Validation plot gallery - progenax — differentiable initial conditions for N-body simulations

A curated visual tour of the physics-validation evidence — one or two headline figures per model family, rendered by the per-suite validation scripts and committed under 50-validation/figures/. The numbers live on the per-suite pages (linked from every caption); this page is for the eyes.

Spatial profiles & velocity DFs¶

Sampled vs analytic Plummer density — the inverse-CDF position sampler against
\rho(r) \propto (1+r^2/a^2)^{-5/2}. Numbers: . — Sampled vs analytic Plummer density — the inverse-CDF position sampler against $\rho(r) \propto (1+r^2/a^2)^{-5/2}$ . Numbers: Plummer equilibrium.

Plummer velocity equilibrium: sampled dispersion against
\sigma_r^2 = GM/(6\sqrt{r^2+a^2}), unscaled Q_{\rm vir} = 0.5.
Numbers: . — Plummer velocity equilibrium: sampled dispersion against $\sigma_r^2 = GM/(6\sqrt{r^2+a^2})$ , unscaled $Q_{\rm vir} = 0.5$ . Numbers: Plummer equilibrium.

The King family across W_0 — concentration c(W_0) against King (1966)
Table II. Numbers: . — The King family across $W_0$ — concentration $c(W_0)$ against King (1966) Table II. Numbers: King profile validation.

King lowered-Maxwellian equilibrium: dispersion falls outward and vanishes at
r_t (cold outskirts). Numbers: . — King lowered-Maxwellian equilibrium: dispersion falls outward and vanishes at $r_t$ (cold outskirts). Numbers: King profile validation.

The EFF power-law-halo family across \gamma (\gamma = 5 is Plummer).
Numbers: . — The EFF power-law-halo family across $\gamma$ ( $\gamma = 5$ is Plummer). Numbers: EFF profile validation.

Michie–King anisotropy: realised \beta(r) rises outward and sits below the
pure Osipkov–Merritt ceiling. Numbers: . — Michie–King anisotropy: realised $\beta(r)$ rises outward and sits below the pure Osipkov–Merritt ceiling. Numbers: Michie-King anisotropy validation.

Initial mass functions¶

Salpeter / Kroupa / Chabrier / Maschberger sampled PDFs against their analytic
forms. Numbers: . — Salpeter / Kroupa / Chabrier / Maschberger sampled PDFs against their analytic forms. Numbers: IMF statistics validation.

The environment-dependent high-mass slope \alpha_3(\rho_{\rm cl}, [\mathrm{Fe/H}])
— the Marks+2012 fundamental plane with the GC anchors.
Numbers: . — The environment-dependent high-mass slope $\alpha_3(\rho_{\rm cl}, [\mathrm{Fe/H}])$ — the Marks+2012 fundamental plane with the GC anchors. Numbers: IMF statistics validation.

Binary populations¶

Moe & Di Stefano mass-ratio statistics: sampled g(q \mid M_1, P) with the
twin excess. Numbers: . — Moe & Di Stefano mass-ratio statistics: sampled $g(q \mid M_1, P)$ with the twin excess. Numbers: Binary-aware IMF validation.

The “confidently wrong” headline: a binary-blind IMF fit biases the recovered
slope with shrinking error bars; the binary-aware fit recovers the truth.
Numbers: . — The “confidently wrong” headline: a binary-blind IMF fit biases the recovered slope with shrinking error bars; the binary-aware fit recovers the truth. Numbers: Binary-aware IMF validation.

Multi-component engines¶

Engine A multimass equilibrium: per-component Q_j = 0.5 unscaled across the
mass spectrum. Numbers: . — Engine A multimass equilibrium: per-component $Q_j = 0.5$ unscaled across the mass spectrum. Numbers: Two-component populations (superseded).

The honest sub-equipartition physics: \sigma(m) saturates at low mass
(escape-speed ceiling) and follows m^{-1/2} in the deep-well limit, with the
DERIVED m_{\rm eq} crossover. Numbers: . — The honest sub-equipartition physics: $\sigma(m)$ saturates at low mass (escape-speed ceiling) and follows $m^{-1/2}$ in the deep-well limit, with the DERIVED $m_{\rm eq}$ crossover. Numbers: Two-component populations (superseded).

Engine B density-defined equilibria: prescribed component densities, the
shared-\Psi Eddington DFs, and the realizability margin.
Numbers: . — Engine B density-defined equilibria: prescribed component densities, the shared- $\Psi$ Eddington DFs, and the realizability margin. Numbers: Multi-component Eddington equilibria (Engine B).

Tidal physics & diagnostics¶

The Jacobi radius against the directly-computed L1 Lagrange distance.
Numbers: . — The Jacobi radius against the directly-computed L1 Lagrange distance. Numbers: Tidal truncation validation.

The CW04 (\bar m, \bar s) plane: substructured, uniform, and centrally
concentrated configurations separate cleanly.
Numbers: . — The CW04 $(\bar m, \bar s)$ plane: substructured, uniform, and centrally concentrated configurations separate cleanly. Numbers: Substructure (CW04 Q) validation.

\Lambda_{\rm MSR} across segregation regimes.
Numbers: . — $\Lambda_{\rm MSR}$ across segregation regimes. Numbers: Mass segregation validation.

Stellar relations & the gradient gate¶

The Tout+1996 ZAMS in the HR diagram (75/75 coefficients PDF-verified).
Numbers: . — The Tout+1996 ZAMS in the HR diagram (75/75 coefficients PDF-verified). Numbers: Test Dashboard.

The 98-case gradient gate: 97 clean, 1 pinned known-limitation, 0 hazards.
Numbers: . — The 98-case gradient gate: 97 clean, 1 pinned known-limitation, 0 hazards. Numbers: Differentiability gradient audit.

Removed suites (history)¶

The fractal-displacement-field generator and the legacy bm19_fdf_suite plot scripts were removed in the 2026-06 clean-room rewrite; the surviving substructure tooling is the CW04 $Q$ diagnostic (Substructure (CW04 Q) validation). The experimental gravoturb acceptance suite prints its numbers (AC1–AC17) rather than committing figures — run PYTHONPATH=src:src/experimental python -m gravoturb.validation.acceptance and see src/experimental/gravoturb/VALIDATION_SUMMARY.md. Publication figures for that subsystem await the jaxstroviz port.

Plot regeneration¶

Figures are produced by the per-suite validation scripts (scripts/validate_*.py; scripts/release_gate.sh runs all 24 and refreshes validation_runs.json). The committed copies under 50-validation/figures/ are the deliberate exception to the otherwise-gitignored validation/plots/. Methodology: Validation methodology.