Papers

Relativistic magnetic reconnection is a key mechanism for particle acceleration in astrophysical plasmas. Recent 3D particle-in-cell simulations have shown that, for weak guide fields, particles can be accelerated at nearly the maximal rate by escaping the reconnected plasma and gaining energy from the large-scale upstream electric field. Here, we investigate whether this fast acceleration channel persists as the guide field becomes comparable to the reconnecting field. We perform 3D simulations of relativistic pair-plasma reconnection, complemented by corresponding 2D runs, using open boundaries along the reconnection outflows to establish a quasi-steady state. We find that increasing the guide field strength reduces the reconnection rate and causes energetic particles to become more closely aligned with the local magnetic field. In 3D, the fast acceleration channel—absent in 2D—persists across the full range of guide fields investigated, but involves a progressively smaller fraction of particles as the guide field increases. Consequently, stronger guide fields produce steeper particle energy spectra and lower maximum Lorentz factors.

We improve an earlier characterization of the Sobolev space $\dot W^{1,p}(\mathbb R^d)$, $1<p<\infty$, in terms of the oscillations of a function on balls of varying centers and radii. In contrast to earlier work, finiteness of the supremum is replaced by the formally weaker assumption of finiteness of the liminf, thereby answering a question by Brezis.

Suspicion is an important, yet elusive concept in anti-money laundering and counter-terrorist financing (AML/CFT), which allows for intervention below the threshold of proof. In its traditional form, suspicion can be understood as a situated legal judgement by human actors within identifiable jurisdictions. It is argued that this understanding is no longer adequate. As artificial intelligence (AI) becomes an integral part of financial surveillance, suspicion is increasingly produced through data-driven processes. This transformation is epistemic, but also spatial. Since AI-driven financial surveillance operates through transnational data infrastructures, regulatory reach is less a matter of where conduct occurs than a question of whether such conduct becomes visible within data systems. This article develops the concept of algorithmic extraterritoriality, understood as a form of regulatory power mediated by data infrastructures rather than formal assertions of jurisdiction. Moreover, since individuals are increasingly constituted as datafied subjects of suspicion, they are rendered governable through dispersed and opaque processes of evaluation. This constitutes a challenge for accountability and contestability because suspicion becomes more difficult to locate, explain or contest.

We study the QWEP property of twisted crossed products and its relation to Fourier multiplier transference on noncommutative $L_p$-spaces. We show that QWEP is not preserved by crossed products of QWEP von Neumann algebras by hyperlinear groups. Our examples include trace-preserving actions of a torsion-free residually finite Kazhdan group on a diffuse abelian algebra and on the hyperfinite type II$_1$ factor. We also obtain non-QWEP crossed products with nontrivial scalar cocycles. For scalar twists, we prove that a finite trace-preserving crossed product is QWEP if and only if its ordinary crossed product and its twisted group von Neumann algebra are QWEP. In the positive direction, we establish a restriction theorem for scalar twists of regular wreath products. These results provide QWEP inputs for Fourier multiplier transference and identify a completely bounded multiplier norm obstruction to QWEP. Finally, operator-valued cocycles give finite QWEP crossed products whose acting groups are not hyperlinear.

Reinforcement learning (RL) for Text-to-3D (T23D) generation requires optimization across multiple quality dimensions such as semantic alignment and texture clarity. Existing methods typically optimize these dimensions simultaneously through multiple reward aggregation, without explicitly modeling inter-dimension dependencies. This can cause imbalanced optimization and persistent interference among conflicting dimensions. To address this limitation, we propose OuroReward, an interference-aware sequential reward scheduling strategy for T23D RL. OuroReward first estimates pairwise dependencies among dimensions and constructs a cyclic optimization path that minimizes cumulative interference. By incorporating the tail-to-head dependency, the cycle captures global compatibility across the entire schedule. Then, OuroReward converts the cycle into a one-pass sequence, and starts optimization from the dimension with the lowest aggregate interference. Rather than assigning a fixed optimization budget to each dimension-wise reward, training adaptively determines when to advance to the next reward according to the remaining optimization headroom of the current one. We further introduce AdaSelect, an adaptive prompt selection strategy that identifies reliable and informative prompts aligned with the model's current capability. By focusing policy updates on these prompts, AdaSelect effectively improves training stability. Extensive experiments across different T23D models and RL algorithms demonstrate that our framework consistently improves generation quality across multiple dimensions.

In this paper we consider groups of complex hyperbolic isometries generated by three complex involutions. Our first main result states that if the group is discrete and at least two of the mirrors of complex reflections intersect, then the group may be put into a normal form involving the ordering of traces of short, even length words. Our second main result refines a conjecture of Schwartz (proved by Grossi) that determines the type of the group in terms of the angles between the mirrors. That is, in the parameter space of complex triangles with given angles, it determines which of two given words becomes elliptic first.

Multimodal large language models (MLLMs) have shown strong visual reasoning abilities, but knowledge-intensive visual question answering often requires external textual evidence beyond the image and the model's parametric knowledge. Existing multimodal RAG systems commonly rely on Top-$K$ retrieval or reranking, which may return redundant passages and provide limited control over whether an answer update is sufficiently supported by the retrieved evidence. We propose CLIMB, a training-free inference-time framework for multimodal RAG. CLIMB first constructs a compact complementary evidence pool using an MMR-style objective that balances query relevance and passage-level redundancy. It then performs confidence-controlled refinement within this fixed pool: an R/E/C critic scores passages by relevance, evidence specificity, and cross-modal alignment, while an evidence-grounded confidence estimator accepts an updated answer only when the estimated confidence increases. This design provides a simple stopping criterion and reduces unnecessary refinement without modifying the underlying retriever or MLLM. Experiments on Encyclopedic-VQA and InfoSeek show that CLIMB consistently improves over retrieval-augmented multimodal baselines. Ablations further indicate that complementary pooling, critic-based scoring, and iterative confidence-controlled refinement each contribute to the final performance.

Bent partitions were introduced as a generalization of partial spread construction of bent functions and they became a hot research topic recently. In this paper, we prove two general constructions of normal bent partitions that are related to vectorial dual-bent functions. They cover many of the currently known bent partitions of this type as partial cases. These constructions also provide a large number of new bent partitions. Relevant properties of bent functions obtained from such partitions are proven.

In this work we formulate ultrasound multistatic recovery from arbitrary transmit sequences as a Bayesian inference problem. To that end, we train a deep generative prior on multistatic data sets to tackle the rank-deficient regime in which classical linear REFoCUS decoders fail. This appproach, which we term Deep Bayesian REFoCUS, outperforms the linear baselines for all regimes of rank-deficiency and noise levels, and regresses to linear decoding when inversion is exact. The model also expresses uncertainty in the null space of the acquisitions, whereas the linear REFoCUS decoders only provide point estimates. Finally, we analyze the impact of distribution shift between simulation and in-vivo acquisitions, showing remarkable generalization ability without any fine-tuning or adaptation.

Epistemic uncertainty should decrease as additional information about the data-generating process (DGP) becomes available to the predictor. Yet, existing graph evidential deep learning (EDL) methods for node classification typically construct epistemic uncertainty from graph-specific properties and evaluate it on downstream tasks such as out-of-distribution detection, which do not test its reducibility as information about the DGP increases. To make reducibility directly testable, we introduce a statistical framework for studying epistemic uncertainty under information growth. Our framework specifies an information-growth experimental protocol and a consistency criterion for epistemic predictors, while using projective graph DGPs to ensure that growing graphs, which in general need not provide increasing information about the same DGP, constitute coherent observations of the same underlying process. We show that EDL methods do not explicitly estimate data uncertainty arising from a single finite graph observation and instead regulate epistemic uncertainty through model hyperparameters, precluding consistency, as corroborated by controlled information-growth experiments. As an alternative, we propose graph bootstrap ensembles, capturing both data and procedural uncertainty through graph resampling and randomized training. Under the same experimental protocol, these ensembles exhibit epistemic uncertainty reduction beyond standard deep ensembles. These findings support bootstrap ensembles as candidate consistent epistemic predictors under information growth.

We show that the set $\mathbb{P}-1$ of shifted primes contains infinitely many sum-product patterns of the form $\{x,x+y,xy\}$ with $x,y$ arbitrarily large distinct integers. More strongly, we can also show that, for any $k\geq 1$, the set $\mathbb{P}-1$ contains longer patterns of the form $\{x,x+y,\ldots, x+ky,xy\}$ with $x,y$ arbitrarily large distinct integers, a statement that contains the Green–Tao theorem as a special case.

We extend the Bethe–Floquet formalism of Joachain and coworkers, originally developed for laser-assisted electron–atom collisions, to inelastic scattering of fast electrons from a many-body condensed-matter target in a time-periodic light field. At first order in the projectile–target interaction, the general Floquet–Fourier cross section separates into exact laser-dressed projectile kernels and a matrix-valued Floquet density response of the target. For spatially structured or translationally non-invariant systems, the latter is the bi-momentum Floquet structure factor; its momentum diagonal defines the Floquet generalization of the dynamic structure factor, constrained by Hermiticity, positivity, and sum rules. As a controlled realization of the general projectile kernel, an eikonal–Volkov approximation for slowly varying inhomogeneous fields yields a finite-momentum-resolution convolution of the target response. In the homogeneous-field dipole limit, the projectile kernel reduces to Bessel-function sidebands and the cross section takes the familiar Bethe–Floquet form. The Floquet density correlator separates exactly into the outer product of the pump-induced coherent mean density and connected fluctuations. In the straight-trajectory nonrecoil limit, the coherent, target-elastic sector defines the weak-coupling PINEM amplitude; repeated coherent insertions generate the PINEM Bessel ladder, with an explicit no-double-counting prescription for combining this channel with connected losses. As worked examples, we evaluate the connected, target-changing cross section analytically for a metal in the Drude and diffusive limits, recovering Bessel-weighted plasmon-loss and diffusive combs, and for a driven two-level model that exhibits off-diagonal Floquet coherences through Bessel-channel interference.

Irregular All-to-All communication is a major bottleneck in expert-parallel Mixture-of-Experts (MoE) models. Even with fixed expert routing and placement, uneven utilization of parallel network Rails and incast can limit communication performance. We present RailWave, a phase-adaptive communication layer built on DeepEP that addresses these bottlenecks below the routing layer through spatial and temporal traffic shaping. RailBalance redistributes source traffic across eligible Rails using source-local information, while a reusable, topology-derived permutation schedule limits concurrent senders per receiver without rebuilding demand-dependent schedules for each communication phase. A lightweight calibrated selector chooses an execution path according to each phase's traffic characteristics and offline profiling results. On training-derived communication workloads from the 106B GLM-4.5-Air model, RailWave delivers up to 5.84x speedup on H800 and 4.36x on H20 over Native. Code is available at https://github.com/CyberSecurityErial/RailWave-EP.

Consistency models (CMs) have become a leading approach for generating high-quality samples in few steps. However, adding steps can improve or degrade sample quality in ways that are highly sensitive to the schedule and that existing theory does not fully explain. To provide accuracy guarantees and guide CM sampler design, we analyze multistep CM sampling as a composition of noising and approximate denoising operators. Under explicit, verifiable stability assumptions, we derive a non-asymptotic error bound that separates contraction of the initialization error from accumulation of approximation error. The bound assigns distinct roles to the schedule: large early noise levels drive contraction, while small late noise levels control the residual bias. As a corollary, we obtain explicit constants for strongly log-concave and semi-log-concave targets. We further establish a complementary guarantee whose assumptions, one-step accuracy and stability, can be estimated for a given trained model. Experiments show that the contraction and approximation profiles entering our bounds can be reliably measured and closely match the predicted functional forms. Together, these results provide a meaningful convergence theory for multi-step CMs and a practical route to sampler design.

Sequential learning systems often make decisions from accumulated experience while receiving high-dimensional inputs whose distribution may change over time. Instance-Based Learning Theory (IBLT) provides a principled case-based framework for such settings through stored situation-decision-utility instances, partial matching, activation, and blending. IBLT relies on symbolic knowledge representation in dictionary-like formats, but text, images, transaction vectors, and user-item histories often require learned similarity rather than hand-specified matching rules. In this paper, we introduce AIBL (Augmented Instance-Based Learning), an instance-learning model formulated in a learned vector space for high- dimensional sequential data. AIBL generalizes symbolic situation matching to neural embedding similarity while retaining instance storage, activation- weighted retrieval, and utility blending. The AIBL model organizes memory into active, forgotten, and surprise stores. Surprise memory separates weakly matched, possible out-of-distribution, or corner-case observations from active memory, reducing forced fitting to the nearest available cases. An observation-driven graduation algorithm promotes recurring surprise instances to active memory, allowing the memory to incorporate repeated novel patterns that may arise under concept drift. We evaluate the same implementation on five machine learning tasks and three controlled simulation tasks, comparing AIBL with classical IBLT variants and task-specific baselines where appropriate. AIBL improves accuracy by 6 to 17 percentage points. The results show where vector-space retrieval improves over symbolic matching and how the added memory mechanisms govern novelty detection, cold-start handling, drift adaptation, and reward learning under the tested protocols.

Smartphone imaging could provide a low-cost turbidity measurement method if illumination and acquisition geometry are controlled. We evaluated a 3D-printed enclosure with fixed illumination and a submerged optical target using 162 milk-based suspensions spanning 0.16–50.2 nephelometric turbidity units (NTU), with a portable turbidimeter as the reference. An EfficientNetB0 regression model evaluated using repeated five-fold grouped cross-validation achieved a mean absolute error (MAE) of 1.208 NTU and $R^2=0.9816$, indicating that predictions followed the reference measurements closely. The MAE was 0.335 NTU below 1 NTU and 0.449 NTU from 1 to below 5 NTU; classification accuracy at the operational 5-NTU threshold was 0.9753. When applied without retraining to 103 paired images from a second smartphone, prediction error remained comparable to that on the development smartphone below 10 NTU, but turbidity was increasingly underestimated at higher values. The results demonstrate the measurement performance attainable with a controlled smartphone acquisition system, quantify an important device-dependent transfer limitation, and motivate standardized multi-device acquisition and prospective natural-water validation.

We study the persistence of non-planarity in boundaries of hyperbolic groups under quotients, focusing on quotients by large enough powers of infinite order elements. We prove that the non-planarity of the boundary of a one-ended hyperbolic group is preserved under such quotients. As a consequence, we obtain an analogous result about the persistence of Menger curve boundaries.

Contrastive representation learning is increasingly used to recover low-dimensional structure from neural recordings, but its output is typically validated by decoding accuracy rather than by the geometry of the manifold it produces. We apply CEBRA to EEG recorded from dyads in conversation, and analyze the resulting embedding, which training constrains to the 2D sphere. Labels describing the dyads, including the absolute difference between partners' autism-quotient scores, decode well above chance (0.77 against a 0.55 majority baseline for binary AQ magnitude; 0.44 against 0.25 for the six-class $|\Delta$AQ$|$ partition). However, the two permutation controls have notable differences in results: permuting labels over a frozen embedding yields p = 0.001, whereas retraining the encoder under each permutation yields p = 0.50. Only the latter tests the label rather than the geometry. Consistent with this, spherical mixture structure and per-class dispersion track identity rather than autism trait differences in dyads; frequency-band and non-oscillatory activity ablation controls do not change the results. However, participant-level model does separate from its identity-aware null (p = 0.0099) while speaker-versus-listener role analysis performs at chance in the same embedding, indicating a manifold organized by individual – and, in contrast with current neurolinguistics models, almost invariant to speaking vs. listening. Based on these results, we suggest that retraining-based nulls should be the default for grouped-data contrastive embeddings.

We give a detailed and complete algebraic proof of Simons' Riemannian holonomy theorem by a single strong induction on the dimension of the linear span of the curvature orbit. The proof uses the construction of flats and root centralizers, but replaces the detailed analysis of the common zero-weight space, the most technical core of previous algebraic proofs, by a trace-vanishing lemma. The lemma applies to curvature operators contained in an ideal that annihilates the curvature module. Restriction to a common geodesic subspace produces a proper invariant kernel. Induction makes this kernel fixed by the holonomy action, after which the trace lemma shows that the root centralizers span the ambient space. Their intersection recovers the maximal flat, and irreducibility completes the proof. For the completeness we also include the detailed derivation of the local symmetry of the underlying Riemannian manifold from the algebraic theorem.

In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from $50\%$ to $1-1/d$ for qudits of dimension $d$ without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.

Let $(\mathcal{M},\tau)$ be a semi-finite von Neumann algebra. We prove that $L_1(\mathcal{M})$ has Talagrand type $(1,\psi_{1,1})$, where $\psi_{1,1}(t)=t/\log(e+t)$. As an consequence, the Schatten trace class $S_1$ has Talagrand type $(1,\psi_{1,1})$, thus settled an open problem of Question 2 in Cordero-Erausquin and Eskenazis (2023). Our proof is based on the noncommutative Mazur maps initiated by Ricard.

We propose an interactive robo-advising framework that learns personalized risk preferences from scores provided by clients. The resulting preference-learning problem is closely related to inverse reinforcement learning (IRL), as the robo-advisor infers the client's latent reward specification from feedback. The robo-advisor interacts with clients iteratively as follows. At each interaction time, the advisor generates investment advice based on the optimal policy distribution derived from an inferred personalized risk preference. The client scores the advice. The advisor updates its assessment of the client's risk preference based on the feedback. This learning procedure motivates us to investigate discrete-time Predictable Forward Exploratory Reward (PreFER) processes and derive an exploratory investment strategy. By interpreting the score as the acceptance probability of a piece of advice, our inverse learning procedure learns the client's exploratory investment distribution using the acceptance-rejection method pioneered by von Neumann. Under CARA preferences, we show that, even though the scores contain noise, the robo-advisor can identify the client's current risk aversion after a sufficiently large number of interactions. The PreFER process then carries the learned preference forward and generates future recommendations under updated market conditions.

This paper introduces PEACE, the first joint embedding of audio effect code and output audio. Building on SLAP's multimodal objective, we pair an AFx-Rep audio encoder with two code encoders for Faust, a functional language for audio signal processing. First, we evaluate a fine-tuned T5 transformer over Faust source code. Second, we evaluate a message-passing graph neural network over an intermediate representation of the Faust compiler, capturing both topology and UI parameters. We evaluate on audio-to-code retrieval, where masking UI parameters at inference yields embeddings that encode effect chain topology alone. When parameters are visible, the two code encoders tie on retrieval of mixed-length chains but have tradeoffs on single-effect galleries. With parameters fully masked, PEACE recovers ordered chain topology far above chance without the limitations of supervised methods. PEACE outperforms pretrained models on an out-of-distribution reverb retrieval benchmark and can improve frozen audio-only representations. Its dual understanding of topology and parameters lays the groundwork for music information retrieval systems that search, generate, and condition on DSP code.

Fracture in large-scale structures — from failing concrete dams to calving glaciers — is dominated by self-weight. Yet, owing to their immense scale, directly studying when and where cracks nucleate and propagate in these systems under gravity is unfeasible. To date, experimental investigations have largely relied on mimicking self-weight in scaled-down specimens via centrifugal forces, necessitating specialized centrifuge facilities. In this Letter, we introduce a simple benchtop test that bypasses the need for this infrastructure. The method utilizes a cantilever beam containing a downward-pointing V-notch, loaded solely by its self-weight. Through appropriate selection of the notch geometry and placement and the beam dimensions, the setup forces a crack to nucleate at the notch tip and propagate through the specimen in a measurable manner. We demonstrate the utility of this self-weight fracture test on a 3D-printable mortar and analyze the results using the fracture theory recently introduced in (\citeauthor{LPKFG2026}, 2026). Inter alia, the findings provide a first validation of the theory for fracture driven by body forces.

Forest point cloud segmentation is fundamental for fine-grained 3D forest scene understanding, yet remains challenging due to irregular tree structures, severe occlusions, density variations, and ambiguous instance boundaries. Recent query-based forest segmentation methods have shown promise for unified semantic and instance prediction, but they still insufficiently exploit forest-specific spatial structure and account for boundary uncertainty. In this paper, we propose ForestQuery, a boundary-aware and spatially anchored query learning framework for unified forest point cloud segmentation. ForestQuery enhances instance and semantic query learning through two complementary designs. Specifically, boundary uncertainty is explicitly modeled to guide reliable instance query construction and modulate query optimization through adaptive loss reweighting. Meanwhile, spatially anchored semantic query enhancement (SA-SQE) introduces learnable 3D anchors encoding forest vertical stratification priors to enrich semantic queries with explicit spatial references. We evaluate ForestQuery on multiple public forest point cloud benchmarks and a self-collected annotated real-world dataset. Extensive experiments demonstrate consistent improvements in both individual-tree segmentation and semantic segmentation across diverse forest scenes. Code and data are publicly available at https://zhan994.github.io/ForestQuery

To deploy deep neural networks on edge hardware, highly efficient inference schemes are necessary that retain high accuracy. This work presents W16A16, a high precision (16-bit), fast speed, low energy quantization method. On a widely applied microcontroller architecture Armv7E-M, our proposed approach achieves faster speed and lower energy consumption on layer- and model-level compared to alternative quantization schemes. We analyze the architecture of Armv7E-M, explain the underlying principles behind the performance advantages of 16-bit approaches, and evaluate the empiric quantization errors for regression and classification tasks, as well as empiric time- and energy consumption in MCU deployment. We observe ca.\ 10 times lower quantization errors compared to 8-bit quantization schemes while achieving similar or better inference times and energy consumption.

Ribet's 1976 proof of the converse to Herbrand's theorem created a new paradigm in algebraic number theory by illustrating that unramified abelian Galois extensions of number fields can be constructed using Galois representations associated to Eisenstein congruences, i.e., cuspidal eigenforms that are congruent to Eisenstein series. In recent years, further progress has been made in investigating the quantity of such Eisenstein congruences, showing that when there are many such congruences, additional and finer information can be gleaned about the arithmetic structure of the related extensions. In this vein, we use new results on the existence of Eisenstein congruences in tame families to explain a computational observation about splitting behavior of primes in a certain metabelian number field.

Reinforcement learning with verifiable rewards has substantially advanced multimodal reasoning, yet it remains fundamentally limited by ambiguous token-level credit assignment. While high-entropy token heuristics encourage possibility exploration, naively extending them to video reasoning tends to induce lengthy reasoning, as the model becomes overly reliant on high-entropy visual activations. Alternative approaches that rely on counterfactual-based visual token localization for credit assignment also tend to over-prioritize visual exploration at the expense of decisive reasoning cues for answer derivation, thereby exacerbating the interference from spurious visual nuances. Moreover, these methods employ static counterfactual strategies that fail to co-evolve with the policy during training. In this paper, we introduce DyCPO, a co-evolutionary framework that jointly optimizes reliable token selection and adaptive counterfactual intervention. It constructs a multi-role dependence metric to balance visual exploration and answer-relevance mining in token-wise contrastive learning, while suppressing exploration-only filler tokens and spurious visual noise. Rather than relying on static counterfactual priors, DyCPO dynamically derives counterfactual signals from the model's own successful and failed rollouts, enabling self-diagnostic analysis and co-evolution of the optimization objective with the policy. Extensive experiments on complex video reasoning and general video understanding benchmarks demonstrate consistent performance improvements, establishing DyCPO as a robust token-level credit assignment paradigm for multimodal reinforcement learning.

Logical error rate is a standard benchmark for quantum error correction, providing an aggregate measure of the overall effect of physical noise. In actual QEC architectures, errors at different circuit locations can have markedly different effects on logical failure even when their probabilities are equal. Here we introduce an error attribution scheme to quantitatively characterize the influence of individual circuit components on the logical error rate and use this refined information to guide targeted intervention and design for improved QEC performance. Our attribution estimator computes all component sensitivities jointly from the same Monte Carlo samples used to estimate the logical error rate. The resulting sensitivity maps identify hotspots where targeted noise reduction can most effectively improve logical performance. We test the scheme in circuit simulations of rotated surface code memories and high-rate lifted product codes: halving the noise strength on about 5%-7% of physical components selected by sensitivity reduces logical error rates by approximately 15%-25%, roughly twice the mean reduction from the same intervention on an equal number of randomly selected components. By connecting performance benchmarking to targeted optimization, our scheme provides a practical strategy for improving quantum error correction with limited resources.

This paper presents a web-based application for navigating and composing microtonal harmony, built on the Harmonic Eigenspace, a four-dimensional psychoacoustically grounded space in which tetrad chord types are located by their spectral dissonance profiles, computed with Sethares's roughness/dissonance model. The coordinate system is transposition-invariant: a coordinate triple ({\alpha}, e̱ta}, {\gamma}) locates the three upper notes in relation to the root, so a chord quality corresponds to a direction in the space, the invariant ray along which transposition acts, while the root frequency sets the scale. The dissonance field over these coordinates can be computed at any register; the locations of its local minima are register-invariant, as they arise from partial-coincidence ratio conditions. The dissonance volume contains 100 local minima that align with just-intonation intervals and act as landmarks, organising the space into basins around the most consonant tetrads. We embed tetrads from three tonal equal temperaments as discrete lattices within this continuous volume. The application presents this space through two components: the Harmonic Eigenspace as a navigable 3D visualisation of the dissonance volume in which all nodes are playable, and a Modal Studio that extends modal interchange logic to the ten-gradation interval vocabulary of 53-TET. The application also functions as a MIDI controller with MIDI Polyphonic Expression support, usable in any digital audio workstation that supports this format. A listening study with 31 participants used both scenes of the application: listeners first rated isolated 53-TET chords alongside chords familiar from Western practice, such as the maj7 and the m7; they then rated chord progressions composed in the Modal Studio, measuring their acceptance or rejection of microtonal progressions heard for the first time.