# Molecular-cloud Jeans: standalone scientific replay This package runs newly written Python for a periodic isothermal Euler–Poisson gas patch and a separate strictly linear uniform-field MHD–gravity mode. It also reads a pinned native Athena++ Jeans input and integrates its equivalent linear Fourier mode. No website, compiled Athena, cloud simulation archive, sink or star-particle model is required. Extract into an empty directory and enter `molecular-cloud-jeans-science`. Install ordinary dependencies once if needed: ```sh python3 -m venv .venv .venv/bin/python -m pip install -r requirements.txt PYTHONDONTWRITEBYTECODE=1 .venv/bin/python replay.py --out-dir rerun ``` After dependency installation the nine-subprocess replay is offline. It verifies complete file bytes/SHA first, then actually recomputes the PDE/reference tests, the sampled bounded parameter rectangle, three saved magnetic-mode records, native-input equivalent mode, SI unit example and scientific figure. It additionally recomputes every specified article example, all eleven complete finite-volume comparison fields, eighty independent SciPy matrix-exponential states, the three historical magnetic records and nine production-step magnetic fields. A receipt is written only after success. Hash verification alone is not a numerical rerun. The environment used here is Python3.9.6, NumPy2.0.2, SciPy1.13.1, Matplotlib3.9.4. ## What the models mean The nonlinear gas calculation is two-dimensional with an invariant third direction, volume density and mass per unit invariant depth. It uses periodic boundaries and solves Poisson only for density minus its instantaneous mean; the uniform Fourier component has zero potential. It is not an isolated spherical cloud. Isothermal pressure closes the mass/momentum equations by prescribing constant sound speed; thermal radiation is not solved. The smooth barotropic energy is a numerical diagnostic, not a measured radiative energy budget. The proposed nonlinear operating rectangle is Jeans number0.7–2, initial crossed-mode amplitude0.05–0.25 and time0–2 at64×64 cells. Ten corners/interiors/subcell translations are compared with128×128, half time steps and an independent overintegrated pseudospectral reference. They are sampled evidence, not a mathematical uniform-error theorem. A separately fixed case at J1.5/amplitude0.2 is checked through time2.5. Do not extend those accuracy claims to the later resolution stress test. The independent reference evaluates rational momentum fluxes and gravity products on an oversampled periodic grid before projecting to a fixed Fourier bandwidth. A 2/3 output mask alone is not an alias-free Galerkin calculation. All ten original support cases plus the fixed longer case separately compare2×/4× quadrature,64/128retained grids and half time steps. A near-zero-density analytic flux counterexample demonstrates the old assumption’s failure. The original results/source and the correction context remain in failures/ and REFERENCE-SPACE-CORRECTION.md. No original case or hydro acceptance threshold was relaxed. The `boundedCollapse` resolution-stress record demonstrates the8-cell local thermal-Jeans stopping rule. The code rejects a candidate state below that rule and retains the last accepted field. The late stress state has not inherited the early-window convergence evidence. A Jeans-cell indicator alone is not sufficient proof of accurate fragmentation. The16-cell underresolved initial attempt and the original nonmonotonic32-cell amplitude result are retained. The latter shows a small coarse-error cancellation, not superior coarse resolution. The second raw reference file also preserves the comparison before converting spectral point values to finite-volume cell averages; the final calculation compares like representations. Magnetism is a separate linear calculation with six coupled Fourier variables: density, three velocities and two transverse field components. DeltaBx is zero for a wavevector along x. Thermal pressure, magnetic tension/pressure, induction, continuity and perturbed gravity all enter. The characteristic quartic and Alfvén pair are checked independently. Field direction matters: along-field compression remains Jeans-unstable even in a strong field; exact perpendicular compression has a different threshold. No isotropic effective-sound-speed substitution is used. Saved fields and plots come from the same six-variable state. Relative perturbations are capped0.15. No nonlinear magnetic support, driven turbulence, sinks, feedback, stellar mass function or actual sky image is computed. ## Original official input and rights The `official/` files are complete small Athena++ Jeans source/input/regression members at commit053bc738d5c85dac717326b4338b34c7db4e715d, distributed under their original BSD3license. The independent native-input calculation derives the rotated wavevector from the rectangular box dimensions. It does not compile Athena or run its3D regression. The source’s extra amplitude-squared seed is explicitly outside the first-order analytic comparison. Both the native stable input and the unstable regression override are identified in the fresh output. New Python and generated controlled fixtures use LICENSE-code.txt. The source papers by Chandrasekhar–Fermi1953, Federrath–Klessen2012v1 and Guszejnov et al.2020v1 are linked in SOURCE-NOTICES.txt, not redistributed. Their PDF compilation dates differ from their version-submission stamps; the research cache freezes the received bytes/SHA and uses the named versions. The original Truelove1997Letter was not obtained: ADS returned403and the publisher returned an HTML bot challenge, not a PDF. No challenge was solved. We do not claim to have reproduced that paper or certified a four-cell criterion. Our8-cell rule is explicitly a conservative numerical stopping indicator combined with measured convergence. No observational molecular-cloud cube or real IMF inference is present. The native benchmark and our controlled numerical states are labeled as such. ## Production magnetic time-step correction The original 0.01-step magnetic benchmark is preserved. An 80-state independent matrix-exponential comparison found a largest component error of 1.5968667e-9, exceeding the unchanged 1e-9 production threshold. Refinement to 0.0025 reduced that maximum to 6.1588e-12; nine complete physical fields at the production step are regenerated too. The initial failed log and refinement table remain in failures/ and reference/. This tests integration of the declared linear equations, not physical nonlinear MHD accuracy. The public archive contains numerical Python and authorized small official source members only. It contains no browser Engine, app TypeScript, paper PDF, large cloud simulation or external-tool binary. File hashes verify provenance before all nine commands actually compute fresh outputs. The website reads its own separately validated numerical solver; it does not replay the comparison fixture as animation.