This paper presents a system combining symbolic execution (KLEE) with a 4-agent multi-LLM architecture for detecting memory vulnerabilities in Rust unsafe code. A central challenge we address is the incomplete-code problem: CVE database entries provide only isolated code snippets that lack struct definitions, imports, and Cargo manifests, causing all existing formal verification tools to fail at compilation with zero output. Our system resolves this through four specialized agents -- an Oracle/Validator for strategic planning, a Safety Checker for vulnerability analysis, a Code Specialist for FFI wrapper generation, and a Fast Filter for execution optimization -- that collaboratively synthesize KLEE-compatible harnesses from otherwise uncompilable fragments. KLEE's output is then ingested by graph_klee.py, which constructs a Graph Database linking CVE files, CWE categories, error types, and symbolic execution paths as typed nodes and labelled edges, enabling structured cross-CVE vulnerability queries. We evaluated our system on 31 real-world Rust CVEs spanning 11 CWE categories, achieving 90.3% wrapper compilation success where all state-of-the-art formal verification tools achieve 0%. Our system detected 1,206 critical errors across 26 files (83.9% detection rate), compared to 14 warnings across 11 files for Clippy (35.5%) and generic labels for Miri. The 4-agent architecture reduced wrapper compilation failures from 42% (single-agent baseline) to 9.7% and increased detected errors from 487 to 1,206, confirming that role specialization and structured context passing produce measurably better results than a single general-purpose model. Our replication package is publicly available at https://github.com/Zeyad-Ab/Symbolic-Execution-with-Multi-LLM-Architecture-for-Rust-Security

Let $G$ be a connected graph of order $n$. A $\{P_3,P_4,P_5\}$-factor is a spanning subgraph $H$ of $G$ such that every component of $H$ is isomorphic to an element of $\{P_3,P_4,P_5\}$. In this paper, we establish a sufficient condition on the size of the graph $G$ with minimum degree $δ$ to have a $\{P_3, P_4, P_5\}$-factor. Subsequently, we provide another sufficient condition on the adjacency spectral radius, ensuring that a connected graph $G$ with minimum degree $δ$ contains a $\{P_3, P_4, P_5\}$-factor.

Neuromorphic, or spiking, processors are increasingly being considered for use in harsh, radiation-prone environments such as space and avionics, where energy efficiency and graceful degradation are essential. In this study, we propose and experimentally validate a radiation-testing methodology specifically designed for neuromorphic processors that employ on-chip synaptic plasticity. We map the open-source ODIN SNN processor with Spike-Dependent Synaptic Plasticity (SDSP) onto the FPGA and expose it to a high-energy neutron beam while continuously monitoring MNIST classification accuracy and recording the synaptic state. From these measurements, we extract SEU cross-sections for ODIN's synaptic memory and develop a calibrated fault model to inform a complementary fault-injection campaign. By comparing inference-only and online-learning configurations, we demonstrate that enabling SDSP can significantly extend the time to application-level failure and enable partial recovery from accumulated bit flips, with modest hardware overhead.

We introduce a single dimensionless landscape function $\Jchem(ρ) = \cosh(ρ\ln \phig) - 1$, $\phig = (1+\sqrt{5})/2$, on the noble-gas-centred coordinate $ρ= d/L_p \in [0,1)$, and show that it organizes four central atomic observables: first ionization energy $\IEone$, electron affinity $\EA$, Mulliken electronegativity $χ_M$, and Pearson chemical hardness $η$, on one periodic-table axis. The outward step $Δ\Jchem^{+}$ delivers $\IEone$; the inward gap $Δ\Jchem^{-} = \Jchem(1) - \Jchem(ρ)$ delivers $\EA$ and $η$; $χ_M$ follows by Mulliken's identity. Three results establish the empirical content. (i) The within-period $\IEone$ envelope reproduces the full noble-gas-to-alkali ordering across periods 2--6: of 34 atoms compiled across periods 2--4, 26 lie on the predicted monotone descent and the 8 upward deviations occur exactly at the textbook anomaly sites $\{p^3, d^5, f^7, s^2, d^{10}\}$. (ii) Two golden-ratio identities, $\IEone(G_p)/\IEone(G_{p+1}) \approx \phig^{1/4}$ on three heavy noble-gas pairs and $\IEone(\text{halogen})/\IEone(\text{alkali}) \approx \phig^2$ on four within-period pairs, agree with NIST data to MAD $\approx 1\%$ and $\approx 5\%$, respectively. (iii) The shared kernel $Δ\Jchem^{-}$ provides single-parameter analytical fits to $\EA$ across periods 4--6 (MAE $0.3$--$0.4$~eV), to Pearson hardness $η$ across periods 2--4 (MAE $\sim 1$~eV on noble-gas maxima up to $10.8$~eV), and to Mulliken $χ_M$ across a 15-atom four-class benchmark ($R^2 = 0.73$). \edit{At the period-averaged scale level, the shared-kernel relation $\EA/η\approx C^{(p)}_{\mathrm{EA}}/C^{(p)}_η$ is supported on period-4 NIST data: the empirical nine-atom mean $\overline{\EA/η} = 0.180$ agrees with the predicted constant $0.182$ to better than $1\%$, although individual-atom scatter ($σ\approx 0.13$) is much larger.}

We quantify the excitonic coupling in the homodimer of dimeric Venus fluorescent protein using a quantum-classical hybrid workflow. Employing a transition-density coupling formalism, we calculate $J = 74.38~\mathrm{cm^{-1}}$, which is 5.6 times stronger than the far-field point-dipole estimate of $13.31~\mathrm{cm^{-1}}$. This disparity highlights the critical role of near-field multipolar effects at the 27.6~Å chromophore centroid separation. Furthermore, we argue that a separation of timescales resolves the apparent theoretical tension between robust experimental excitonic couplings and the highly decoherent biological environment. While it has been hypothesised that the fluorescent protein $β$-barrel scaffold sustains coupling by attenuating thermal fluctuations, we emphasise that the separation of timescales fundamentally applies irrespective of the exact degree of environmental noise suppression. Collective photoexcitation imprints the Davydov splitting under optical-limit dielectric screening upon absorption, preceding bulk solvent relaxation and sub-picosecond environmental dephasing. To characterise the subsequent post-absorption evolution, we employ stochastic simulations for quantum parts to model the transition from a delocalised exciton superposition to incoherent hopping between localised chromophore states.

After the Planck mission's launch in 2009, bolometers of its High Frequency Instrument (HFI) were considerably affected by cosmic rays, which necessitated several years of post-treatment to clean the data. To study the susceptibility of high sensitivity cryogenic detectors to particle impacts, IAS has developed the DRACuLA facility. We present the results of the latest two test campaigns performed on new generation of detectors.

This paper develops the logical extension of the JFR-rg framework introduced in Part I within the same observables-centered and regime-conditional architecture. Six extensions are formalized: the Virtuous Ratchet (E1), the corrected Repression Dividend Multiplier (E2), the Debt Reduction Paradox (E3), the Multi-Country Repression Equilibrium (E4), the Demographic-$ϕ$ Clock (E5), and the Institutional Control Rights Index (E6). Together, these clarify the dynamic implications of a JFR-rg regime for path dependence, institutional erosion, growth-enhancing investment, and regime transition in high-debt, low-growth economies. The paper's claim of logical completion is architectural rather than universal. It does not claim a full welfare-theoretic or political-economy microfoundation. Rather, it shows that the principal dynamic implications internal to Part I can be stated in closed form, and that two natural excluded generalizations -- bounded stochastic perturbations and endogenous fiscal responses -- preserve the regime logic. A Minimal Equilibrium Closure is then introduced to endogenize the sovereign risk premium through a two-layer domestic demand structure and a complementarity condition. The paper also formulates the statistical problem of inferring a latent regime boundary under one-sided regime dominance. The inferential contribution is conservative by design: it constructs outer statistical summaries of the relevant boundary objects rather than forcing point classification when the observables remain compatible with multiple nearby regime readings. Comparison with Blanchard (2019), Hoshi-Ito (2014), and Mehrotra-Sergeyev (2021) shows where JFR-rg adds explanatory value in the Japanese case: not by replacing standard debt-sustainability analysis, but by endogenizing the institutional conditions under which low sovereign rates are sustained, weakened, or lost.

Waste heat recovery improves energy efficiency and reduces greenhouse gas emissions; however, much industrial and environmental heat is wasted at low temperature. Thermomagnetic recovery of waste heat has a high potential for sustainable production of electric energy, especially for low-grade waste heat where conventional technology is inefficient or infeasible. Of particular interest are thermomagnetic generators (TMG) as they require almost no mechanically moving parts, which is beneficial for high reliability. However, all existing prototypes have two remaining challenges: low efficiency and low cycle frequency. In this work, we develop a digital twin of a recent TMG with genus 3 by using multi-physics simulations. We identify shortcomings of previous simulation approaches, and describe why simulations in three dimensions are necessary, which consider coupling between magnetic, thermal, fluid flow, and electrical physics domains. We validate our model, which only uses known geometry and material parameters, by experimental data of the TMG with highest power density today, and attain 96% accuracy in open-circuit voltage and 95% accuracy in power output. This high accuracy allows us to identify the origin of both challenges for TMGs, which are not accessible by experiments. First, we uncover inefficiencies by analyzing the energy flow within a Sankey diagram. Second, we trace the transient heat flow through the generator, which identifies the factors limiting frequency. This paves the way for more efficient and faster TMGs, and their development will be accelerated by our validated digital twin.

This study examines the disposition effect in both long and short exposure positions in FTSE MIB tracking ETFs using a unique dataset of almost 9 million individual transactions. Building on the integrated framing approach, we extend the analysis to explicitly incorporate leverage and long short exposures, allowing us to assess how portfolio context and systematic risk exposure jointly are associated to investors realization behavior. Methodologically, we generalize Odean canonical Count and Total measures to wide and integrated framing, introduce a novel Value metric that captures the return thresholds required to realize gains versus losses, and implement these measures in dispositionEffect, an open-source R package for large-scale intraday data. We show that short positions exhibit a weaker disposition effect than long positions under narrow framing, but that this asymmetry reverses in positively performing portfolios under integrated framing. Systematic risk further amplifies these behavioral asymmetries across positions. Overall, our findings demonstrate that the disposition effect is not solely asset-specific, but is critically shaped by the interaction between portfolio context, position type, and systematic risk exposure. More broadly, the results are consistent with the joint predictions of Prospect Theory and Regret Theory, highlighting the central role of framing in investor decision-making.

The analyses presented herein demonstrate that neuronal electrical activity can be consistently interpreted as a manifestation of murburn redox-mediated electronic dynamics rather than as a process fundamentally driven by transmembrane ionic flux. By integrating comparison with established models, quantitative predictions, and diverse experimental observations, the murburn framework emerges as a unified and chemically grounded description of excitability. A key strength of the model lies in its predictive structure. Unlike phenomenological frameworks that rely on parameter fitting, the murburn formulation links measurable electrophysiological outputs: such as conduction velocity, waveform morphology, and threshold behavior; to physically interpretable variables including redox kinetics, transport efficiency, and environmental conditions. This enables direct experimental validation through perturbations in oxygen availability, redox balance, solvent properties, ionic strength, and external fields. Importantly, the framework extends beyond neurons to a broader class of excitable systems, including cardiac tissue, photoreceptors, and artificial redox-active materials, suggesting that excitability is a general physicochemical phenomenon rooted in reaction-transport dynamics. While the present work establishes the mid-scale dynamics of neuronal electricality, further developments are required to connect quantum-level electron transfer processes with macroscopic electrophysiological signals such as EEG and EMG. These extensions, along with targeted experimental tests, will determine the ultimate scope and applicability of the murburn paradigm.

The spin representation $(\mathbb C^2)^{\otimes n}$ has a dual canonical basis introduced by Lusztig that is important in many areas of algebra, geometry, and physics. Khovanov observed that a portion of the dual canonical basis can be viewed diagrammatically through the Temperley-Lieb algebra. We provide a simpler construction that we generalize to the entire dual canonical basis, and write explicit formulas to compute the dual canonical basis, and thus the canonical basis of the spherical module, as a byproduct. We reprove some of Khovanov's results using our new perspective. Furthermore, we use the Hecke algebra to reprove the fact that the canonical basis is indeed dual to the dual canonical basis, leading to similar results about the canonical basis in $\mathcal M^*$ and $\mathcal N^*$, the dual spaces to the spherical and aspherical modules, as a byproduct. Finally, we present an alternative axiomatic definition of the canonical basis using diagrams.

We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal, in-orbit servicing, or asteroid belt exploration. We model these problems as a variant of the Traveling salesperson problem (TSP), which we term the Keplerian TSP (KTSP). Unlike the well-studied TSP, the KTSP accounts for the motion of orbital targets, leading to time-dependent and asymmetric transfer costs that capture key real-world effects in astrodynamics. We provide a rigorous formalization of the KTSP and release a benchmark suite to support its study. Central to our approach is a time-unfolding technique that reformulates the continuous problem as a discrete optimization task in a time-expanded network. This representation makes the benchmark accessible to researchers in discrete optimization even without prior knowledge of celestial mechanics. We also develop an alternative encoding as an integer linear program using Interval-based Dynamic Discretization Discovery to handle the time-dependent nature of transfers. We leverage state-of-the-art ILP solvers to solve the KTSP instances, accompanied by a detailed computational study that highlights their strengths and limitations. We complement these exact methods with an initial solution heuristic, an improvement heuristic, and preprocessing routines that preserve optimality.

In the current work, we propose a generalization of angles and orthogonality from $L^2$ to generic Banach spaces, starting from a $L^p$ version of the Pythagorean theorem, $p\in [1,\infty)$. The starting point is conservation of energy measured in $L^1$ norm, as it occurs when considering the intrinsic mode functions decomposition in signal processing. This conservation of energy measure in $L^1$ norm is exactly the $L^1$ Pythagorean theorem. Besides the theoretical analysis, we apply the new notions in the context of preconditioning for structured large linear systems, by obtaining new classes of preconditioners. The present work contains numerical experiments and various remarks on the possible use of the given framework.

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform models are analyzed and closed-form expressions for optimal quantizers and mean-square errors are derived. (I) For $N$ equally spaced points on the equator, exact error formulas are obtained for both divisible and non-divisible cases, showing that optimal Voronoi cells form contiguous arcs with midpoint representatives. (II) For two antipodally symmetric small circles at latitudes $\pmϕ_0$, each with $M$ longitudes, we establish a no-cross-circle Voronoi phenomenon, symmetry-preserving optimality, and finite-sum error formulas with curvature-dependent bounds and asymptotics. (III) For a single small circle at latitude $ϕ_0$, analogous formulas are proved and curvature is shown to reduce distortion by a factor $\cos^2ϕ_0$ while preserving the $n^{-2}$ decay rate. Across all models we rigorously formulate the block-midpoint principle: optimal Voronoi cells are contiguous azimuthal blocks whose representatives are azimuthal midpoints. These explicit benchmark models clarify curvature effects and support further developments in quantization on curved manifolds.

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.

We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with the multiobjective problem, yielding a deterministic and structure-preserving continuation path. Under mild regularity assumptions, we establish global convergence of the homotopy trajectory to a Pareto-stationary solution for any initial point chosen in the interior of the feasible region. In numerical experiments, the method exhibits robust convergence even when initialized from nonfeasible points, indicating stability beyond the theoretical guarantees. Efficient predictor-corrector continuation strategies are employed to trace the homotopy path. Numerical results on benchmark problems compare the proposed approach with classical scalarization methods and the evolutionary algorithm NSGA-II, demonstrating competitive computational efficiency and consistent solution quality. These results highlight the effectiveness of the homotopy framework for constrained multiobjective optimization and motivate extensions to more general problem settings and adaptive parameter strategies.

This paper proposes novel fixed-time (FXT) convergent neurodynamic approaches for solving mixed variational inequality problems (MVIs). A class of first-order proximal neurodynamic models (PNMs), including time-varying proximal neurodynamic models (TVPNMs), is developed to guarantee FXT convergence to the solution of MVIs from arbitrary initial conditions. Rigorous convergence and stability analyses are established under the assumptions of strong pseudomonotonicity and Lipschitz continuity, using Lyapunov stability theory. The proposed methods exhibit FXT convergence from any initial point, with convergence speed significantly enhanced through the strategic design of time-varying coefficients. Explicit upper bounds on the settling time are derived for the time-varying neurodynamic models. In addition, the robustness of the proposed approaches against bounded noise disturbances is analyzed. The applicability of the proposed framework is further demonstrated for composite optimization problems and minimax optimization problems. Also, numerical examples are presented to demonstrate the effectiveness and convergence behavior of the proposed methods.

This paper is a sequel to arXiv:2511.01024 (Base 1), where an axiomatic framework for angles and the foundations of difference-angle geometry were introduced. In difference-angle geometry, where the difference of slopes of lines is treated as a primary angular quantity (the difference angle), we reconstruct the focal structure of parabolas from a difference-angle-theoretic viewpoint and develop the associated algebraic and analytic structures. First, we introduce the difference-angle focal function and define the focus of a parabola constructively as its zero set. This approach yields a formulation of the parabolic power that differs from that presented in Base 1. Next, by interpreting the power as a classical representation of an inner product, we derive a difference-angle version of the parallelogram theorem via a polarization identity, and thereby define the difference-angle inner product as a pseudo-inner product. The robustness of this structure is substantiated by deriving a difference-angle version of Stewart's theorem based solely on computations involving the difference-angle inner product. Furthermore, we define the parabolic trigonometric functions cosp(theta) and sinp(theta) (together with related functions) associated with a difference angle (theta), and show that they satisfy identities corresponding to the first and second cosine laws in Euclidean geometry. Finally, we reexamine the Cayley-Klein angle and distance derived from Laguerre's formula, and in particular verify that the existing Cayley-Klein angle satisfies the axiomatic system for angles introduced in Base 1. We then show that, in the parabolic limit of the absolute conic, the difference angle and the difference-angle norm arise naturally as the linear degeneration of the logarithmic cross ratio.

We advance Matkovič ideas, originally applied to complete the classification of tight structures on small Seifert fibred $L$-spaces, to show the existence of contact structures on Brieskorn spheres which are tight and zero-twisting. This uncovers a phenomenon that has never appeared in literature before: namely, that a contact structure $ξ$ on a 3-manifold can be such that $\widehat c(ξ)$ is non-vanishing, but $c^+(ξ)$ is zero.

We adapt the Ozsváth-Szabó full path algorithm to every star-shaped graph and establish a correspondence between negative-twisting tight contact structures on any Seifert fibred space over $S^2$, and its Heegaard Floer homology groups equipped with the Alexander filtration induced by the regular fibre. This provides the complete classification of negative-twisting structures on these manifolds; in particular, we distinguish them by their contact invariant $c^+$. We prove that every such structure is symplectically fillable and extend a known obstruction to Stein fillability. In addition, we show that the number of negative-twisting structures can be expressed combinatorially in terms of the Seifert coefficients of the star-shaped graph, while their $d_3$-invariant and homotopy type are determined explicitly through our correspondence. Our results also complete the classification of fillable structures on any small Seifert fibred space.

We numerically study a formation of near extremal horizons from a gravitational collapse of radially symmetric gravitational waves in $4+1$ dimensions within the framework of pure Einstein gravity with positive cosmological constant. Evolution of a regular initial data with cosmological horizon leads to a formation of a black hole with mass exceeding $99\%$ of the extremal value corresponding to the black hole and cosmological horizons coinciding. We demonstrate how our results fit within the framework of characteristic gluing, and present some evidence that the third law of black hole thermodynamics may not hold in the cosmological context, where the extremality corresponds to the maximal mass of the Schwarzschild black hole in de--Sitter space.

A search is presented for a light charged Higgs boson H$^\pm$ in top quark pair production ($\mathrm{t\bar{t}}$), where one of the top quarks decays to an H$^\pm$ and a bottom quark, while the other decays to a W$^\mp$ boson and a bottom quark. The H$^\pm$ is assumed to decay into a charm and a strange quark, whereas the W$^\mp$ boson decays into a charged lepton (electron or muon) and a neutrino. Results are reported based on proton-proton collision data at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The analysis probes H$^\pm$ masses in the range 40 to 160 GeV using the invariant mass spectrum of the two light jets, where light jets are defined as jets that do not satisfy the bottom quark tagging requirement. The observed yield is found to be consistent with standard model predictions. Upper limits are set on the branching fraction $\mathcal{B}$(t $\to$ H$^\pm$ b), with values in the range of 0.07$-$1.12% at 95% confidence level, under the assumption that $\mathcal{B}$(H$^\pm$ $\to$ cs) = 100%. These are the first direct limits on charged Higgs bosons produced in top quark decays for masses between 40 and 50 GeV, and the most stringent limits to date in the 70$-$110 GeV range.

This paper addresses the stability analysis and state estimation of generalized Persidskii systems subject to time-varying delays and external disturbances. The generalized Persidskii class, which couples linear dynamics with sector-bounded nonlinear feedback loops, offers a tractable yet expressive framework for modeling electromechanical and neural network systems. We develop delay-dependent conditions for input-to-state stability (ISS) via Lyapunov--Krasovskii functionals incorporating Persidskii-type integral terms, and cast these conditions as linear matrix inequalities (LMIs). A structured robust observer is proposed for systems with partial state measurement, and its convergence is guaranteed through an $H_\infty$ synchronization criterion. To handle plant uncertainty, the system matrices are identified from trajectory data using a stability-preserving Koopman lifting procedure, in which the ISS-LMI constraint is embedded as a convex side condition during parameter regression. The identified model populates the prediction horizon of an ICODE-MPPI (Input-dependent Control-oriented Dynamical Estimation -- Model Predictive Path Integral) controller. The complete framework is validated on a 1.5 kW Permanent Magnet Synchronous Motor (PMSM) drive equipped with a programmable load brake. Experimental results confirm a 35\% reduction in velocity estimation RMSE relative to an Extended Kalman Filter and a 67\% improvement in speed-tracking accuracy relative to standard Field-Oriented Control, corroborating the theoretical ISS bounds established herein.

We show that the operational quantum formalism -- the Born rule, Lüders state updating, quantum interference, non-Markovian effective dynamics, and Bell inequality violation at the Tsirelson bound $2\sqrt{2}$ -- arises within Accessibility Theory (AT) from the Aperture construction together with explicit coherence and locality assumptions stated in the paper. AT is a framework built on real graded spectral triples and a single algebraic selection principle. The Principle of Universal Accessibility Balance requires three independent measures of the complexity of a spectral triple -- its algebraic, gauge-theoretic, and geometric content -- to be exactly equal and minimized, uniquely selecting the algebra $\mathbb{C} \oplus \mathbb{H} \oplus M_3(\mathbb{C})$ and with it the Standard Model gauge group, particle content, four-dimensional Lorentzian spacetime, three generations, and gravitational dynamics. Restriction to a codimension-one geometric boundary reduces this algebra to its commutative center $\mathbb{C} \oplus \mathbb{C} \oplus \mathbb{C}$ -- the Aperture -- which defines a permanent information bottleneck for any embedded observer. Coherence conditions on inference through this bottleneck, together with Gleason's theorem on the 48-dimensional internal Hilbert space, uniquely determine the Born rule; the remaining operational features follow from the same observer-level framework under the stated assumptions. At the ontological level the theory is deterministic and state-realist, while the operational quantum formalism appears at the observer level as a consequence of structurally limited access to the underlying algebraic reality.

Limited connectivity makes nonlocal quantum gates expensive on near-neighbor hardware, where compilation typically relies on SWAP transport, inheriting both depth overhead and path congestion. We present a swap-free routing framework in which higher levels of a qudit act as orthogonal spectral buses that transport control information without moving the computational state. We show that exact congestion relief in nearest-neighbor architectures requires local Hilbert-space expansion. In this model, a nonlocal operation over a path of length $L$ requires $2L+1$ logical routing primitives, compared to the $3L$ baseline. Overlapping routes remain distinguishable through bus labels encoded in the same physical qudits. This routing algebra extends to Boolean fan-in at a common target: multiple controls arriving on distinct buses trigger a local unitary based on an arbitrary Boolean function of bus digits, yielding multi-control operations of depth $2L + D_g + O(1)$ for fan-in size $K$ and target-synthesis cost $D_g$. We prove decodability, reversibility, and correctness for CNOT and Boolean fan-in, along with a state-count lower bound $d \geq 2^{K+1}$ for exact overlap routing. Cirq simulations confirm single-control correctness and zero crosstalk. Compiler-level benchmarks on QFT, QAOA, and mirror-interaction circuits verify the predicted congestion law and transport reduction. Noisy QuTiP simulations show that the architectural advantage depends on higher-level coherence and speed. These results identify spectral qudit routing as a congestion-relief architecture that separates nonlocal control delivery from local target-side aggregation, providing a minimal mechanism for overcoming qubit routing limitations.

\emph{Literate programming}, introduced by Knurth, interleaves code and prose so that a program can be read as both executable and explanatory text. We propose \emph{literate execution}, which inverts this relationship: rather than embedding code within a static narrative, we treat documentation -- and other expository elements such as visualisations -- as first-class artefacts that can be computed alongside a running program and then integrated into a view of its execution. We explore this idea through Fluid, a programming language with a provenance-tracking runtime that records fine-grained dependencies between inputs and outputs. These provenance relationships can be surfaced as interactions that allow readers to explore how intermediate values contribute to a result. By integrating visualisation, provenance, and exposition, literate execution aims to make programs more explorable and self-explanatory, and explorable explanations easier to program.

This paper studies exact fixed-cardinality Solow--Polasky diversity subset selection on ordered finite $\ell_1$ point sets, with monotone biobjective Pareto fronts and their higher-dimensional staircase analogues as central applications. Solow--Polasky diversity was introduced in biodiversity conservation, whereas the same inverse-matrix expression appears in metric geometry as magnitude: for a finite metric space $(X,d)$ with exponential similarity matrix $Z_{ij}=e^{-q d(x_i,x_j)}$, the quantity $\1^\top Z^{-1}\1$ is the magnitude of the scaled finite metric space $(X,qd)$ whenever the weighting is defined by the inverse matrix. Thus, in this finite exponential-kernel setting, Solow--Polasky diversity and magnitude are mathematically the same object viewed through different motivations. Building on the linear-chain magnitude formula of Leinster and Willerton, the paper gives a detailed proof of the scaled consecutive-gap identity $ \SP(X)=1+\sum_r \tanh(qg_r/2),$ where the $g_r$ are the gaps between consecutive selected points. It then proves an exact Bellman-recursion theorem for maximizing this value over all subsets of a prescribed cardinality, yielding an $O(kn^2)$ dynamic program for an ordered $n$-point candidate set and subset size $k$. Finally, the paper proves ordered $\ell_1$ reductions showing that the same algorithm applies to monotone biobjective Pareto-front approximations and, more generally, to finite coordinatewise monotone $\ell_1$ staircases in $\R^d$. These are precisely the ordered $\ell_1$ chains for which the $\ell_1$-distance becomes a line metric along the chosen order, so the one-dimensional dynamic program applies without modification. Keywords: Solow--Polasky diversity; magnitude; metric geometry; dynamic programming; ordered points; $\ell_1$ geometry; Pareto-front approximation.

In pedestrian dynamics, the internal drive that propels individuals toward their goals is typically captured by a single, fixed parameter, the desired walking speed. This simplification overlooks that motivation fluctuates in response to changing spatial and social conditions within a crowd. This paper proposes a dynamic motivation model grounded in expectancy-value theory from psychology, in which each agent's motivation evolves over time depending on proximity to the goal, relative position among other pedestrians, and individual goal importance. The resulting motivation modulates multiple movement parameters simultaneously, including walking speed, gap-closing behavior, and interpersonal spacing. The model is evaluated in simulated pre-bottleneck waiting scenarios using paired statistical comparisons across multiple random seeds and population sizes, and compared with trajectory data from the CROMA concert-entry bottleneck experiments under low- and high-motivation framings. Simulations show that the dynamic model produces structured heterogeneity in the crowd: agents self-organize into differentiated positions near the bottleneck, with those closer to the front occupying less space, a pattern absent in the static baseline but clearly present in the experimental data. These findings suggest that motivation in crowds should be understood not as a uniform increase in urgency, but as a mechanism that reorganizes competitive positioning along spatial and social axes. Future work should extend the framework to open-door throughput scenarios, larger populations, and richer social interactions such as group cohesion and cooperative strategies.

Lutwak's affine quermassintegral theory is a foundational component of modern affine Brunn--Minkowski theory. Developed in the 1980s, it provides affine analogues of the classical quermassintegrals and has led to a rich family of sharp affine isoperimetric inequalities. A central question in this program, going back to Lutwak's 1988 work, is an Alexandrov--Fenchel-type monotonicity principle for the normalized $L^{-n}$-moment quermassintegrals $I_{k,-n}$. In one form, this principle predicts that \[ I_{m,-n}(K)^{1/m}\ge I_{k,-n}(K)^{1/k}, \qquad 1\le m<k\le n . \] The question was recorded in Gardner's 2006 book Geometric Tomography as part of its problem list, and the comparison with the top dimension, $k=n$, was established by Milman and Yehudayoff in their 2023 JAMS paper. We show that the proposed monotonicity does not persist in the full range. More precisely, for every triple of integers $m,k,n$ satisfying $1\le m<k\le n-1$ and $n>(m+2)(k+2)-2$, there exists an origin-symmetric $C^2_+$ convex body $K\subset\mathbb R^n$ such that \[ I_{m,-n}(K)^{1/m} < I_{k,-n}(K)^{1/k}. \] The example is obtained from the Euclidean ball by an arbitrarily small degree-four spherical harmonic perturbation. On the positive side, we prove that the endpoint chain is true in dimension three: for every convex body $K\subset\mathbb R^3$, \[ I_{1,-3}(K)\ge I_{2,-3}(K)^{1/2}\ge I_{3,-3}(K)^{1/3}=1. \] The equality cases in both non-trivial inequalities are exactly ellipsoids, up to translation and nonsingular affine transformations.