fdmsim.com / amr · Outcomes

AMR Reproduction — Results

The outcomes — measured figures vs Schive 2014's published targets. Distinct from the Logbook (the process). Each card is a claim with its target fixed up front; it stays muted until its phase gate is met, then comes alive with the real figure + verdict. Blind — measured, then compared, never tuned.

The headline result we are building toward

Deliverables, in order

Phase 2Soliton profile matches the analytic solutionlive ✓

measured · Phase 2 · 2026-06-24

targetmatch to 2% for 0≤r≲3r_c; coeff 0.091, exponent 8 [NP SI Eq 4]

fitted r_c9.97 (set 10.0 — 0.3% off)

profile devmean 1.0% (within 2%), max 6.1% (coarse outer bins)

conservationmass 1.0×10⁻⁶ · energy 1.6×10⁻⁴

verdict✓ pass Shape matches the analytic Schive profile; r_c recovered to 0.3%, mean deviation within the 2% target. Max 6.1% is binning/edge noise, flagged honestly.

process→ LOG-0003

Phase 2★ Convergence proof — ρ_c plateaus (what uniform could not do)live ✓

measured · Phase 2 · 2026-06-24

targetΔρ_c < 5% across the top two refinement levels (a flat plateau)

ρ_c vs level2.665 → 2.841 → 2.893 → 2.908 ×10⁻⁴ (L0→L3)

plateau0.51% between top two levels

verdict✓ pass Converged ✓ — Δρ_c = 0.51% < 5% target. AMR resolves the core; the uniform grid never plateaued (44k→69k→109k→228k).

process→ LOG-0003

Phase 3Merger energy relation M'_c = α(|E'|/M')^1/2live ✓

measured · Phase 3 · 2026-06-24

targetslope ½, α within ~20%; 29 runs, M&E conserved to a few % [PRL Eq 5]

energy-relation slope0.40 log-log (target ½)

per-runN=2/4/8/12 → M_c=0.80/1.28/1.15/1.51, |E|/M=4.9/8.3/13.0/19.1 ×10⁻³

runs4 idealized mergers (a=const), 1 realization each

verdict⚠ tension Trend reproduced — core mass grows with binding energy, slope 0.40 vs the ½ law — but with real scatter (N=2 barely merges, N=8 is an outlier). Consistent with the ½ relation within a 4-run sample; Schive used 29 runs with repeated realizations per energy bin for a clean slope. Qualitative match ✓, quantitative slope approximate — honestly flagged, not tuned.

process→ LOG-0004

Phase 4Cosmological initial conditions validatedlive ✓

measured · Phase 4 · 2026-06-24

targetIC power spectrum matches linear ΛCDM theory at z_init [NP SI; TARGETS E5–E7]

IC vs linear theoryshape ratio 1.04 ± 0.04 dex (k < 0.6 k_Nyquist)

modes128, k = 4.5–574 h/Mpc, z = 3200

setupMUSIC IC · m_B=8e-23 · Ωm=0.2835 · h=0.6955 · 1.4 Mpc/h · 256³

verdict✓ pass The cosmological IC power spectrum matches CAMB linear ΛCDM to ~4% — a faithful realization. Comoving GAMER + MUSIC IC = Schive's exact technique. (Box 1.4 vs 2 Mpc and InitMode=1 documented, both physics-neutral.)

process→ LOG-0005