Beam-Plasma Collective Oscillations in Intense Charged-Particle Beams: Dielectric Response Theory, Langmuir Wave Dispersion, and Unsupervised Detection via Prometheus

We develop a theoretical and computational framework for beam-plasma collective oscillations in intense charged-particle beams at intermediate energies (10-100 MeV). In Part I, we formulate a kinetic field theory governed by the Vlasov-Poisson system, deriving the Lindhard dielectric function and random phase approximation (RPA) polarization tensor for three beam distribution functions. We prove via the dielectric function epsilon(omega,q)=0 the existence of undamped Langmuir wave modes above a critical beam density n_c, obtain explicit beam-plasma dispersion relations, and show that Landau damping vanishes above the particle-hole continuum. The plasma frequency Omega_p^2 = ne^2/(m*epsilon_0) is fixed by the f-sum rule independently of distribution shape; higher dispersion coefficients depend on velocity moments. Space charge effects drive anomalous beam broadening with sqrt(n-n_c) onset and Friedel oscillations at q=2k_F. The beam-plasma transition belongs to the 3D Ising universality class via renormalization group analysis. In Part II, we validate these predictions using Prometheus, a beta-VAE trained on static structure factor data S(q) from particle-in-cell (PIC) beam simulations. Prometheus detects collective plasma oscillation onset in Gaussian and uniform distributions, confirms their absence in the degenerate Fermi gas (n_c -> 0), and resolves the Kohn anomaly at q=2k_F. Dispersion analysis of S(q,omega) from PIC simulations verifies the distribution-independent Omega_p predicted by the f-sum rule. All six validation checks pass. Predicted signatures -- density-tunable plasma resonances at omega_p proportional to sqrt(n), anomalous beam broadening with sqrt(n-n_c) onset, and Friedel oscillations -- are accessible at existing intermediate-energy beam facilities.

Molt Dynamics: Emergent Social Phenomena in Autonomous AI Agent Populations

MoltBook is a large-scale multi-agent coordination environment where over 770,000 autonomous LLM agents interact without human participation, offering the first opportunity we are aware of to observe emergent multi-agent coordination dynamics at this population scale. We introduce \textit{Molt Dynamics}: the emergent agent coordination behaviors, inter-agent communication dynamics, and role specialization patterns arising when autonomous agents operate as decentralized decision-makers in an unconstrained multi-agent environment. Through longitudinal observation of 90,704 active agents over three weeks, we characterize three aspects. First, spontaneous role specialization: network-based clustering reveals six structural roles (silhouette 0.91), though the result primarily reflects core-periphery organization -- 93.5\% of agents occupy a homogeneous peripheral cluster, with meaningful differentiation confined to the active minority. Second, decentralized information dissemination: cascade analysis of 10,323 inter-agent propagation events reveals power-law distributed cascade sizes ($α= 2.57 \pm 0.02$) and saturating adoption dynamics where adoption probability shows diminishing returns with repeated exposures (Cox hazard ratio 0.53, concordance 0.78). Third, distributed cooperative task resolution: 164 multi-agent collaborative events show detectable coordination patterns, but success rates are low (6.7\%, $p = 0.057$) and cooperative outcomes are significantly worse than a matched single-agent baseline (Cohen's $d = -0.88$), indicating emergent cooperative behavior is nascent. These findings establish an empirical baseline for coordination dynamics in decentralized autonomous agent systems, with implications for multi-agent system design, agent communication protocol engineering, and AI safety.

Geodesic Semantic Search: Learning Local Riemannian Metrics for Citation Graph Retrieval

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean distances, \gss{} learns a low-rank metric tensor $\mL_i \in \R^{d \times r}$ at each node, inducing a local positive semi-definite metric $\mG_i = \mL_i \mL_i^\top + \eps \mI$. This parameterization guarantees valid metrics while keeping the model tractable. Retrieval proceeds via multi-source Dijkstra on the learned geodesic distances, followed by Maximal Marginal Relevance reranking and path coherence filtering. On citation prediction benchmarks with 169K papers, \gss{} achieves 23\% relative improvement in Recall@20 over SPECTER+FAISS baselines while providing interpretable citation paths. Our hierarchical coarse-to-fine search with k-means pooling reduces computational cost by 4$\times$ compared to flat geodesic search while maintaining 97\% retrieval quality. We provide theoretical analysis of when geodesic distances outperform direct similarity, characterize the approximation quality of low-rank metrics, and validate predictions empirically. Code and trained models are available at https://github.com/YCRG-Labs/geodesic-search.

Unsupervised Discovery of Intermediate Phase Order in the Frustrated $J_1$-$J_2$ Heisenberg Model via Prometheus Framework

The spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice exhibits a debated intermediate phase between Néel antiferromagnetic and stripe ordered regimes, with competing theories proposing plaquette valence bond, nematic, and quantum spin liquid ground states. We apply the Prometheus variational autoencoder framework -- previously validated on classical (2D, 3D Ising) and quantum (disordered transverse field Ising) phase transitions -- to systematically explore the $J_1$-$J_2$ phase diagram via unsupervised analysis of exact diagonalization ground states for a $4 \times 4$ lattice. Through dense parameter scans of $J_2/J_1 \in [0.3, 0.7]$ with step size 0.01 and comprehensive latent space analysis, we investigate the nature of the intermediate regime using unsupervised order parameter discovery and critical point detection via multiple independent methods. This work demonstrates the application of rigorously validated machine learning methods to open questions in frustrated quantum magnetism, where traditional order parameter identification is challenged by competing interactions and limited accessible system sizes.

From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems

We extend the Prometheus framework for unsupervised phase transition discovery from 2D classical systems to 3D classical and quantum many-body systems, addressing scalability in higher dimensions and generalization to quantum fluctuations. For the 3D Ising model ($L \leq 32$), the framework detects the critical temperature within 0.01\% of literature values ($T_c/J = 4.511 \pm 0.005$) and extracts critical exponents with $\geq 70\%$ accuracy ($β= 0.328 \pm 0.015$, $γ= 1.24 \pm 0.06$, $ν= 0.632 \pm 0.025$), correctly identifying the 3D Ising universality class via $χ^2$ comparison ($p = 0.72$) without analytical guidance. For quantum systems, we developed quantum-aware VAE (Q-VAE) architectures using complex-valued wavefunctions and fidelity-based loss. Applied to the transverse field Ising model, we achieve 2\% accuracy in quantum critical point detection ($h_c/J = 1.00 \pm 0.02$) and successfully discover ground state magnetization as the order parameter ($r = 0.97$). Notably, for the disordered transverse field Ising model, we detect exotic infinite-randomness criticality characterized by activated dynamical scaling $\ln ξ\sim |h - h_c|^{-ψ}$, extracting a tunneling exponent $ψ= 0.48 \pm 0.08$ consistent with theoretical predictions ($ψ= 0.5$). This demonstrates that unsupervised learning can identify qualitatively different types of critical behavior, not just locate critical points. Our systematic validation across classical thermal transitions ($T = 0$ to $T > 0$) and quantum phase transitions ($T = 0$, varying $h$) establishes that VAE-based discovery generalizes across fundamentally different physical domains, providing robust tools for exploring phase diagrams where analytical solutions are unavailable.

Calibrating Behavioral Parameters with Large Language Models

Behavioral parameters such as loss aversion, herding, and extrapolation are central to asset pricing models but remain difficult to measure reliably. We develop a framework that treats large language models (LLMs) as calibrated measurement instruments for behavioral parameters. Using four models and 24{,}000 agent--scenario pairs, we document systematic rationality bias in baseline LLM behavior, including attenuated loss aversion, weak herding, and near-zero disposition effects relative to human benchmarks. Profile-based calibration induces large, stable, and theoretically coherent shifts in several parameters, with calibrated loss aversion, herding, extrapolation, and anchoring reaching or exceeding benchmark magnitudes. To assess external validity, we embed calibrated parameters in an agent-based asset pricing model, where calibrated extrapolation generates short-horizon momentum and long-horizon reversal patterns consistent with empirical evidence. Our results establish measurement ranges, calibration functions, and explicit boundaries for eight canonical behavioral biases.