point communication system, where one RCA is deployed at the transmitter to serve a single user equipped with a fixed antenna. Based on multi-port circuit theory, we establish the channel model and characterize the mutual coupling coefficients as a function of coupler rotations. We formulate a new problem to maximize the received signal-to-noise ratio (SNR) at the user by optimizing the 3D rotations of all couplers, subject to practical coupler rotation constraints. To tackle this nonconvex problem, we develop a spherical-cap conditional-gradient-based algorithm with cross-entropy-method initialization. Simulation results demonstrate that the proposed RCA system can significantly improve communication performance in comparison with benchmark schemes, while requiring substantially fewer active antennas and RF chains.

We prove that the short-time Fourier transform with Gaussian window performs $L^2$-local stable phase retrieval at the constant function. The proof involved significant interplay between mathematicians and LLMs. An autoformalization in Lean 4 of an extension of our result to $L^2$-local stable phase retrieval for all Hermite windows and all elements in the finite span of the canonical basis vectors is also presented.

We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.

Let $\Bbbk$ be an algebraically closed field of characteristic zero, and let $\mathcal A_q=\Bbbk_q[x,y]$ be the quantum plane, with $q\in\Bbbk^\ast\setminus\{1\}$. For a fixed automorphism $\sigma$ of $\mathcal A_q$, we study $\sigma$-derivations and their isotropy groups under the conjugation action of the centralizer of $\sigma$ in $\operatorname{Aut}(\mathcal A_q)$. For $q\neq\pm1$, we use Jordan's classification of skew derivations for toric automorphisms, which generalizes the description of Almulhem and Brzeziński for the quantum plane, to describe these groups by character equations on the torus $(\Bbbk^\ast)^2$, obtaining an arithmetic criterion for finiteness. In this case, we also prove that, for every fixed $\sigma$, every finite subgroup of the torus occurs, up to isomorphism, as the isotropy group of a $\sigma$-derivation, including when $q$ is a root of unity. For $q=-1$, we classify the $\sigma$-derivations for both toric and flip automorphisms $\sigma$ and describe their isotropy groups. In particular, we explicitly determine the isotropy groups of ordinary derivations of $\mathcal A_{-1}$.

We introduce FLASH-MAX, a shallow, exact-by-construction neural network architecture for predicting homogeneous electromagnetic fields from sparse pointwise observations. Each hidden neuron represents a separate exact solution to Maxwell's equations, so that the network satisfies the governing equations symbolically by construction and can be trained end-to-end from sparse data within seconds. We prove a universal approximation result showing that this exact model class remains universal on arbitrary domains. FLASH-MAX reaches sub-1% relative validation error from about 1K sparse pointwise observations in seconds, all while maintaining a zero PDE residual, and keeps single-digit errors even for only 100 observations sampled from 3D space. These results suggest that moving governing structure from the loss into the hypothesis class can dramatically improve the trade-off between precision and optimization speed in scientific machine learning.

Given balls and boxes both enumerated by the positive integers, we consider a sequential allocation of the balls into the boxes. We fix $\ell \ge 2$. Proceeding in increasing order of box labels, assign to each box the next $r$ smallest balls for some $ 1\leq r\leq\ell$. Given an integer $k\ge 3$, is there a natural number $N$ such that in any placement of $N$ balls into boxes, there exist $k$ balls whose labels and box labels each form a $k$-term arithmetic progression? We address this question by identifying abelian power-free fixed points of morphisms over a binary alphabet. We present sufficient conditions under which a morphism is abelian $k$-power-free. Our conditions extend Dekking's result over a binary alphabet and offer a weaker, yet more effective alternative to Carpi's. Combining Dekking's result with the template method of Currie and Rampersad, we develop a sieve technique that significantly reduces the number of parents that must be examined to establish abelian power-freeness. We then identify a binary morphism that is abelian 16-power free (but not abelian $15$-power free) with an abelian 14-power free fixed point, demonstrating the strength of our technique in verifying abelian power-freeness. Furthermore, we give a binary morphism which is not abelian power-free, yet has an abelian $5$-power free fixed point. These results offer novel examples of morphisms whose fixed points exhibit stronger abelian power-freeness than the corresponding morphisms.

The design of structures and vehicles subject to fluid-structure interaction (FSI) often requires high-fidelity coupled analysis. While the design variables pertain to the structure, the computational cost is dominated by the fluid solver, making iterative optimization prohibitively expensive. This paper presents an adaptive multi-fidelity optimization method combining high-fidelity FSI analysis with a lightweight surrogate for fluid-induced loads and a decision model that selects between surrogate and high-fidelity fluid evaluations. During optimization, completed FSI analyses incrementally update a non-intrusive surrogate model based on nearest-neighbor search and radial interpolation. A hybrid Lagrangian-Eulerian mapping function is developed to transfer fluid loads between structural designs. The evolution of surface orientation is handled by decomposing the traction vectors into local orthonormal bases. An adaptive Gaussian process regression model is employed to predict surrogate error and quantify uncertainty, allowing risk-aware selection of when coupled analysis is required. As design evaluations cluster near the optimum, the accuracy of the surrogate model naturally improves, thereby reducing the reliance on the fluid solver. It requires no offline training, preserves the high-fidelity structural model in all design evaluations, and ensures that the final design is evaluated by high-fidelity FSI analysis. The fundamental idea is justified theoretically using a simplified model problem, which shows that the leading-order error is a monotonically increasing, concave, and bounded function of the fluid added mass. The framework is demonstrated on two benchmark problems. For shape optimization of a flexible panel under shock loading, results show an $80\%$ reduction in computational cost while maintaining accuracy within $2.3\%$ of fully high-fidelity FSI optimization.

We extend the tensor-product direct solver from the Laplacian to the Schrödinger operator $-\Delta + V$. When the potential $V_1$ is separable, the operator $-\Delta + V_1$ is inverted or exponentiated at cost $O(N^{1+1/d})$ in $d$ dimensions via per-axis eigendecomposition. On a single NVIDIA A100 GPU, this costs less than one second for $10^9$ degrees of freedom in 3D. For non-separable potentials $V = V_1 + V_2$, the same solver provides a preconditioner $(-\Delta + V_1)^{-1}$ for the preconditioned conjugate gradient (PCG) method and a propagator for operator-splitting time integrators. For bounded $V_2$, we prove that the preconditioned operator has a bounded condition number and a clustered spectrum with at most finitely many outlier eigenvalues, independently of the mesh size, and also independently of the domain size when $V_1$ is a confining potential. This explains the mesh- and domain-independent PCG iteration counts observed in practice. We apply this method to ground state computation via inverse iteration for linear problems and via the $a_u$ gradient flow for Gross–Pitaevskii energy in 3D, and also Hamiltonian simulation via the approximated qHOP and Magnus-2 splitting methods from 3D to 9D on a single NVIDIA GH200 GPU.

We introduce a variational notion of essential spectrum for the Dirichlet $p-$Laplacian. We then extend the classical Persson Theorem to this nonlinear setting. This result provides a geometric characterization of the bottom of the essential spectrum, in terms of the sharp $L^p$ Poincaré constant “at infinity”. We also show that in the case $p=2$ our construction of the essential spectrum is perfectly consistent with the classical theory. Finally, as an example, we compute the full spectrum of the Dirichlet $p-$Laplacian on a rectilinear strip: it is purely essential, with no embedded eigenvalues. The arguments of the proofs are elementary and new already for the linear case $p=2$.

It is a well known fact that the eikonal equation is well posed in complete length spaces. Among the studied notions of solutions in the literature, there is one that can be defined in any metric space using the local (descent) slope and considering pointwise solutions: functionals such that their slope coincides with the prescribed data at every point of the domain. In this work we explore the question “Can we characterize the class of compact metric spaces in which every slope eikonal equation (under standard assumptions) always admits a pointwise solution?”. We provide a purely metric characterization of these spaces, as well as some interesting examples and counterexamples that illustrate the reach and limitations of the concept.

We prove that for many pairs $H_1, H_2$ of root subgroups of the automorphism group $\text{Aut}(\mathbb{C}^2)$ the diagonal action of the group generated by $H_1, H_2$ on $(\mathbb{C}^2)^m$ has an open orbit for any positive integer $m$. The result is based on the study of the Lie algebra of polynomials in two variables with the standard Poisson bracket.

A unitary perfect number is a positive integer n satisfying \sigma^*(n)=2n, where \sigma^* sums unitary divisors. Only five examples are known, and no sixth has been found. We revisit the Subbarao-Warren problem by keeping the seed factor 2^a+1 explicit in the full balance (2^a+1)\prod_i(p_i^{e_i}+1)=2^{a+1}\prod_i p_i^{e_i}. Within a bounded enumeration of source components in the odd dependency graph, every admissible source kernel is either one of the two kernels occurring in the known nonsquarefree examples, 3^2 and 5^4, or one of five additional impostor kernels. We give a reproducible three-filter certificate eliminating those impostor kernels for all relevant seed classes with 1 <= a <= 10000. The filters combine Zsigmondy-type exponent obstructions, inherited non-3-Higgs witnesses, and deterministic 2-adic budget overshoot. The remaining obstruction is the auxiliary set H_even of even m for which every prime divisor of 2^m+1 is 3-Higgs. A structural lemma reduces finiteness of H_even to the prime branch m=2p, while allowing finite computations to leave composite candidates inherited from unresolved prime divisors. Using the supplied factor cache and APR-CL primality-verification transcripts, we prove |H_even \cap [2,40000]| <= 201 and |H_even \cap [2,50000]| <= 272, with explicit undecided frontier lists. Ford's theorem for downward-closed prime sets gives an unconditional power-saving thinness bound for H_even, but not finiteness. The remaining task is a divisor-level problem for the cyclotomic values \Phi_{4p}(2). Thus the paper does not prove finiteness; it gives a bounded-box elimination, a verified finite frontier, and a precise analytic target for closing the remaining branch.

Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric means (e.g., arithmetic, geometric, or harmonic evaluations), including their related expansions for asymptotic entropy conservation. The proposed formulation works via centralized convective terms and can naturally adhere to additional structures of the flow equations such as kinetic-energy- and pressure-equilibrium-preservation.

The ${\alpha}$-quantile of a stochastic process $M_{t,{\alpha}}$ has been introduced in Miura (Hitotsubashi J Commerce Manag 27(1):15-28, 1992), and important distributional results have been derived in Akahori (Ann Appl Probab 5(2):383-388, 1995), Dassios (Ann Appl Probab 5(2):389-398, 1995) and Yor (J Appl Probab 32(2):405-416, 1995), with special attention given to the problem of pricing ${\alpha}$-quantile options. We straightforwardly extend the classical monodimensional setting to $\mathbb{R}^d$ by introducing the hyperplane ${\alpha}$-quantile, and we find an explicit functional continuity set of the ${\alpha}$-quantile as a functional mapping $\mathbb{R}^d$-valued cadlag functions to $\mathbb{R}$. This specification allows us to use continuous mapping and assert that if a $\mathbb{R}^d$-valued cadlag stochastic process $X$ a.s. belongs to such continuity set, then $X^n \Rightarrow X$ (i.e., weakly in the Skorokhod sense) implies $M_{t,{\alpha}}(X^n) \to^\textrm{w} M_{t,{\alpha}}(X)$ (i.e., weakly) in the usual sense. We further the discussion by considering the conditions for convergence of a 'random time' functional of $M_{t,{\alpha}}$, the first time at which the ${\alpha}$-quantile has been hit, applied to sequences of cadlag functions converging in the Skorokhod topology. The Brownian distribution of this functional is studied, e.g., in Chaumont (J Lond Math Soc 59(2):729-741, 1999) and Dassios (Bernoulli 11(1):29-36, 2005). We finally prove the fact that if the limit process of a sequence of cadlag stochastic processes is a multidimensional Brownian motion with nontrivial covariance structure, such random time functional applied to the sequence of processes converges, jointly with the ${\alpha}$-quantile, weakly in the usual sense.

We survey recent progress on the cohomology of moduli spaces of stable curves through the lens of the Hodge and Tate conjectures, especially their generalized coniveau forms, which relate Hodge structures and l-adic Galois representations on cohomology to algebraic cycles. We explain how the inductive structure of the boundary stratification verifies these conjectures in a surprisingly wide range of cases, describe the guiding inspiration from arithmetic, and discuss open problems and directions for future research.

This paper studies the limits of recursive classifications in proof theory and program extraction, using the refined $A$-translation as a central example. The refined $A$-translation, due to Berger, Buchholz, and Schwichtenberg, is based on recursively defined classes of formulas in minimal arithmetic $\mathsf{MA}^\omega$, in particular the classes of definite and goal formulas. One of its basic properties is that $D[\bot := F] \to D$ is derivable for every definite formula $D$. Schwichtenberg and Wainer observed that this property also holds for formulas outside the class of definite formulas and asked for a useful characterization of all formulas $D$ for which $D[\bot := F] \to D$ is derivable. In addition to definite formulas, the refined $A$-translation involves three further classes of formulas satisfying related properties. We show that none of these four properties admits a recursive characterization. In addition to this negative result, we extend the framework of refined $A$-translation in two directions. First, we add conjunction $\wedge$ to the language of $\mathsf{MA}^\omega$, whose original formulation contains only the logical connectives $\forall$ and $\to$, and adapt the formula classes accordingly. Second, we present the corresponding slightly extended formulation of the refined $A$-translation theorem and discuss possible recursive extensions of these classes. Finally, we discuss a prover written in Rust which implements the theory $\mathsf{MA}^\omega$ and the four formula classes. The prover is not used as a formal verification of the results, but serves as a case study for examining Rust as a programming language for proof assistants. We highlight some advantages and drawbacks of Rust in this setting, including its type system, support for partial constructions, ownership and borrowing model, modularity, and testing infrastructure.

For any smooth bounded domain $\Omega \subset \mathbb{R}^3$, we construct a divergence-free velocity field $u \in L_t^1 W^{1,p}(\Omega)$ for all $p < \infty$, and magnetic fields $B^\epsilon \in L_t^p C^{m}(\Omega)$ for all $p < \infty$ and $m\in \mathbb{N}$, that solve the kinematic dynamo equation and exhibit arbitrarily fast growth of any magnetic energy mode, uniformly in the vanishing-diffusivity limit $\epsilon \to 0$. The construction is based on the convex integration scheme of Modena-Székelyhidi and Cheskidov-Luo. The main novelty lies in the introduction of explicit potentials, which allow the solutions to be localized and avoid the need to work with the anti-curl operator. In addition, we present a unified scheme for the geometric transport equation (GTE), which encompasses both the transport and Maxwell equations.

We study the distribution of eigenvalues of Haar-random matrices over $\mathbb{Z}_p$ among algebraic extensions of $\mathbb{Q}_p$. Our results give $p$-adic analogues of the real-eigenvalue counting results of Edelman-Kostlan-Shub for the real Ginibre ensemble, but with a different degree behavior: while real eigenvalues form only a vanishing proportion in the real Ginibre ensemble, $p$-adic eigenvalues are asymptotically evenly distributed among possible extension degrees. We also show that the maximal unramified extension $\mathbb{Q}_p^{\mathrm{un}}$ captures all but a bounded expected number of eigenvalues, and that the expected number of eigenvalues outside $\mathbb{Q}_p^{\mathrm{un}}$ has a finite positive limit with an explicit upper bound. The proof uses correlation function formulas from the author's previous joint work with Van Peski (arXiv:2601.06283), together with uniform estimates over varying finite extensions. We also prove analogous results for roots of random Haar polynomials over $\mathbb{Z}_p$, using the correlation function formulas of Caruso (arXiv:2110.03942). These polynomial results are $p$-adic analogues of the real-root counting results of Edelman-Kostlan, again with behavior different from the real setting.

Symmetry determines which physical responses of molecules and crystals are allowed and underlies many models used throughout the physical sciences. Yet several widely used machine-learned models learn symmetry only approximately from data, raising the question of whether approximate symmetry is sufficient for scientific prediction. Using the Orb-v3 force field, we show that it is often not: the relaxed space group of a crystal depends on the orientation of the input for $47\%$ of a $150$-crystal subsample, and relaxation lowers the space group for half of all $399$ crystals studied. To characterize, quantify, and correct such failures, we introduce a tensor algebra, $\star_G$, defined by convolution over a finite symmetry group and applicable to tensors with noncommuting entries. We prove that the symmetry group determines the algebra's block-diagonal transform and use this structure to analyze model errors on symmetric targets. The resulting projections decompose the average squared error into orthogonal components arising from selection-rule violations, inconsistencies across symmetry-related inputs, and residual error. The removable components reveal how much error arises from broken symmetry, provide reference-free lower bounds on prediction error, and can be eliminated without sacrificing accuracy. For operators, projection followed by blockwise truncation yields the optimal symmetric low-rank approximation. Applying these projections to force predictions reduces both rates of space-group change to at most $2\%$. Exact selection rules, reference-free error bounds, and symmetry-preserving corrections are therefore available for any trained model without retraining.

We establish a new a priori estimate on solutions to the space-inhomogeneous Landau and Boltzmann equations. As a consequence, we prove a new continuation criterion, based on a weighted $L^\infty$-norm, without requiring bounds on the hydrodynamic quantities. This complements existing conditional regularity results from a rather different perspective. Consequently, we show that the singularities present in the fluid equations are largely incompatible with the Boltzmann and Landau equations. More precisely, we largely rule out “lifting a singularity” from the 3D Euler equations to the physical range of kinetic equations, a widely expected mechanism for singularity formation. Under general considerations, this mechanism is essentially excluded for soft potentials, whereas for hard potentials the situation is more nuanced: one cannot produce blowup through the standard hydrodynamic ansatz using known imploding solutions to the Euler equations.

We introduce the notion of $p$-adic asymptotics, or $p$-asymptotics, to the context of finite-index subgroup and subalgebra enumeration. For finitely generated groups and finite-dimensional algebras, we connect these asymptotics with the poles of their associated local zeta functions. Our two main results establish the smallest real pole for local zeta functions associated with residually nilpotent algebras, as well as its simplicity and residue whenever this algebra is graded. We thereby provide proof to parts of two conjectures raised by Rossmann and give a precise description of the $p$-asymptotic behaviour inside these algebras.

In this article, we define a locally finite graph $X$ as $\eta$-polynomially hyperbolic if there exists a Lipschitz map $\varphi : X \to Z$ to some hyperbolic space $Z$ satisfying the following condition: there exists $C \geq 0$ such that $$|B(p,R_1) \cap \varphi^{-1} (B(q,R_2))| \leq (C R_1)^{\eta(C R_2)} \text{ for all } p,q \in X, R_1,R_2 \geq 0.$$ The picture to keep in mind is that coarse fibres of $\varphi$ have polynomial growth with a degree coarsely controlled by $\eta$ as the thickness of the fibres grows. The map $\eta$ quantifies how brutal we have to be in order to turn $X$ into a hyperbolic space. Our main result is that, among cocompact special groups, being $\mathrm{lin}$-polynomially hyperbolic amounts not to contain $\mathbb{F}_2 \times \mathbb{F}_2$ as a subgroup. Consequently, containing $\mathbb{F}_2 \times \mathbb{F}_2$ as a subgroup turns out to be quasi-isometric invariant for cocompact special groups.

Models of opinion dynamics aim to capture how individuals' opinions change when they interact with each other. One well-known model of opinion dynamics is the Deffuant–Weisbuch (DW) model, which is a type of bounded-confidence model (BCM). In the DW model, agents have pairwise interactions, and they are receptive to other agents' opinions when their opinions are sufficiently close to each other. In this paper, we extend the DW model by studying it on networks with heterogeneous and adaptive edge weights between pairs of agents. These edge weights govern the interaction probabilities between the agents and thereby encode the idea that people are more likely to communicate with individuals with whom they have previously compromised or had other positive interactions. We prove theoretical guarantees of our adaptive edge-weighted DW model's convergence properties, the long-time dynamics of its edge weights, and the model's associated “effective graph", which is a time-dependent subgraph that includes edges only between agents that are receptive to each other's opinions. We support our theoretical results with numerical simulations of our adaptive edge-weighted DW model on a variety of networks and find that including adaptive edge weights yields different qualitative dynamics for different types of networks. In particular, for small confidence bounds, we observe that incorporating adaptive edge weights decreases the convergence time for dense networks but increases the convergence time for sparse networks.

We use the Brascamp–Lieb inequality from functional analysis to prove novel inequalities for the upper box, packing, and Assouad dimensions of fractal sets in terms of the dimensions of certain projections. Analogous inequalities do not hold for Hausdorff or lower box dimensions. We apply these fractal Brascamp–Lieb inequalities to establish new exceptional set estimates for orthogonal projections and to provide sharp dimension estimates for certain constrained sumsets. We also establish analogous nonlinear inequalities via the nonlinear Brascamp–Lieb inequality.

We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class of regular matroids of rank at most six. To accomplish this, we show that it is increasing under matroid extensions and then estimate it for each of the maximal simple regular matroids of rank at most six.

In this paper we construct classifying localic categories and groupoids for various bundles equipped with logical structure. When these bundles are local homeomorphisms, we recover the localic groupoids that classify geometric theories, demonstrating that these groupoids satisfy a stronger universal property than that of their corresponding classifying toposes. We also prove a dual result that there exist classifying localic categories and groupoids for proper separated bundles satisfying a dual geometric theory. Thus, localic groupoids classify strictly more kinds of logical theories than toposes. Our approach provides a concrete construction of the localic categories and the generic bundles involved in terms of generalised frame presentations. To accommodate our approach, we prove en passant a constructive, pointfree version of the Alexandroff–Hausdorff theorem and that internal functors that are fully faithful and effective descent morphisms on objects induce equivalences between the categories of discrete opfibrations over the source and target categories.

The first $\ell^2$ Betti number of a group is non-decreasing under various embeddings arising from first order logic. Strict inequality is proved for elementary embeddings of non-abelian proper subgroups within torsion free hyperbolic groups using Perin's classification of such inclusions. The monotonicity is further demonstrated for existential embeddings of arbitrary finitely generated groups.

Optimizing schedules in real-world settings often requires considering workload constraints, specially for human resources, to ensure regulatory compliance, impose rest periods, or level the workload over the working horizon. This paper focuses on tackling this family of constraints in the context of preemptive jobshop scheduling, as preemption is particularly relevant when human resources are involved (allowing personnel to flexibly switch between tasks). Preemption also offers theoretical insights as a relaxation of non-preemptive problems. The main contribution of this paper is a Constraint Programming approach designed to handle effectively maximum workload constraints in a preemptive setting, without decomposing activities into unit-duration tasks (which may be computationally prohibitive). Since workload constraints introduce significant additional complexity, we further propose a method that iteratively introduces the workload constraints into the problem, along with tailored heuristics specifically designed to guide the search efficiently. The experimental results demonstrate the effectiveness of our approach on a large set of instances, highlighting its performance compared to a well-known industrial solver, IBM's CP Optimizer.