Manticore-Local Suite: Digital Twin of Local Universe

• Manticore-Local Suite is a Bayesian cosmological reconstruction program that creates digital twins of the Local Universe using the 2M++ galaxy catalogue and BORG inference.
• It integrates flexible galaxy-bias modeling, COLA dynamics, and full N-body resimulations to capture nonlinear density fields, halo catalogues, and peculiar velocity fields with rigorous uncertainty quantification.
• Its validated outputs support catalogues of voids and clusters, tSZ calibration, and investigations of local dynamics such as the Great Attractor, aligning observations with ΛCDM predictions.

Manticore-Local Suite is a cosmological reconstruction program that generates Bayesian “digital twins” of the nearby Universe from galaxy redshift data, principally the 2M++ compilation, by inferring initial conditions with BORG and evolving them into fully non-linear structure with gravity. In its core form, it provides posterior ensembles of initial conditions, density fields, halo catalogues, and peculiar-velocity fields for the Local Universe, with uncertainty quantification propagated from survey masks, selection effects, redshift-space distortions, and galaxy bias. Subsequent studies use these realizations to construct catalogues of massive clusters and voids, analyze caustic topology in the local cosmic web, revisit the Great Attractor problem, and calibrate thermal Sunyaev–Zel’dovich analyses; a broader project extension connects the local reconstruction to the survey-depth Manticore-Deep inference (McAlpine et al., 15 May 2025).

1. Definition, scope, and scientific role

Manticore-Local is defined as a suite of Bayesian constrained realizations of the Local Universe built by fitting a physical structure-formation model to the 2M++ galaxy catalogue with the BORG field-level inference framework. Its stated purpose is to deliver a statistically rigorous digital twin of the local cosmic web: initial conditions, nonlinear density, and peculiar velocities that are self-consistent with $\Lambda$CDM and with the survey’s selection effects (McAlpine et al., 15 May 2025).

The observational input is the 2M++ galaxy compilation. One project description specifies $\approx 69{,}000$ galaxies to $z<0.1$, split into 32 subcatalogues by absolute $K$-band magnitude, apparent $K$-band magnitude, and redshift, with an angular completeness mask and a Schechter-based radial selection function. Other analyses describe the same observational basis more compactly as an all-sky redshift catalogue covering $z\lesssim 0.1$, with the farthest galaxies at $\approx 250$ Mpc, or as a nearby supervolume directly constrained to $R\lesssim 300$ Mpc. Across these descriptions, the region of highest signal-to-noise is consistently the inner Local Universe: one paper emphasizes $R<200$ Mpc, another states that constraints are strongest to $\approx 250$ Mpc, and the published void catalogue contains voids within $\approx 69{,}000$0 of the observer (McAlpine et al., 15 May 2025, Malandrino et al., 9 Jul 2025, McAlpine, 18 Oct 2025).

The suite was built to address problems that require both spatial fidelity and non-linear dynamics. Early project goals include testing claims of a large local underdensity, reconstructing nearby massive clusters, and predicting peculiar velocities relevant to flow studies and $\approx 69{,}000$1 analyses. Later work extends the same posterior ensemble into object-level cataloguing, multi-probe validation, cosmic-web topology, and future dynamical evolution (McAlpine et al., 15 May 2025, Stiskalek et al., 13 Jan 2026).

2. Bayesian field-level inference and physical model

The inference engine is BORG, augmented in the Manticore program with flexible galaxy-bias modelling, a generalized Poisson count likelihood with over-dispersion, and physics-informed priors. In one formulation, the posterior over fields and parameters is written as

$\approx 69{,}000$2

where $\approx 69{,}000$3 collects the latent fields, including initial and final density and velocity, $\approx 69{,}000$4 denotes nuisance and bias parameters, and $\approx 69{,}000$5 denotes the galaxy data. A related presentation writes the posterior schematically as

$\approx 69{,}000$6

with $\approx 69{,}000$7 encoding the initial density field and nuisance parameters, $\approx 69{,}000$8 the likelihood, and $\approx 69{,}000$9 the prior (McAlpine et al., 15 May 2025, Malandrino et al., 9 Jul 2025).

The prior on the initial conditions is Gaussian and isotropic, with the initial power spectrum computed by CLASS for the DES Y3 “3x2pt + All Ext.” $z<0.1$0CDM cosmology. The parameter values repeatedly quoted in the local analyses are

$z<0.1$1

The Local Universe inference is therefore not a free-form density reconstruction; it is a posterior over realizations conditioned jointly on galaxy data and cosmological priors (McAlpine et al., 15 May 2025, Malandrino et al., 9 Jul 2025, Stiskalek et al., 13 Jan 2026).

During inference, gravitational evolution is modeled with a COLA-type approximate non-linear solver in a periodic cube. Galaxy counts are forward-modeled by combining this dynamics with survey response operators and stochastic bias prescriptions. In the local analysis, the 2M++ catalogue is decomposed into 32 subcatalogues to allow luminosity- and redshift-dependent bias calibration in situ. Redshift-space distortions, the angular mask, radial selection, and incompleteness are built directly into the forward response; no separate redshift-space “deprojection” stage is required (McAlpine et al., 15 May 2025).

Posterior samples of the inferred initial conditions are then resimulated with full $z<0.1$2-body dynamics. One description states that each initial condition is generated with second-order Lagrangian perturbation theory and evolved with SWIFT to $z<0.1$3. Another gives the same logic more generally: independent BORG posterior samples are augmented with random small-scale modes below the survey’s constraint scale, then evolved with an $z<0.1$4-body code to produce full-particle digital twins. This separation between inference-time forward modeling and posterior resimulation is central to the suite’s design, because it allows tractable sampling while retaining high-fidelity late-time predictions (Malandrino et al., 9 Jul 2025, Stiskalek et al., 13 Jan 2026).

3. Numerical realizations, ensembles, and released products

The suite is numerically instantiated in several closely related forms. The initial project paper reports a parent $z<0.1$5CDM volume of $z<0.1$6 Mpc with periodic boundaries, inferred on a $z<0.1$7 grid, and 50 gravity-only posterior resimulations with SWIFT at $z<0.1$8 particles evolved to $z<0.1$9. Later cluster and dynamics analyses describe an 80-realization posterior ensemble of fully non-linear nearby-Universe digital twins. Derived suites include high-resolution zooms for tSZ studies and a Beyond-Present-Time ensemble evolved to $K$0 (McAlpine et al., 15 May 2025, Stiskalek et al., 22 Jan 2026, Stiskalek et al., 13 Jan 2026, McAlpine, 18 Oct 2025).

Product	Numerical setup	Principal use
Core posterior resimulations	$K$1 Mpc, inference on $K$2, SWIFT $K$3 DMO realizations	Local density, halo, and velocity reconstruction
Later posterior ensemble analyses	80 fully non-linear realizations in a periodic $K$4 Mpc box	Cluster associations and Great Attractor dynamics
CSiBORG-Manticore zooms	50 posterior zoom simulations, $K$5, Gadget-4	tSZ and halo-mass validation
Beyond-Present-Time suite	50 realizations evolved to $K$6 with Gadget-4	Future dynamics of the Local Group

The resolution quoted for the core local resimulations is high by constrained-simulation standards. One specification gives $K$7 particles with particle mass $K$8, yielding $K$9 resolved haloes of minimum mass $K$0 identified with HBT+. Another local analysis quotes an 80-realization suite with particle mass $K$1, with density and velocity fields sampled on a $K$2 Cartesian grid of voxel size $K$3 for dynamical calculations (Malandrino et al., 9 Jul 2025, Stiskalek et al., 13 Jan 2026).

Published data products extend beyond snapshots. For caustic analysis, the suite is explicitly described as providing initial white-noise fields $K$4, the corresponding linear displacement potential $K$5, $K$6 dark matter particle snapshots, final peculiar velocity fields, and derived density fields estimated with Phase-Space DTFE. Other releases include $K$7 halo catalogues, gridded matter-density fields, 3D velocity fields, HEALPix maps, radial density profiles, and higher effective resolution over the constrained 2M++ region; the public-facing project sites additionally host specialized void and cluster catalogues (Read et al., 24 Apr 2026, McAlpine et al., 15 May 2025, McAlpine, 18 Oct 2025).

4. Statistical fidelity and empirical validation

A defining feature of Manticore-Local is that it is validated both statistically against $K$8CDM expectations and empirically against independent observations. In the parent volume, posterior resimulations are reported to match CAMB or $K$9CDM control predictions for the matter power spectrum $z\lesssim 0.1$0, the bispectrum $z\lesssim 0.1$1, the halo mass function, and the Gaussianity of the inferred initial white-noise field. The local supervolume likewise shows no significant deviation from cosmological expectations: the cumulative mass-density profile fluctuates within $z\lesssim 0.1$2 of the cosmic mean over $z\lesssim 0.1$3 Mpc, and at $z\lesssim 0.1$4 Mpc the mean density is $z\lesssim 0.1$5 below the cosmic mean. The project’s stated conclusion is that there is no evidence for a large local underdensity (McAlpine et al., 15 May 2025).

Object-level spatial fidelity is tested through nearby massive clusters. The first project paper reports high-significance counterparts for fourteen prominent galaxy clusters within $z\lesssim 0.1$6 of the observed sky positions. Across 700 counterparts $z\lesssim 0.1$7, the median $z\lesssim 0.1$8-value is $z\lesssim 0.1$9, corresponding to a median significance of $\approx 250$0, with a 10–90% range of $\approx 250$1–$\approx 250$2. Reconstructed masses and recession velocities are reported to agree closely with observational estimates, including for Coma, Perseus, Norma, Virgo, Hydra, and Centaurus (McAlpine et al., 15 May 2025).

Velocity-field validation is comparably strong. Using five independent datasets—2MTF Tully–Fisher, SFI++, CF4 Tully–Fisher, LOSS SNe Ia, and Foundation SNe Ia—the Manticore-Local velocity field attains the highest Bayesian evidence across all five, surpassing state-of-the-art nonlinear, Wiener-filter, and machine-learning reconstructions under the comparison protocol cited in the project paper (McAlpine et al., 15 May 2025).

The tSZ-focused CSiBORG-Manticore analysis adds an external multi-wavelength calibration layer. Relative to the previous CSiBORG2 generation, the new Manticore-based digital twins show more accurate velocity fields and cluster positions and masses, better mass calibration against weak-lensing-calibrated eROSITA X-ray masses, and a tighter $\approx 250$3–$\approx 250$4 scaling. For Planck $\approx 250$5 versus BORG $\approx 250$6, the quoted fit is $\approx 250$7 with intrinsic scatter $\approx 250$8 dex for the Manticore-based suite, compared with $\approx 250$9 and $R\lesssim 300$0 dex for the earlier generation; Perseus is specifically noted as being recovered in the new suite but not in the old one (Stiskalek et al., 22 Jan 2026).

5. Catalogues of voids, clusters, and cosmic-web topology

A major output of the suite is posterior cataloguing: structures are not extracted from a single galaxy realization, but from recurrence across statistically independent posterior samples.

For voids, the methodology begins with 50 posterior realizations of the large-scale structure inferred from 2M++ and evolved to $R\lesssim 300$1. VIDE, an enhanced implementation of ZOBOV, is run on each halo distribution to produce 50 independent void catalogues. Posterior clustering is then performed in the space of void centers and sizes, using hierarchical agglomerative clustering with a Ward linkage and a linkage threshold tied to the radius bin, so that matched voids overlap spatially. Spurious cluster statistics are calibrated from the unconstrained outer region of the periodic box, and a conventional particle-physics threshold of $R\lesssim 300$2 is used to define 5$R\lesssim 300$3 void detections. The resulting public catalogue contains $R\lesssim 300$4 voids at 5$R\lesssim 300$5 significance, with posterior distributions for center position and effective radius, and with morphology templates represented by weighted “Voronoi clouds.” A truncation threshold $R\lesssim 300$6 is identified as volume preserving to sub-percent, with a truncated-cloud radius to KDE $R\lesssim 300$7 ratio of $R\lesssim 300$8 (Malandrino et al., 9 Jul 2025).

For massive structures, the cluster catalogue paper builds associations across 80 posterior realizations by clustering $R\lesssim 300$9 central haloes in 3D Cartesian space with DBSCAN, using $R<200$0 Mpc and $R<200$1, while permitting at most one member per realization. Persistence is quantified by

$R<200$2

with $R<200$3. The fiducial public catalogue contains 225 associations with mean masses $R<200$4 and $R<200$5. Positional coherence is typically $R<200$6–3 Mpc. Independent Planck PR4 NILC Compton-$R<200$7 stacking yields a clear tSZ detection: for the mass bin $R<200$8 and $R<200$9, the stack reaches $\approx 250$0, while a mask-aware null test on random positions gives $\approx 250$1. The same paper further reports that constrained progenitors are localized to volumes 2–5 times smaller than mass-matched haloes in unconstrained $\approx 250$2CDM controls, with a convex-hull volume ratio $\approx 250$3 of median $\approx 250$4 and an information gain of median $\approx 250$5 bits (McAlpine, 18 Oct 2025).

The suite also supports topological cosmic-web analysis. Applying caustic skeleton theory to three posterior realizations drawn from a larger suite of 50, one study reconstructs the multi-scale caustic network of the Coma region and the Pisces–Perseus ridge from the initial deformation tensor. The classification distinguishes $\approx 250$6 swallowtail filaments from $\approx 250$7 umbilic filaments, which are morphologically similar in Eulerian space but topologically distinct in folding history. A hierarchical proximity-based environment scheme labels galaxies as $\approx 250$8, $\approx 250$9, $\approx 69{,}000$00, or Void within 5 Mpc of the corresponding caustic sets. The main result is that the extended Coma/Stickman structure is $\approx 69{,}000$01-dominated at larger smoothing scales but shifts toward $\approx 69{,}000$02 prominence at smaller scales, whereas Pisces–Perseus is distinctly $\approx 69{,}000$03-dominated across scales (Read et al., 24 Apr 2026).

6. Dynamical interpretations, limitations, and project extensions

The suite has been used to revisit the Great Attractor problem in a way that separates three historically conflated questions: what sources the Local Group velocity in the cosmic microwave background frame, where present-day streamlines converge, and where the Local Group is moving to in the future. Using 80 present-day realizations and a 50-realization Beyond-Present-Time suite evolved to $\approx 69{,}000$04, the analysis finds that matter within $\approx 69{,}000$05 accounts for only $\approx 69{,}000$06 of the observed Local Group velocity magnitude, with a $\approx 69{,}000$07 directional offset. Streamline convergence is explicitly smoothing-scale dependent: Virgo dominates at small smoothing, the Hydra–Centaurus region at intermediate smoothing, and Shapley at large smoothing. At $\approx 69{,}000$08, the classical streamline-defined convergence point lies near Abell 3565 at

$\approx 69{,}000$09

with basin mass

$\approx 69{,}000$10

Norma is excluded from this basin. In the future evolution, local particles drift only $\approx 69{,}000$11 toward Virgo by $\approx 69{,}000$12 and remain unbound, leading the authors to conclude that the classical Great Attractor is not a dynamically dominant structure but an artifact of the instantaneous velocity field (Stiskalek et al., 13 Jan 2026).

Several caveats recur across the literature. The constrained region is embedded in a periodic parent box, so predictions degrade outside the survey-dominated volume. Small-scale modes above the inference Nyquist are stochastically completed rather than directly constrained. The simulations are dark-matter-only in the core suite, so baryonic observables such as tSZ must be compared indirectly or with auxiliary modelling. The Zone of Avoidance remains observationally difficult, even though the posterior machinery explicitly reconstructs structure behind the Galactic plane. Structure definitions are also method-dependent: the void catalogue uses VIDE/ZOBOV and a strict 5$\approx 69{,}000$13 threshold, while cluster associations use DBSCAN persistence cuts, both favoring robustness over completeness (Malandrino et al., 9 Jul 2025, McAlpine et al., 15 May 2025, McAlpine, 18 Oct 2025).

The local suite is also the basis for broader project expansion. Manticore-Deep extends the same field-level Bayesian framework to a parent volume of $\approx 69{,}000$14, out to $\approx 69{,}000$15, using 64 tiles in a $\approx 69{,}000$16 layout, of which 27 contain survey data from 2M++, 6dFGS, 2dFGRS, SDSS Main, and BOSS. That paper states that P1 and P2 together constitute interoperable Bayesian digital twins spanning local-to-deep volumes. The deep reconstruction is validated statistically against $\approx 69{,}000$17CDM and observationally by a conservative CMB-lensing cross-correlation detection of $\approx 69{,}000$18, a median kSZ detection of $\approx 69{,}000$19 from velocity-weighted stacking of 64,750 galaxy clusters, and recovery of the BOSS Great Wall as a $\approx 69{,}000$20 overdensity. This broader framing situates Manticore-Local not as an isolated local reconstruction, but as the nearby-Universe anchor of a multi-volume digital-twin program (McAlpine et al., 8 Jun 2026).