Yasser Al Eryani | Searcharxiv

arXiv2026

Beyond the "G" Frontier: A Time Traveler's Century-Long Vision for Wireless Intelligence

This article travels one century into the future--from 2025 to 2125--through the analytical lens of the Information--Curvature Efficiency Law (ICEL), an organizing ansatz that reframes wireless capacity around the curvature of the information manifold. It contends that wireless evolution will not proceed through incremental generations such as 6G or 7G, but through a curvature-managed integration of electromagnetics, biology, and thermodynamics. The technical instantiation of ICEL for phase-coded continuous apertures--where curvature is realized as the affine-quotient second derivative of the aperture phase, with a compact synthesis operator and a Fredholm-determinant capacity--is developed rigorously in a companion theory paper and stress-tested against SVD, Fourier, Zernike-like, matched-focus, and RIS baselines in a companion benchmark paper. The present essay supplies the physical intuition, the century-scale narrative, and a set of cross-domain extensions (biology, thermodynamics, ecology) that are explicitly labeled as illustrative extrapolations, not independent derivations.

cs.IT↗

arXiv2026

Curvature-Domain Wireless Communications: Gauge-Fixed Signal Spaces, Fredholm Capacity, and Differentiation-Limited Scaling for Continuous Apertures

We develop a curvature-domain formulation for continuous-aperture signaling, in which the transmit phase is represented through its second spatial derivative after quotienting out affine piston-and-tilt gauge freedom. The resulting gauge-fixed synthesis operator is bounded and compact, with sharp Poincare-Wirtinger constant $C_L=L^2/β_1^2$, and its modal Gram spectrum is available in closed form, $ρ_m=(L/β_m)^4$, with $β_m$ the roots of $\cosβ\coshβ=1$. Under a bounded-support square-integrable propagation kernel the tangent operator is Hilbert-Schmidt, so the infinite-dimensional capacity is a well-defined Fredholm-determinant supremum. The optimal signaling law is a dual-budget generalized water-filling with one Lagrange multiplier for curvature power and one for phase excursion. From the exact nonlinear phase-only aperture law we derive the coherent tangent channel with an explicit Frechet remainder bound and a multi-chart atlas for large excursions. At the receiver, curvature inferred from noisy phase samples by second differences has a pentadiagonal noise covariance with spectral norm $Θ(Δx^{-4})$. A deterministic diagnostic suite measures each mechanism against its closed form, with a null run beside every claim: the computed spectrum matches $(L/β_m)^4$ to relative error $3.78\times10^{-15}$; the tangent remainder has fitted slope 1.0000; the dual-budget law is solved with both multipliers strictly active to a KKT residual of $3.90\times10^{-15}$; the derivative-noise bound is approached to 0.999981; and the differentiation-limited branch is observed at exponent 0.2175, then collapses to 0.0576 once the mode count saturates at the Shannon number, while a flat-propagation null run holds at 0.2019. Curvature is thus a well-posed, gauge-invariant coordinate, and below the Shannon number the gauge, rather than the medium, governs the scaling.

eess.SP↗