Automotive radars are increasingly susceptible to mutual interference from neighboring radar systems, which can lead to false target detections and the masking of valid targets. While current interference levels remain manageable due to the relatively low penetration of radar-equipped vehicles, this assumption is expected to break down as radar adoption and per-vehicle radar density continue to increase. This paper presents a comprehensive analysis of automotive radar performance in high-density interference environments. A realistic end-to-end simulation framework is developed at the intermediate frequency (IF) level, incorporating analytical interference modeling and detailed radar signal processing. The study evaluates the impact of interference across a range of future scenarios characterized by increased radar density and multiple radar configurations per vehicle. Conventional interference mitigation techniques are systematically assessed to validate the simulation results, controlled experiments were conducted using a host radar exposed to up to 30 interfering radars in both anechoic and real-world environments. The results demonstrate significant performance degradation under high interference conditions, with substantial reductions in detection probability and effective range. Among the evaluated techniques, time-frequency coding consistently provides the most robust performance, maintaining high detection probability even at elevated radar penetration rates. These findings highlight the limitations of current mitigation approaches and emphasize the need for coordinated and scalable interference management strategies in future automotive radar systems.

On-Policy Self-Distillation (OPSD) is a unified learning framework in which a single large language model acts simultaneously as both teacher and student. Unlike conventional knowledge distillation that relies on a separate, often larger teacher model, OPSD operates under different contextual roles: the teacher policy is granted privileged access to verified reasoning traces, while the student policy observes only the problem statement. OPSD is trained to minimize per-token distributional divergence between the two roles over trajectories sampled from the student itself, thereby aligning its own reasoning behavior with solution-aware rationalizations. OPSD eliminates the need for an external teacher, directly leverages ground-truth solution information, and resolves the distribution mismatch inherent in off-policy distillation. OPSD typically reduces GPU memory consumption by approximately 40%-60% compared to standard On-Policy Distillation (OPD). In this paper, we present a brief analysis of the conceptual foundations, methodological innovations, and principled designs underlying recent advances in OPSD for large language models. This discussion, crafted from the perspective of beginners in this field, aims to provide a concise overview of the design principles and emerging patterns of OPSD in LLMs, intended for researchers who are similarly new to this area.

We develop a unified algebraic theory of the weighted Tower of Hanoi with arbitrary nonnegative symmetric move costs depending on both disc index and pegs. Starting from a general optimality recurrence with two competing strategies -- one largest-disc move (one-LDM) and two largest-disc moves (two-LDM) -- we derive complete matrix formulations for both regimes and obtain explicit closed forms for the minimal transfer cost. The one-LDM dynamics is governed by a nontrivial linear operator whose spectral decomposition reveals a fundamental connection with the Jacobsthal and Lichtenberg sequences, while the two-LDM dynamics exhibits pure exponential growth. This framework yields exact solutions for broad classes of weight models, including peg-symmetric, disc-symmetric, polynomial, geometric, arithmetic, and sequence-induced costs. In particular, choosing classical integer sequences (Fibonacci, Lucas, Jacobsthal, Pell, Euler, etc.) as disc weights produces new derived sequences with explicit formulas and recurrences, establishing the Tower of Hanoi as a sequence-generating transform. We further introduce and analyze models with forbidden moves and move-type-dependent weights, uncovering a phase transition phenomenon in which the optimal strategy switches from two-LDM behavior for small discs to one-LDM behavior beyond a finite threshold. Our results provide a comprehensive algebraic and combinatorial understanding of weighted Hanoi dynamics and expose deep connections between optimal solutions and classical integer sequences.

We investigate the model of spontaneous baryogenesis, considering two extensions to the background paradigm. Firstly, we introduce a non-minimal coupling between gravity and the inflaton, increasing the effective mass squared of the latter. In this way, the inflaton decays more likely into fermion-antifermion pairs during reheating, through baryon-number violating processes. Accordingly, we obtain an overall baryon asymmetry consistent with cosmological observations. Then, we consider a complex scalar spectator field interacting with the inflaton through a biquadratic coupling and non-minimally with gravity, and analyze the impact in terms of baryon asymmetry production. In this scenario too, the background model results significantly enhanced, but the predicted baryon-to-entropy ratio remains smaller than the experimental data.

We analytically prove the linear radial stability of non-Abelian black holes with quartic self-interactions. The background, constructed from the Wu--Yang magnetic monopole ansatz, is an exact black-hole solution carrying a non-Abelian magnetic charge $Q_{\rm NA}^2$ controlled by a single coupling parameter $χ$, and admits two distinct branches. The odd sector is always stable, while in the even sector the effective potential is positive for branch~I and negative for branch~II, establishing stability and potential instability, respectively. The potential instability of branch~II is consistent with its connection to the perturbatively unstable Einstein--Yang--Mills Reissner--Nordström solution. Branch~I remains linearly stable throughout the physical domain of $χ$ where the solutions are regular and free of naked singularities. Our results prove the existence of the first linearly stable asymptotically flat hairy black holes in four dimensions with a minimally coupled non-Abelian Proca self-interaction.

The formation of baryon asymmetry in the Universe is considered in the left-right asymmetry model of weak interaction. In this model, the nature of CP violation is associated with the presence of a right vector boson admixture, with a mixing angle of different signs for W^- and W^+. This leads to the fact that lifetimes of neutrons and antineutrons that decay through W^- and W^+ differ. This difference gives rise to baryon asymmetry during the hadronization of quark-gluon plasma at temperatures below 150 MeV. During the phase transition from quark-gluon plasma to hadronic liquid, all three of A.D. Sakharov's conditions for the generation of baryon asymmetry in the Universe are satisfied: CP violation and process nonstationarity, resulting in baryon number violation due to the difference in the decay probabilities of neutrons and antineutrons. The generation of lepton asymmetry in the Universe in the left-right asymmetry model is associated with the presence of sterile (right) neutrinos, which do not thermalize and leave the cosmic plasma, takes away a lepton asymmetry with a sign opposite to the baryon asymmetry. Generally, baryon-lepton asymmetry arises during the hadronization of quark-gluon plasma, preserving the difference between the baryon and lepton numbers. A mechanism for the formation of dark matter by sterile neutrinos is presented. The possibility of increasing the experimental accuracy of neutron decay asymmetry measurements is noted, increasing the level of confidence in the validity of the left-right asymmetry model of weak interactions.

In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than $2\log^2{p_n}$. We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence.

We construct a new Ricci-flat metric by demagnetizing the recently reported Kerr-Bertotti-Robinson (KBR) solution. The metric is a deformation of the Kerr metric characterized by a parameter $B$, so that the asymptotic Kerr becomes a regular dome of spindle shape with north and south poles. Despite lacking an asymptotically-flat region, we find that the first law of black hole thermodynamics can be established. Some thermodynamic relations are identical to those of the Kerr black hole, as if the constant $B$ is absent. Our Ricci-flat rotating metric serves a neutral seed for a variety of inequivalent schemes of magnetizing the Schwarzschild and Kerr black holes.

We show that the mean-field underdamped Langevin process (associated to the non-linear Vlasov-Fokker-Planck equation) achieves a Nesterov acceleration with respect to the Wasserstein gradient flow of a displacement-convex free energy, in the sense that it converges at a rate of order given by the square-root of the Polyak-Łojasiewicz constant of the free energy (which is the optimal convergence rate for the corresponding gradient flow). This result has been made possible by the recent breakthrough [42] by Jianfeng Lu, which establishes such a \emph{diffusive-to-ballistic} improvement in term of entropy in the linear case.

The characterisation of exoplanetary systems depends on the accurate determination of host star parameters. The Ariel mission will probe the atmospheres of a statistically significant sample of exoplanets, and so requires a precise characterisation of the stellar properties well before its launch in 2029. The homogeneous determination of stellar parameters for Ariel will enable both the optimisation of the final target list and set roots for a reliable interpretation of the formation and evolution of planetary systems. Such a homogeneous characterisation has thus far only been carried out for the cool (\teff\ $\lesssim 7000\,$K) host stars among the Ariel target candidates. We present a uniform determination of fundamental stellar parameters for 18 hot stars in the Tier 1 candidate list of the Ariel mission candidate sample. We adopted an iterative spectro-trigonometric approach optimised for high-temperature stars. High-resolution spectra were analysed using the \textsc{zeeman} code with $χ^2$ minimisation, combining model fits to metal and Balmer lines. Surface gravity was refined using photometry-based radii and masses from stellar evolutionary tracks. We derived effective temperatures, surface gravities, projected rotational velocities, microturbulent velocities, overall metallicities, iron abundances, stellar masses, and radii for our sample of $18$ hot stars. Our results were validated against a set of benchmark stars previously presented in the literature. The derived parameters provide an internally consistent basis for studying the link between stellar properties and planetary characteristics in intermediate-mass stars. Building on our previous work on FGK host stars, we show that correlations between stellar mass, metallicity, and planetary radii also extend to early-type stars, and stellar properties influence the architecture of multi-planet systems.

We introduce a battery-explicit thermodynamic witness of post-quantum Bell correlations. In each round, a single supplied excitation is routed into an explicit two-level battery if and only if a Bell-game condition is satisfied. The routing operation is implemented by an energy-preserving controlled SWAP, with all logical control registers taken to be degenerate. Thus the correlation resource does not create energy; it only determines the probability that the supplied excitation reaches the battery. The construction is first formulated for finite two-player XOR games. For any such game, the mean battery charge is exactly the game success probability multiplied by the battery gap. Optimizing over local, quantum, or nonsignalling behaviours therefore turns the corresponding game values into local, quantum, or nonsignalling thermodynamic ceilings. For the CHSH game, Tsirelson's bound becomes a strict quantum ceiling on the mean battery charge, while a PR-box behaviour reaches the single-excitation cap. The witness is trusted-module rather than device-independent: it assumes calibrated Hamiltonians, correct classical wiring, and a trusted energy-preserving battery module. We also discuss a reversible-controller implementation, finite-statistics certification from work data, robustness to imperfect battery readout, and cyclic bookkeeping showing that no positive net work is obtained once fuel restoration and memory erasure are included.

We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.

This paper investigates the distributed fixed point seeking problem of sum-separable stochastic operators over the multi-agent network. Based on inexact Krasnosel'ski\uı--Mann iterations, the communication-efficient distributed algorithm is proposed under the relaxed growth bias and variance conditions, generalizing traditional unbiased and bounded additive variance assumptions. To enhance communication efficiency, we integrate communication compression and dynamic period skipping techniques, particularly adopting a unified compressor that allows both relative and absolute compression errors. By introducing a surrogate function for general non-contractive and contractive operators, we establish convergence guarantees of the distributed fixed point iteration, achieving among the first theoretical unifications with distributed non-convex optimization algorithms. Finally, numerical simulations validate the effectiveness of the theoretical results.

We demonstrate in situ removal of a transport-blocking defect on a surface-electrode ion trap device using a Q-switched Nd:YAG 532 nm pulsed ablation laser. This approach eliminates the need to vent and rebake the vacuum system, providing a low-overhead defect-remediation technique well suited for ion-shuttling architectures where system modifications typically incur substantial downtime - particularly in shuttling focussed experiments operating at temperatures that necessitate bakes. Additionally, the hardware used is readily available in many ion trap laboratories, making this solution attractive to experiments operating in such regimes. Following ablation, we observe near-unity shuttling success rates across the previously obstructed region and measure micromotion levels that remain within acceptable limits. This technique enables rapid, reliable restoration of transport pathways without interruption to experimental operation.

We propose a mixed quantum-classical hydrodynamic framework to model short-time inertial effects in the non-adiabatic evolution of a quantum solute coupled to a classical polar solvent. Drawing upon the work of Burghardt and Bagchi [Chem. Phys. 329 (2006), 343], we employ the Hamiltonian approach to incorporate consistent backreaction and preserve quantum decoherence beyond standard Ehrenfest dynamics. The solvent is treated as an ideal polar fluid and the quantum solute state is coupled to both the position and molecular orientation coordinates of the liquid. This approach retains essential solute-solvent correlations while significantly reducing the computational complexity of previous approaches. We further incorporate dissipative terms to capture both inertial effects and polarization relaxation. After establishing the general setting for non-local dielectric continua, the Marcus local approximation is integrated into the model thereby extending traditional solvation theory to account for collective fluid sloshing on fast timescales.

Motivated by recent proposals relating non-supersymmetric Type 0A theory to M-theory compactified on a singular wedge geometry, we study an M-theory compactification on a seven-manifold with G_2 structure, realized as a deformed K3 fibration over a compact three-manifold. In the Morrison--Vafa limit, the deformed K3 may be described locally as a non-trivial torus fibration over a base that is itself a pinched circle fibered over an interval. Once the doubled-spectrum decomposition and the local pinched structure are specified, we show that the G_2 torsion classes provide a natural and efficient way to characterize both the torsion of the seven-manifold and the resulting supersymmetry breaking in four dimensions. Reducing the system to ten dimensions in two inequivalent ways leads respectively to Type 0A and Type 0 heterotic theories compactified on two different non-Kahler manifolds, for which the SU(3) torsion classes furnish the appropriate mathematical description. In particular, we argue that the pinching deformation lies in the 27 of G_2, and that under the two reductions it is distributed differently into the W_2 and W_3 torsion classes of the corresponding SU(3) structures. In the supersymmetric limit, and under suitable assumptions, the two resulting theories may become U-dual to one another. Away from that limit, however, we argue that any such duality should be treated with considerable caution.

In this paper, we propose a framework of source encryption, where cryptographic processing is applied to a prescribed fixed length source code. The proposed source encryption framework is based on the secure communication framework of the Shannon cipher system. In the proposed framework, we use the mutual information as a measure of information leakage to an adversary. For the proposed framework, we explicitly establish the necessary and sufficient condition for reliable and secure communication under the condition that error probability and information leakage, respectively, are upper bounded by prescribed constants $ε\in (0,1)$ and $δ\in (0,\infty)$. We also show that the obtained necessary and sufficient condition does not depend on the constants $ε\in (0,1)$ and $δ\in (0,\infty)$, demonstrating that we have the strong converse theorem for the proposed framework of source encryption. We further prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text and those of the key used for the encryption.

Textile drying is a key operation in the textile production cycle as it represents one of the most energy-intensive stages and plays a critical role in determining both product quality and overall process efficiency. In this work we propose a mathematical model for the drying process of a generic textile material using heated cylinders, operating under low-pressure conditions. The model's parameters are estimated by nonlinear least squares regression. Given a specific fabric, the developed model allows to predict the drying time and the residual moisture content. The model is validated using real world data provided by a major Italian textile company.

We introduce a new family of cosmological attractors with non-minimal coupling of gravity and non-canonical kinetic terms. In the Einstein frame, these models transform into a class of exponential and polynomial attractors with the spectral index $n_{s}$ spanning a broad range $1-2/N \leq n_{s} < 1-1/N$, and $r$ can decrease to zero in the limit $ξ\to \infty$. This is sufficient to match any combination of Planck, BICEP/Keck, ACT, SPT, and DESI data. We present a supergravity implementation of these models.

This paper investigates the chaotic properties of Arnol'd cat maps (ACMs) coupled on the nodes of a circulant graph. By demanding that the system's evolution matrix be symplectic, we determine the coupling matrix, which is naturally interpreted as the adjacency matrix of a circulant graph. Specifically, the study analyses the system's Lyapunov spectra and Kolmogorov-Sinai (K-S) entropy. Numerical simulations yield the counterintuitive result that the entropy production does not increase as the connectivity of the graph increases, due to the translational symmetry of the circulant graph. Moreover, we analyse the spectra of the periods of the evolution matrix on a finite toroidal phase space of the dynamical system.

The "binding problem" of how distributed neural activity unifies into conscious experience has remained an open challenge since its articulation in 1890. We present evidence that conscious integration relies on self-organized criticality maintained by brain-body resonance, placing human cognition within the universality class of critical systems. Using 64-channel EEG data, we demonstrate that conventional preprocessing inadvertently eliminates the very integrative dynamics it seeks to measure. Removing physiological signals conventionally treated as "artifacts" drastically reduces the shared variance between global phase synchronization and stimulus-evoked amplitude, an effect highly specific to physiological components. We trace this to a fundamental brain-body resonance at 78 milliseconds that establishes zero-lag synchronization driven by robust bidirectional causality. Crucially, raw data exhibits heavy-tailed avalanche dynamics indicative of a near-critical regime, whereas conventionally cleaned data definitively rejects power-law distributions, signaling an artificial shift to subcriticality. Finally, we show these critical dynamics enable holographic information encoding, evidenced by a significant emergence of spatial interference patterns post-resonance. Together, these findings indicate that physiological signals actively and selectively support the coupling between large-scale neural coordination and event-related processing.

An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant cobordisms between involutive links. This gives a set of $39$ equivariant movie moves that suffice to go between any two movie presentations of a pair of equivariantly isotopic cobordisms. Along the way, we give a singularity-theoretic proof of the equivariant Reidemeister theorem and study loops of equivariant Reidemeister moves. Our approach proceeds by analyzing codimension $2$ singularities of equivariant maps from $S^1$ to $\mathbb{R}^2$, as well as utilizing embedded equivariant Morse theory.

We present a complete computational tabulation of all 961,619,972 P-positions in 4xn Chomp for n <= 3000, obtained via a new O(n^4) shadow-array sieve that replaces the O(n^5) hash-set approach of prior work. Three structural results are reported. First, we prove the Unique Extension property: for any triple (a,b,c), there is at most one value of d such that (a,b,c,d) is a P-position. The proof is a short contradiction using the move structure of Chomp and generalizes immediately to all k-row Chomp. Second, the P-positions exhibit a persistent bimodal decomposition into two subfamilies, HIGH and LOW, separated by a clean gap in the per-a median of d/a that grows monotonically from 0.040 at n=500 to 0.062 at n=3000, with the HIGH subfamily maintaining a stable density of 56.2% throughout. The previously conjectured global limit d/a -> 2/9 is shown to be a mixture artifact. Third, within each family the two larger row-length ratios satisfy an exact quadratic relation at machine precision, and numerical evidence suggests d/a -> 1/4 in the HIGH family, though a power-law convergence fit gives an asymptote of approximately 0.248 with exponent alpha ~ 0.05, leaving the exact limit open. The LOW family limit L3 ~ 0.183 is not well approximated by 3/16; the best rational with denominator at most 2000 is 20/109. Code and the n <= 500 dataset are available at https://github.com/gargarnav/chomp-4xn-v2.

We study a linear map on symmetric functions that ``divides'' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partitions of $n$. We determine its Schur expansion explicitly for Schur and skew Schur functions, showing that the coefficients are enumerated by a new family of combinatorial objects, called $k$-Yamanouchi tableaux, which generalize the classical ballot (Yamanouchi) tableaux appearing in the Littlewood--Richardson rule. We also study the images of elementary symmetric functions under this map, derive the power-sum expansion of their $ω$-images, and establish power-sum positivity. A further application establishes a connection to work of Tewodros Amdeberhan, John Shareshian, and Richard Stanley on alternating permutations and Euler numbers.

We present a microscopic theory of chirality-induced orbital selectivity (CIOS) in helical crystals, in which truly chiral phonons selectively transfer angular momentum to electronic orbital degrees of freedom. For a threefold helical crystal with line-group symmetry $L3_1$, we show that phonon-induced local rotations generate a rotational electron-phonon interaction proportional to $\hat{L}^{\pm}$, which drives the orbital transfer $m_{\ell}\to m_{\ell}-m_{s}$ in accordance with crystal angular momentum (CAM) conservation, where $m_{s}=\pm 1$ denotes the eigenvalue of the phonon rotational mode. Evaluating $\langle\hat{L}^{z}\rangle$ to leading order in perturbation theory, we find that the orbital response is suppressed near the $Γ$ point and the BZ boundary, and enhanced at intermediate wave vectors -- a feature intimately tied to the degeneracy structure of the phonon bands.

The crust of a neutron star (NS) provides a unique laboratory for studying matter under extreme density and magnetic field conditions that cannot be realized in terrestrial experiments. However, direct observational constraints on its composition have remained very limited. Magnetar bursts provide a promising means to probe the nuclear composition of the outer crust, as their energy release may be associated with stress-driven yielding of the crustal Coulomb lattice (including plastic deformation) and magnetic reconnection in the surrounding magnetosphere. We develop a general-purpose radiative transfer framework for a strongly magnetized electron--ion thermal plasma (MEITP) and apply it to the observed X-ray burst spectra. The spectral fits disfavor light-ion compositions and instead favor plasmas characterized by effective charge numbers around $Z \sim 37$. These results provide spectral evidence for the participation of heavy nuclei in magnetar bursts, offer new observational constraints on the baryonic content and the location of the emitting fireballs, and further imply a crustal origin of the heavy ions.

Stride-to-stride fluctuations in human walking carry a fractal correlation structure that reverses sign under external cueing: self-paced gait is persistent, whereas metronomic or visually cued gait is anti-persistent. Three decades of detrended fluctuation analysis (DFA) have established this reversal as a scaling-exponent shift, but DFA cannot distinguish genuine long-memory dynamics from short-memory autoregressive moving-average (ARMA) processes that produce the same apparent exponent. We fit the full eight-model ARFIMA(1,d,1) family to stride interval and stride speed series from three datasets (N = 70 subjects) spanning overground walking, fixed-speed treadmill walking, metronomic and visual cueing, and graded positional constraint. Model evidence is aggregated through BIC-based Schwarz weights, and the fractional differencing parameter d together with the autoregressive and moving-average coefficients phi and theta are estimated by Bayesian model averaging. Three findings emerge. (i) Long-memory specifications decisively outweigh ARMA alternatives under both persistent and anti-persistent conditions, establishing cued gait anti-persistence as a genuine fractional phenomenon. (ii) DFA alpha overestimates d + 0.5 by 0.25 to 0.34 units, a discrepancy jointly attributable to short-memory components that DFA conflates with long-memory persistence and to a finite-sample negative bias inherent to exact ML-ARFIMA estimation. (iii) The estimated (d, phi, theta) parameters are consistent with a corrective sensorimotor model in which a fractal intrinsic generator, a reactive feedback correction, and a motor-delay component together shape stride-to-stride fluctuations. Whether a single mechanistic model can account quantitatively for the observed parameter ranges across rhythmic, spatial, and unconstrained conditions is a question that the present analysis motivates but cannot alone resolve.

We identify a structural property of term-rewriting proof systems called operational inexpressibility: no derivation depends on a specified input dimension and also constrains the target question. The canonical instance is direct aggregation on the primitive recursion duplicator $F(x,y,Z)\to x$, $F(x,y,S(n))\to G(y,F(x,y,n))$, where the step argument $y$ is duplicated on the right. Under any direct whole-term measure the recursor's mass profile coincides with that of a true circular reference; the boundary operator's channel-preservation axiom and the dependency-pair soundness license separate them. Sound responses split into construction methods (polynomial interpretations, path orderings) extending the proof language, and confession methods (dependency pairs, counter-projection, size-change termination, argument filtering) projecting away the unincorporable dimension under external license; all four share a projection rank and certified-forgetting interface. Arts-Giesl soundness is $Π^0_2$-combinatorial, formalizable in $\mathrm{I}Σ_1$, with an artifact-facing $ω^3$ termination measure inside $\mathrm{RCA}_0$, far below the $\varepsilon_0$-scale of classical Gödelian reflection. The confessed burden grows quadratically across the canonical trace while residual proof work grows linearly. An architectural necessity theorem shows that any first-order step rule emitting a per-step record frame while preserving its generator must duplicate. A Layer-Crossing-Under-External-License (LCEL) schema places the confession in the Feferman-Beklemishev reflection family rather than the Lawvere-Yanofsky diagonal family, recovering the six-step structural identity with Gödel 1931 as a specialization. A witness-language hierarchy with minimal order $κ^{}$ identifies the boundary as $κ^{}(x)>0$.

Sati and Schreiber [arXiv:2402.18473, arXiv:2512.12431] have proposed that charge quantisation in quantum field theory and string theory is governed by a homotopy type $\mathcal A$. We provide a refinement of this postulate, incorporating other currents including matter, connecting it to adjustments in higher gauge theory and providing a prescription for determining $\mathcal A$, and show that, while the homotopy groups of $\mathcal A$ classify the possible brane charges, the homology groups of $\mathcal A$ classify the invertible higher-form symmetries. Furthermore, we show that the charge-quantisation postulate implies a number of non-trivial constraints on quantum field theories similar to those implied by swampland conjectures; in particular, it rules out noncompact gauge groups and one-form field strengths that form a non-nilpotent Lie algebra. Finally, we argue that for theories of quantum gravity the space $\mathcal A$ must be contractible, in accordance with the swampland conjectures on the absence of global generalised symmetries and the completeness of the spectrum of charges, and explain how this explicitly arises in the case of Type I string theory.

Motivated by the problem of the small-scale sign distribution of Laplace eigenfunctions, we introduce a strong notion of sign-balance for (eigen)functions, and prove that random eigenfunctions are sign-balanced above a precisely determined scale with almost full probability. The scale is proven to be optimal up to a logarithmic power of the energy. Our results include the important case of random spherical harmonics, as well as more general band-limited random waves on smooth Riemannian manifolds. Extending the notion of balance to arbitrary levels, we determine the precise optimum scale above which random eigenfunctions are volume-balanced with respect to non-zero levels. Beyond their intrinsic interest, our results serve as a model for a natural conjecture on the optimal scale at which deterministic Laplace eigenfunctions are sign-balanced.