NexusCosmos: Unified Cosmic Web Analysis

Updated 15 December 2025

NexusCosmos is a unified framework that identifies cosmic environments by applying multiscale Hessian-based filters and log-space smoothing.
It segments nodes, filaments, walls, and voids through rigorous morphological analysis on both observed and simulated cosmic density fields.
The approach enhances cosmological constraints by enabling environment-specific power spectra and network analyses in precision surveys.

NexusCosmos is a unified, multiscale framework for identifying, classifying, and studying the structural environments of the cosmic web—specifically, nodes, filaments, walls, and voids—based on the mathematical morphology of the cosmic density field. Grounded in Hessian-based analysis, log-space filtering, and rigorous segmentation of observed and simulated datasets, NexusCosmos underlies both cosmological structure classification algorithms and interoperable, open computational tools for space science research. The term encompasses a body of methodologies, software pipelines, and community-driven data systems that provide the infrastructure for advanced large-scale structure analysis, legacy survey science, and open-source orbital simulation environments (&&&0&&&, Shen et al., 22 Aug 2024, Sahu, 8 Dec 2025).

1. Mathematical and Algorithmic Foundations

At the core of NexusCosmos lie the NEXUS and NEXUS+ algorithms—multiscale, Hessian-based morphology filters. These identify cosmic web environments by analyzing the local curvature of the (smoothed) density field in both simulation and observational data (Cautun et al., 2012, Cautun et al., 2015, Cautun et al., 2014).

The methodology proceeds as follows:

Scale-space construction: The density field, typically expressed as the overdensity δ(x) = ρ(x)/⟨ρ⟩ - 1, is smoothed at multiple scales R using Gaussian or log-Gaussian kernels. NEXUS+ employs log-space filtering (i.e., smoothing ln(1+δ)) to ensure equal sensitivity to faint and prominent structures and to prevent dominant clusters from suppressing tenuous filaments in underdense regions (Cautun et al., 2012, Cautun et al., 2014).
Hessian eigendecomposition: For each smoothing scale R, the Hessian H_ij(x;R) = ∂²f_R(x)/∂x_i∂x_j of the smoothed field is computed and diagonalized. The ordered eigenvalues λ₁, λ₂, λ₃ at each position encode the principal local curvatures.
Morphological classification: The sign and relative magnitude of the Hessian eigenvalues determine environment type. For log-Gaussian filtering, this proceeds as:
- Nodes/clusters: λ₁ > 0, λ₂ > 0, λ₃ > 0
- Filaments: λ₁ > 0, λ₂ > 0, λ₃ < 0
- Walls: λ₁ > 0, λ₂ < 0, λ₃ < 0
- Voids: λ₁ < 0, λ₂ < 0, λ₃ < 0
Multiscale maximum response: For each environment type, a scalar "signature" function of the eigenvalues is computed as a function of scale, and the maximum across all scales selects the optimal identification (Cautun et al., 2012, Sunseri et al., 14 Mar 2025).

Thresholds for tagging environments are set using physically motivated criteria, including matching mass/volume fractions or maximizing mass contrast (peak of dM²/d log S_E). The pipeline systematically tags every voxel in a 3D field as node, filament, wall, or void, outputting segmentation masks and structural statistics (Sunseri et al., 14 Mar 2025).

2. Structural Properties and Evolution in Cosmology

NexusCosmos enables the quantitative measurement and tracking of web environments across cosmic time in large-volume simulations and surveys.

Mass and volume fractions: At z=0, filaments and clusters contain the majority of mass (~50% and ~11%, respectively), while voids and sheets dominate the volume (voids ~77%) (Cautun et al., 2014, Cautun et al., 2012).
Density distributions: Each morphology spans a broad density range, and their density PDFs overlap, requiring morphological signatures rather than simple density thresholds for robust classification (Cautun et al., 2014).
Halo populations: Massive halos (M_{200}>10^{{14} h^{–1}M_⊙)} reside almost exclusively in clusters; intermediate mass halos are typically found in filaments; low-mass halos populate sheets and voids (Cautun et al., 2014).
Geometric statistics: The total length, width, and linear density of filaments, as well as the surface densities of walls, are computed by compressing the 3D sets to their 1D spines or 2D mid-surfaces, enabling direct analysis of structure evolution (Cautun et al., 2015, Cautun et al., 2014).
Time evolution and mass transport: The cosmic web evolves from a network of tenuous filaments and sheets at high redshift (z~2) to one dominated by prominent, massive filaments and clusters at z=0. Mass flows anisotropically: voids feed into sheets, sheets feed filaments, and filaments channel matter into nodes, reflecting the sequence void→sheet→filament→cluster (Cautun et al., 2014, Cautun et al., 2015).

A universal void boundary profile emerges when density is averaged as a function of signed distance from the true void boundary, revealing the shell-crossing caustic, in contrast to non-universal, smooth barycenter-based profiles (Cautun et al., 2015).

3. Information Content and Cosmological Constraints

By splitting large-scale structure data into NexusCosmos web environments, significant gains in cosmological parameter estimation are achieved (Sunseri et al., 14 Mar 2025).

Four-environment decomposition: Segregating the density field into nodes, filaments, walls, and voids, and combining the power spectra of each, yields much tighter cosmological constraints than a global power spectrum.
Neutrino mass constraints: Using the total matter field and small-scale smoothing (R ≈ 2 Mpc/h), NexusCosmos tagging delivers up to 80-fold improvement in constraints on summed neutrino mass relative to the unsplit P(k). Even at large scales (R ≈ 12.5 Mpc/h), a 20-fold improvement is observed. For the CDM+baryon field, relevant for galaxy surveys, gains are ×3.6 (small scales) and ×1.7 (large) (Sunseri et al., 14 Mar 2025).
Pipeline and implementation: The pycosmommf codebase encapsulates the full NexusCosmos methodology. Pipelines natively segment 3D gridded density fields and quantify the resulting environment masks, mass/volume fractions, and power spectra (Sunseri et al., 14 Mar 2025).

These gains underscore the rich cosmological information encoded in environment-dependent statistics, justifying environment-level modeling in precision cosmology.

4. Network Modeling and Universality

Beyond morphological segmentation, NexusCosmos incorporates network-theoretic abstractions to analyze connectivity, topology, and the universality of web statistics in both simulated and observed datasets (Coutinho et al., 2016).

Graph construction: Seven models (M1–M7) have been explored for network construction; the directed nearest-neighbor spatial-proximity model M3 is found optimal, maximizing the correlation of physical properties among connected nodes.
Universal network properties: Degree distributions, clustering coefficients, and assortativity are invariant across simulations and galaxy catalogs (e.g., Illustris, SDSS), distinctively non-random and sub-Poissonian. The emergence of a giant strongly connected component occurs at a critical mean degree ⟨k_c⟩ = 4, robust to redshift and dataset (Coutinho et al., 2016).
Physical correlations: Peculiar velocity, metallicity, specific star-formation rate, and color show significant nearest-neighbor correlations in the M3 network; no heavy-tailed distributions (e.g., scale-free hubs) are observed, indicating an intrinsic universality of the cosmic web connectivity at the galaxy level.

This network formulation provides the foundation for studying higher-order topology and informing halo-finding and environmental metrics in NexusCosmos.

5. Application to Observational Surveys and Data Systems

NexusCosmos extends beyond methodology to encompass open-data frameworks, modular simulation pipelines, and survey science infrastructures.

JWST NEXUS Survey: The NEXUSCosmos concept is anchored by major observational projects such as the NEXUS JWST survey (Cycles 3–5, 368 hours), which executes a two-tier imaging and spectroscopy program at the North Ecliptic Pole. Its “Wide” (400 arcmin²) and “Deep” (50 arcmin²) tiers enable simultaneous, multi-epoch, multi-instrument imaging and spectroscopy (NIRCam, NIRSpec, MIRI), yielding continuum sensitivity to S/N/pixel > 3 at F200W ≲ 27–29 mag and emission-line detection at unprecedented depths (Shen et al., 22 Aug 2024).
Science drivers: The survey supports environment-dependent galaxy and AGN classification (physical parameters, clustering, time-domain variation), large-scale structure demography at z > 6, transient investigations (supernovae, TDEs), and reverberation mapping of AGN. The dataset is timely released, supporting community-driven data challenges and serving as a benchmark for future missions (Shen et al., 22 Aug 2024).

This integrated approach links environmental segmentation, legacy data products, and rapid, open collaboration—central to the NexusCosmos ecosystem.

6. Computational Frameworks and Open-Source Science

NexusCosmos also denotes an emerging open-source computational ecosystem, exemplified by the Interstellar Signature platform (Sahu, 8 Dec 2025).

Design principles: The framework is open by default, modular by architecture, and community-governed in a Linux-style meritocratic model. Components span data ingestion (JPL Horizons, PDS, MPC connectors), physics-based integration engines (two-body, N-body), real-time 3D visualization (WebGL/Three.js), and standardized developer SDKs (Python, C++, JavaScript) (Sahu, 8 Dec 2025).
Simulation and analysis tools: Data flow is orchestrated through microservices and message buses, supporting both live and batch analysis of orbital trajectories, with plugin support for extending gravity models and integrating AI-driven modules for anomaly detection and orbit prediction.
Ecosystem role: NexusCosmos aspires to a “Linux for the space race”: an interoperable operating system for space science, promoting reproducibility, accessibility, and scalable community-driven research across physical and computational domains (Sahu, 8 Dec 2025).

7. Special Cases: Void Structure and Multiscale Typologies

NexusCosmos methodologies have been rigorously validated in special environments like cosmic voids, emphasizing their ability to recover tenuous walls and filaments even in the deepest underdensities.

Multiscale skeletons: NEXUS+ identifies walls and filaments within voids using eigen-analysis of the log-smoothed density Hessian over a suite of scales, yielding structures with thicknesses of ~0.4 Mpc h⁻¹ for walls and intra-void filaments, consistent with both simulation and observational systems like VGS-31 (Rieder et al., 2014).
Hierarchical connectivity: Void systems often reside inside coherent walls that span multiple Mpc and are occasionally pierced by fragile filaments, enabling mild anisotropic infall and aligning galaxy interactions in environments traditionally treated as isolated (Rieder et al., 2014).
Implications: Detection of intra-void substructures supports hierarchical cosmological scenarios in which voids themselves contain a scaled-down cosmic web—a powerful probe for ΛCDM models on Mpc scales (Rieder et al., 2014).

These results affirm the robust, parameter-free, and multiscale nature of NexusCosmos classification across all cosmic environments.

References: