Libraries and sources

Code

All of the project's code — the spherical solver, the 3D modules for GRTeclyn and GRChombo, the analysis scripts and the verified diagnostics module. Read the sources right here or download them as archives.

Running it

The pbhgr library needs Python ≥ 3.12 with numpy, scipy, psutil, pyyaml, h5py, plus a small C kernel:

tar xzf pbhgr-*.tar.gz && cd pbhgr
make            # builds pbhgr/_kernels.so from csrc/kernels.c
make test       # pytest: FLRW, vacuum, dust collapse, decay, static solutions
python3 scripts/v1_ladder.py --help

The 3D modules are built inside the GRTeclyn (AMReX) and GRChombo (Chombo) source trees: how this was done on the server is described in the build document (Russian) and in scripts/grchombo/build_grchombo_ax102.sh; production parameter files sit next to the sources (params_*.txt) and are generated by scripts/grchombo/stage1b_params.py.

The archives are built from the latest commit of each repository, with server addresses removed. The files below are shown with syntax highlighting and line numbers; the "raw" link serves the unprocessed file.

pbhgr-9e8e13d.tar.gz3.1 MB · commit 9e8e13d · 2026-10-08 sphdiag-03375a2.tar.gz100.9 KB · PBH-VERIFY-01 · 2026-09-29

pbhgr

14 files · 2 196 lines · pbhgr

Main Python + C library: spherical Einstein–Vlasov in the horizon-penetrating areal–CMC gauge, the exact LTB solution, peak profiles, a Newtonian 3D particle-mesh code, initial data and run provenance. The C kernel does particle substeps and constraint integration.

File	lines
`pbhgr/__init__.py`pbhgr: Stage-A spherical Einstein-Vlasov + decay solver and campaign scaffolding.	6	raw
`pbhgr/analytic.py`Analytic references for the mandatory Stage-A tests.	41	raw
`pbhgr/background.py`Homogeneous flat FLRW with cold X + radiation + X -> radiation decay.	48	raw
`pbhgr/cosmo_ev.py`Spherically symmetric Einstein-Vlasov solver in the areal-CMC gauge with an expanding FLRW exterior (Stage A step 2; equations in Appendix B of brief_verification/verification_and_plan.md).	656	raw
`pbhgr/cosmo_id.py`Cosmological initial data for the areal-CMC spherical Einstein-Vlasov solver (Stage A step 2).	125	raw
`pbhgr/initial_data.py`Initial data families for the spherical solver.	64	raw
`pbhgr/ltb.py`Exact growing-mode LTB solution for a Gaussian curvature profile (Yoo et al. 2026, arXiv:2609.14218).	119	raw
`pbhgr/pm3d.py`Newtonian 3D particle-mesh code for one triaxial peak in an Einstein-de Sitter background (item 3b of the plan).	160	raw
`pbhgr/profiles.py`Curvature profiles zeta(r) beyond the Yoo Gaussian: mean peak profiles of log-normal spectra (BBKS conditioning on the peak height nu and the mean curvature x_bar(nu, gamma)) and a broad near-top-hat control.	63	raw
`pbhgr/provenance.py`Run provenance record, as required by the specification (section 12, Reproducibility).	84	raw
`pbhgr/scan.py`Outcome-map scan driver for the spherical solver (Stage A, section 4 'Скан').	77	raw
`pbhgr/spherical_ev.py`Spherically symmetric Einstein-Vlasov system with X decay (Stage A prototype).	492	raw
`pbhgr/steady_state.py`Static spherically symmetric Einstein-Vlasov solutions (isotropic polytropes, Rein-Rendall type ansatz f = (E0 - e^mu E)_+^k) and particle sampling from them.	89	raw
`csrc/kernels.c`Compiled kernels for the spherical Einstein-Vlasov solver (polar-areal gauge). mass_integrate: integrate the Hamiltonian constraint dm/dr = s_k * sqrt(1 - 2 m / r) across K cells [r_e[k], r_e[k+1]] with piecewise-constant coordinate…	172	raw

PBHVlasov (GRTeclyn)

19 files · 3 558 lines · pbhgr

3D Vlasov particle module for GRTeclyn/AMReX: deposition across AMR levels, geodesic push with proper time, the PBH gauge, early start from Yoo data, ray and sphere horizon diagnostics.

File	lines
`grteclyn/PBHVlasov/GNUmakefile`Line extraction uses the particle interpolator.	42	raw
`grteclyn/PBHVlasov/Main_PBHVlasov.cpp`Engage!	80	raw
`grteclyn/PBHVlasov/PBHAHFinder.hpp`Copy of GRTeclyn's AHFinder (branch AHFinder, fd76177, BSD-3) with an iteration cap, quiet iterations and public accessors, for use inside a PBHVlasov run.	163	raw
`grteclyn/PBHVlasov/PBHAHFinder.impl.hpp`Copy of GRTeclyn's AHFinder (branch AHFinder, fd76177, BSD-3) with an iteration cap, quiet iterations and public accessors, for use inside a PBHVlasov run.	513	raw
`grteclyn/PBHVlasov/PBHGaugeTeclyn.hpp`PBHVlasov example (pbhgr project).	53	raw
`grteclyn/PBHVlasov/PBHVlasovAmr.hpp`PBHVlasov example for GRTeclyn (pbhgr project).	70	raw
`grteclyn/PBHVlasov/PBHVlasovLevel.cpp`PBHVlasov example for GRTeclyn (pbhgr project, stage 2).	1217	raw
`grteclyn/PBHVlasov/PBHVlasovLevel.hpp`PBHVlasov example for GRTeclyn (pbhgr project, stage 2): BSSN/CCZ4 + Vlasov particles.	64	raw
`grteclyn/PBHVlasov/ParticleMatter.hpp`PBHVlasov example for GRTeclyn (pbhgr project). matter_t for CCZ4RHSWithMatter / ConstraintsWithMatter: the energy-momentum tensor is read from the grid variables deposited from the particles (rho_p, S_i, S_ij, all measured by the…	96	raw
`grteclyn/PBHVlasov/ParticleMatterVars.hpp`PBHVlasov example for GRTeclyn (pbhgr project).	26	raw
`grteclyn/PBHVlasov/SimulationParameters.hpp`PBHVlasov example for GRTeclyn (pbhgr project).	33	raw
`grteclyn/PBHVlasov/StateVariables.hpp`PBHVlasov example for GRTeclyn (pbhgr project, stage 2).	46	raw
`grteclyn/PBHVlasov/VlasovParticles.cpp`PBHVlasov example for GRTeclyn (pbhgr project, stage 2).	787	raw
`grteclyn/PBHVlasov/VlasovParticles.hpp`PBHVlasov example for GRTeclyn (pbhgr project, stage 2).	149	raw
`grteclyn/PBHVlasov/params_flrw.txt`PBHVlasov: FLRW dust test (periodic box, geodesic slicing).	33	raw
`grteclyn/PBHVlasov/params_flrw_amr1.txt`PBHVlasov: FLRW dust test (periodic box, geodesic slicing).	35	raw
`grteclyn/PBHVlasov/params_yoo_flrw.txt`Early-start test 1: FLRW (mu = 0) from t_i = 2/(3 H_i) with the expansion-aware step and adaptive subcycling.	42	raw
`grteclyn/PBHVlasov/params_yoo_mu0.3_e0_prod.txt`Stage 1b production template: Yoo long-wavelength data from t_i, seven levels, same box and coordinates as the validated late-start runs (a_ref = a(0.5 t_C(0)) for mu = 0.3).	57	raw
`grteclyn/PBHVlasov/params_yoo_mu0.3_l2.txt`Early-start test 2: Yoo profile mu = 0.3, e = p = 0 on three levels (same box and coordinates as the validated late-start runs: a_ref = a(0.5 t_C(0)), L' = 6194.41), from t_i to 0.97 t_C(0); shell check against LTB.	52	raw

PBHCosmo (GRChombo)

16 files · 1 272 lines · pbhgr

Stage 1: a scalar field in GRChombo — LTB initial data, a gauge with a profile-referenced K, diagnostics. It showed the coherent core bounce (Kaup limit).

File	lines
`grchombo/PBHCosmo/ConstraintsExtraction.hpp`!	117	raw
`grchombo/PBHCosmo/CosmoDiagnostics.hpp`!	66	raw
`grchombo/PBHCosmo/CosmoDiagnostics.impl.hpp`error "This file should only be included through CosmoDiagnostics.hpp"	55	raw
`grchombo/PBHCosmo/CustomExtraction.hpp`Function to convert double to string with precision	124	raw
`grchombo/PBHCosmo/DiagnosticVariables.hpp`assign an enum to each variable	38	raw
`grchombo/PBHCosmo/GNUmakefile`-- Mode: Makefile -- PBHCosmo example: copy this directory into $GRCHOMBO_HOME/Examples/PBHCosmo and run make all	24	raw
`grchombo/PBHCosmo/InitialLTBData.hpp`PBHCosmo example for GRChombo (pbhgr project, plan 6.12 stage 1).	122	raw
`grchombo/PBHCosmo/Main_PBHCosmo.cpp`Chombo includes	112	raw
`grchombo/PBHCosmo/PBHCosmoLevel.cpp`PBHCosmo example for GRChombo (pbhgr project).	243	raw
`grchombo/PBHCosmo/PBHCosmoLevel.hpp`PBHCosmo example for GRChombo (pbhgr project).	36	raw
`grchombo/PBHCosmo/PBHGauge.hpp`PBHCosmo example (pbhgr project).	59	raw
`grchombo/PBHCosmo/Potential.hpp`!	40	raw
`grchombo/PBHCosmo/ScalarFieldRef.hpp`PBHCosmo example (pbhgr project).	89	raw
`grchombo/PBHCosmo/SimulationParameters.hpp`PBHCosmo example for GRChombo (pbhgr project).	70	raw
`grchombo/PBHCosmo/SphereTaggingCriterion.hpp`PBHCosmo example (pbhgr project): nested-sphere tagging — level l+1 is created inside radius radii[l] around the centre (coordinate radius). criterion = 100 inside, 0 outside; use regrid_threshold < 100.	39	raw
`grchombo/PBHCosmo/UserVariables.hpp`assign an enum to each variable	38	raw

scripts

31 files · 2 460 lines · pbhgr

Run drivers, scans, benchmarks, 3D-vs-1D/LTB comparisons, parameter generators, the GRChombo build script.

File	lines
`scripts/build_gallery.py`Assemble reports/gallery.html: the figure set with reading notes, PNGs embedded as data URIs.	132	raw
`scripts/debug_ah.py`	23	raw
`scripts/debug_caustic.py`	23	raw
`scripts/debug_inner.py`	27	raw
`scripts/debug_ueq.py`	27	raw
`scripts/ellipsoidal_collapse.py`Bond-Myers (1996) ellipsoidal collapse of a homogeneous ellipsoid in a matter-dominated background, external tide in linear theory, Zel'dovich initial conditions (lambda_1 >= lambda_2 >= lambda_3, delta = sum lambda, e = (l1 - l3)/(2…	74	raw
`scripts/make_figures.py`Build the visualisation set in reports/figures from runs/viz, runs/scan_pilot, runs/resource_probe.json.	235	raw
`scripts/newton_shells.py`Newtonian spherical shell code started from the exact LTB state at 0.9 t_C(0) (LTB shell dynamics are Newtonian in form, so this is exact until the first crossing).	44	raw
`scripts/pm3d_peak.py`Item 3b: Newtonian 3D PM run of one triaxial peak.	36	raw
`scripts/pm3d_shelltest.py`Lagrangian-shell test of the PM code against the exact LTB solution (spherical Yoo profile, mu = 0.1).	28	raw
`scripts/resource_probe.py`Measure wall time per RK4 step and peak RSS vs particle number / grid size, then extrapolate the Stage-A workload to see where this VPS stops being sufficient.	31	raw
`scripts/run_scan.py`Pilot outcome scan on the dev VPS.	21	raw
`scripts/run_showcase.py`Run representative cases with full snapshot storage for visualisation -> runs/viz/*.pkl	41	raw
`scripts/v1_caustic_bench.py`Caustic benchmark: cold dust sphere at rest (time-symmetric, weak field), evolved with the GR areal/maximal-slicing code (StaticBackground) and with a Newtonian multi-stream shell code on IDENTICAL shells.	80	raw
`scripts/v1_caustic_polar.py`Cross-code check of the caustic benchmark: the same cold Gaussian sphere at rest evolved with pbhgr's polar-areal Einstein-Vlasov code (spherical_ev.py: polar slicing, zero shift, independent implementation) and sampled at equal central…	47	raw
`scripts/v1_ladder.py`V1 validation ladder, steps 1-3 (areal-CMC gauge): flrw homogeneous FLRW to a chosen t/t_H: alpha = 1, A = 1, Kth = -H, particles static in x, P ∝ 1/a idcheck Yoo spherical CMC initial data vs the exact LTB functions (mass and energy…	161	raw
`scripts/v1_static_test.py`Ladder step 4: an Einstein-Vlasov steady state (isotropic polytrope from pbhgr.steady_state) must stay static in the areal gauge with maximal slicing (K = 0).	41	raw
`scripts/verify_bh_convergence.py`Convergence of the horizon-approach case (nu=0.3, flat=3, L_rms=0.5) in time step, grid and particles.	35	raw
`scripts/verify_cold_convergence.py`Cold-limit convergence: nearly cold cloud (L_rms=0.05) at three (K, N) resolutions.	28	raw
`scripts/verify_static.py`Static Einstein-Vlasov benchmark: sampled steady state must remain steady under evolution.	42	raw
`scripts/verify_static_res.py`Static benchmark: does the slow secular drift of max 2m/r shrink with grid resolution / time step?	28	raw
`scripts/warm_summary.py`Summary table of the warm campaign: python3 scripts/warm_summary.py [dir]	28	raw
`scripts/grchombo/build_grchombo_ax102.sh`============================================================================ build_grchombo_ax102.sh — GRChombo + Chombo + GRTresna on Hetzner AX102-1 (AMD Ryzen 9 7950X3D 16C/32T, 128 GB DDR5 ECC, 2x1.92 TB NVMe, Ubuntu 24.04 LTS)…	397	raw
`scripts/grchombo/chk_diag.py`Diagnostics of a GRTeclyn/PBHVlasov checkpoint: per-level min/max of the state, an x-line through the centre on the finest level, coordinate-speed bound of the particle push, and the spherical expansion Theta(r).	111	raw
`scripts/grchombo/ltb_to_grchombo.py`Late-start initial data for the GRChombo PBHCosmo example from the exact LTB solution (e = 0 test, plan 6.12 stage 1).	320	raw
`scripts/grchombo/pbh_analyse.py`Analyse a PBHCosmo (GRChombo) run directory: data/data_out.dat, data/*_lineout.dat, AH stats.	65	raw
`scripts/grchombo/stage1b_params.py`Parameter file for a stage-1b early-start run (Yoo long-wavelength data, seven levels, geodesic phase to 0.5 t_C(0), then the profile-referenced 1+log lapse and the Gamma-driver) for given (mu, e, p).	93	raw
`scripts/grchombo/vlasov_gauge_check.py`Gauge check of the particle push: central density versus the proper time of the core, compared with LTB.	52	raw
`scripts/grchombo/vlasov_ltb_compare.py`Compare a PBHVlasov (GRTeclyn) LTB e = 0 particle run in geodesic slicing with the analytic LTB solution.	72	raw
`scripts/grchombo/vlasov_shell_check.py`Invariant check of the 3D particle run against LTB before the caustic, shell by shell.	45	raw
`scripts/grchombo/vlasov_tau_compare.py`Invariant comparison of the 3D particle run with the 1D Einstein-Vlasov references and LTB: horizon mass M_AH versus the proper time of the matter at the horizon.	73	raw

tests

7 files · 274 lines · pbhgr

Phase 1 pytest suite: FLRW, Schwarzschild vacuum, dust collapse, decay, static solutions.

File	lines
`tests/conftest.py`	16	raw
`tests/test_background.py`	35	raw
`tests/test_decay.py`Proper-time decay of macroparticles, daughter emission, energy bookkeeping, Gamma -> 0.	53	raw
`tests/test_dust_collapse.py`Cold dust collapse (LTB / Oppenheimer-Snyder): every shell is a radial Schwarzschild geodesic of the mass m(r0) enclosed initially, in its own proper time; the outermost shell also follows the exterior coordinate-time law.	65	raw
`tests/test_static_exterior.py`	18	raw
`tests/test_static_solution.py`Known Einstein-Vlasov benchmark: an isotropic polytropic steady state (f = (E0 - e^mu E)_+) sampled into macroparticles must reproduce the analytic metric at t = 0 and remain static.	33	raw
`tests/test_vacuum.py`Schwarzschild vacuum regression: excised interior mass, zero-weight test particles.	54	raw

sphdiag (PBH-VERIFY-01)

6 files · 1 466 lines · pbh_verify_01

Verified diagnostics for a spherical 3+1 slice: matter projections, constraint residuals, Misner–Sharp mass, θ±, apparent-horizon candidates with status flags.

File	lines
`src/sphdiag/__init__.py`sphdiag -- physical diagnostics of spherically symmetric 3+1 slices (PBH-VERIFY-01).	20	raw
`src/sphdiag/diagnose.py`diagnose(): physical diagnostics of a spherically symmetric slice (contract §5-§10).	839	raw
`src/sphdiag/fd.py`Finite-difference machinery for sphdiag (contract §8).	187	raw
`src/sphdiag/matter.py`Matter adapters (contract §4): n-frame projections rho, j_r, S^r_r, S^theta_theta.	152	raw
`src/sphdiag/slice.py`SphericalSlice: container + validation of the 3+1 slice data (contract §2, §3, §8, §9).	176	raw
`src/sphdiag/README.md`sphdiag	92	raw

Running it #

pbhgr

PBHVlasov (GRTeclyn)

PBHCosmo (GRChombo)

scripts

tests

sphdiag (PBH-VERIFY-01)

Running it