arXiv subjects

Hassan Mehmood

Publications and source records attributed to Hassan Mehmood.

8 recordsLinked to original sources

arXiv2026

Credibility Trilemma in Polymatroidal Service Markets

Mechanism-mediated service markets with polymatroidal feasibility admit efficient, dominant-strategy incentive-compatible (DSIC) allocation, but these guarantees implicitly assume truthful execution by the marketplace operator. Modelling the operator as a strategic player, we establish a credibility trilemma: for single-parameter agents on a non-modular polymatroid carrying a competitive prior profile, no static sealed-bid mechanism is simultaneously revenue-optimal, DSIC for agents, and credible for the operator. We introduce the Cost of Non-Credibility (CoNC) as a price-of-anarchy-style welfare-loss measure and prove a per-pair lower bound scaling with the polymatroid's non-modularity gap, turning the trilemma into a quantitative diagnostic. Three structurally distinct resolutions follow: public broadcast or deferred-revelation commitment, administrative domain separation under settlement separation and four side conditions, and integrator competition orthogonal to mechanism execution under disjoint actors. An instance-level grounding over the edge-pricing market of Amin et al. shows that the economic content carries over to a refereed external setting. Marketplace neutrality is thus a first-order design constraint on polymatroidal service markets rather than an implementation detail: where the operator is a strategic player, credibility trades off against revenue optimality and agent incentive compatibility along structurally characterised lines.

cs.GT↗

arXiv2026

The Behavioral Credibility Trilemma: When Calibrated Autonomy Becomes Impossible

We prove that no reinforcement learning policy with confidence-gated autonomy can simultaneously achieve maximum helpfulness, optimal calibration, and full autonomy under rational oversight, whenever some tasks exceed the agent's reliable competence: the Behavioral Credibility Trilemma. The impossibility is geometric: adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness, so an agent rewarded for both calibrated confidence and autonomous action systematically inflates its reported confidence on tasks below the principal's approval threshold whenever the autonomy stake exceeds the calibration cost of clearing it. The Behavioral Perturbation Lemma quantifies the inflation (scaling as $w_A/(2 w_C)$ for the Brier score) and shows detection requires $\Omega(1/\Delta^2)$ observations for interior reports. We prove that, in the unsaturated regime, no affine oversight rule is optimal for the principal and the optimum is attained by a sharp threshold satisfying the trilemma's own hypotheses, so the impossibility is endogenized rather than assumed; moreover, for symmetric, log-concave, full-support location policy families under the Brier score, calibration is not even a stationary point of policy-gradient training. We formalize the Confidence-Gated Decision Problem, map existing methods onto the trilemma, and identify two constructive resolution pathways (commitment, role separation). A 540-configuration Best-of-N experiment tests five hypotheses, all strongly confirmed (effect sizes $d = 1.10$ to $5.35$, the upper end from a per-completion estimator inflating magnitude over per-task aggregates) and replicated under a pre-specified protocol on two further model families, and adds a descriptive analysis of the achievable-$(H, C, A)$ surface geometry showing a plateau-truncated frontier consistent with the predicted inflation saturation.

cs.LG↗

arXiv2026

Correction to Hawking radiation in non-singular gravitational collapse

Recent studies have shown that quantum gravity introduces important corrections to the process of spherically symmetric gravitational collapse expected from general relativity. In particular, instead of falling into a central singularity, the collapsing body undergoes a bounce and eventually exits its Schwarzschild radius, and this entire process of collapse and rebound can occur in a single asymptotic region. In this paper, particle creation during such non-singular gravitational collapse is studied. It is shown that the probability of spontaneous emission of particles differs from the well-known probability of Hawking radiation from classical gravitational collapse. It is argued that the different result implies a deviation from thermality. Some arguments are also adduced concerning how the Hawking process during non-singular dust collapse could potentially remove shell crossing singularities.

gr-qc↗

arXiv2026

Shock waves in classical dust collapse

During gravitational collapse of dust in spherical symmetry, matter particles may collide forming shell crossing surfaces (SCS) on which the Einstein equations become indeterministic. We show that there is a unique evolution beyond SCS such that a propagating shock wave forms, the metric remains continuous, and the stress-energy tensor dynamically becomes that of a thin shell. We give numerical simulations that exhibit this result.

gr-qc↗

arXiv2025

On weak solutions in Einstein theory and beyond

In spherical symmetry, gravitational collapse of dust may give rise to the so-called shell-crossing singularities, beyond which spacetime can be extended using weak solutions to the integrated version of the equations of motion. We argue that the paradigm of weak solutions is ill-suited for dynamical extension beyond shell crossings through shock waves because it is based implicitly on an assumption that turns out to be unphysical for the shock and leads to the unwanted prospect of shock waves of dust particles moving faster than light.

gr-qc↗

arXiv2025

An Exactly Soluble Group Field Theory

We present a Group Field Theory (GFT) quantization of the Husain-Kuchař (HK) model formulated as a non-interacting GFT. We demonstrate that the path-integral formulation of this HK-GFT provides a complete spinfoam model and a unique Fock representation that describes the quantum three-geometries of the HK model. These results provide a link to the canonical quantization of the HK model and demonstrate how GFTs can bridge distinct quantization schemes.

gr-qc↗

arXiv2024

General covariance and dynamics with a Gauss law

We present a 4-dimensional generally covariant gauge theory which leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the Hamiltonian. We describe its observables, quantization, and some generalizations.

gr-qc↗

arXiv2023

Quantum Gravity as a Theory of Connections

Consider the interior of a black hole or the very early universe: matter is so densely localized that neither the effects of gravity nor those of quantum theory can be ignored. But this entails that neither general relativity nor quantum theory on its own can fully describe such a situation, for some of the most fundamental principles inhering in these two theories are haunted by the specter of incompatibility. Quantum gravity is the name for the bewildering penumbra of theories that seek to exorcise this demon. But it turns out that the metrical variables of general relativity constitute a lamp too narrow to bottle the phantom, and loop quantum gravity is a fascinating enterprise that seeks the Aladdin who does possess the required lamp. This is achieved by recasting general relativity as a theory of connections, rather than that of metrics. This shift of emphasis allows one to use a number of mathematical tools that make it possible to arrive at a fully consistent, almost background-independent theory of quantum gravity. This thesis endeavours to probe these ideas in detail.

gr-qc↗