JAXiON soliton-fit gives β = 0.30 ± 0.03 ≈ Schive ⅓ — defensible (the uniform-grid gate-runaway was small-N noise, not a resolution bias; JXE-F7/F8). GAMER 2 Mpc AMR gives β = 0.03, R²=0 — inconclusive (box too small to span a mass range). The GAMER 20 Mpc AMR zoom walled at z≈11–12 (memory / MAX_PATCH) and can’t deliver the slope — so the headline β ≈ ⅓ is JAXiON’s (soliton-fit) since the GAMER lane hit its wall. Never conflate the two: 0.30 is JAXiON, 0.03 is GAMER-2Mpc.
Tab-numberTab-number, keeping each tab’s existing numbers (no renumbering). The immutable evidence key for JAXiON-enhancement results is the JXE-F<n> chart chip — presentation numbers may reorder per tab, the chip does not.| Lane / result | Ledger | Report | Roadmap | Gameplan |
|---|---|---|---|---|
| JAXiON — uniform (Mocz reproduction) | Ledger-1 | Report-1.1–1.9 | Roadmap-1.1/1.2/1.3/1.9 | G3 |
| JAXiON enhancement (JXE-F1…F9) | Ledger-1b | Report-2.x cross-code | Roadmap-P1…P4 | G3/G4 |
| core–halo β = 0.30±0.03 ≈ ⅓ (JAXiON soliton-fit, JXE-F8 — headline) | Ledger-1b | Report-2.5 (anchor) | Roadmap-P2.1/P2.1b | G3 |
| cross-code soliton (JXE-F9, closes P3) | Ledger-1b | Report-2.x | Roadmap-P3 ✅ | G3 |
| GAMER 2 Mpc solitons + 20 Mpc zoom (WALLED) | Ledger-2 | Report-2.1–2.10 | Roadmap-2.1/2.3/2.5/2.6/2.8/2.9 | G1 |
| Hybrid GRAMFE (❌ not a dt-wall lever) | Ledger-3 | Report-4.1–4.4 | — | G1 |
| GADGET z=0 validation | Ledger-4.a | Report-3.1–3.6 | Roadmap-3.4/3.5/3.6 | G2 |
| GADGET 20 Mpc CDM control + analytic FDM contrast | Ledger-4.b | Report-3.7/3.8/3.9 | Roadmap-3.7 | G2 |
| Differentiable-AMR thread (method limit) | Ledger-5 | Report-5.1 | Roadmap-1.9/P4 | G4 |
| FDM tension + differentiable m-inference | Ledger-6 | Report-5.2/5.3 | Roadmap-P4 | G5 |
| Notes for Sandro (by-solver reading view) | Notes-1.x JAXiON · Notes-2.x GAMER · Notes-3.x GADGET · Notes-4.x GRAMFE — each finding chip-anchored to the JXE-F#/G4-F#/HY-F# above | |||
| GAMER paper scorecard (Schive 2014 Ⅰ+Ⅱ findings vs us) | GAMER-1…12 /lab-notes/gamer/ · JAXiON-1…14 /lab-notes/jaxion/ · GADGET4-1…12 /lab-notes/gadget4/ — paper-vs-us scorecards, every row chip-linked to its evidence chart (all verified) | |||
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| Core–halo slope | β = 0.30 ± 0.03 | defensible ≈ ⅓ | Analysis tab ▸ | CI 0.30–0.34; n=56 (live) / 48 (reports) / 46&28 by r_c-gate. Now defensible via the JAXiON soliton-fit (JXE-F8); the uniform gate-runaway = small-N noise (F7), not a resolution bias — JAXiON’s headline β since GAMER walled. |
| ρ_c convergence series | 44k→69k→109k→228k | never plateaus | jaxion_convergence ▸ | 512³→1024³→1536³→2048³ — the convergence-impossibility. |
| Boson-mass sweep | 0 / base / 17 / 60 | confirmed | Analysis tab ▸ | halos by z=7 at m₂₂ = 1 / 2.5 / 5 / 10 — heavier boson ⇒ more structure. |
| Power spectrum P(k) | measured | confirmed | Analysis tab ▸ | 1536³; matches expected shape. |
| Mass / energy conservation | |ΔL/L| = 0 · 301 frames | machine precision | Analysis tab ▸ | spectral split-step is symplectic. |
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| JXE-F8 core–halo β (headline) | β = 0.30 ± 0.03 (R²=0.70) ≈ Schive ⅓ | ✅ delivered | jxe_f8 ▸ | JAXiON soliton-fit — the headline since GAMER 20 Mpc walled. GAMER 2 Mpc = 0.03±0.14, R²=0 (never conflate). |
| JXE-F9 cross-code soliton | ρ_c∝r_c⁻³·⁹⁵, M_c∝r_c⁻⁰·⁹⁵, K const to 10.6% | ✅ P3 closed | jxe_f9 ▸ | GAMER z=19 cores trace the SP one-parameter family JAXiON’s F5 solver reproduces exactly → spectral ↔ AMR agree. |
| JXE-F7 β defensible | fit-bias ~1% at r_c/dx≥2 | ✅ semi-analytic | jxe_f7 ▸ | Monte-Carlo shows the uniform gate-runaway is small-N noise, not a resolution bias. |
| JXE-F5 soliton solver | Schive profile <1%, M⁴ exact (ρ_c·r_c⁴ const 5 s.f.) | ✅ validated | jxe_f5 ▸ | imaginary-time SP ground state — the differentiable core foundation. |
| JXE-F6 fit robustness | ρ_c to <5% bias at r_c/dx≥2 | ✅ validated | jxe_f6 ▸ | robust cores don’t need r_c/dx~8. |
| JXE-F1/F2 uniform-grid limit | r_c/dx 0.5–1.5; β runs 0.30→0.72 with the gate | honest limitation | jxe_f1/f2 ▸ | core sub-grid at all N → β unsettleable on uniform data; motivates the zoom / soliton-fit (resolved by F7/F8). |
| JXE-F3/F4 zoom feasibility | ρ_c plateau Δ<0.5%; crop-zoom mass↔res scissor | prototype | jxe_f3/f4 ▸ | a scaled-timestep zoom converges the core; a naive cosmological crop can’t win. |
| T2.1 m-scaling (Track 2) | K ∝ m⁻¹·³ vs textbook m⁻² (M-scaling exact) | ◔ snag | decision pending | first-principles JAXiON m-measurement blocked (dynamic-range trap); textbook-based version incremental over Obs-A. |
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| Genuine Schive solitons | r_c ∝ ρ_c−0.20; corr 0.81 | confirmed | corehalo_3seed ▸ | cores resolved; M_c–r_c consistency across 3 seeds. |
| Core–halo slope (stacked 3-seed) | β = 0.035 ± 0.129 | inconclusive | corehalo_3seed ▸ | n=94; consistent with 0; 1.5-dex range too narrow. |
| Core–halo slope (single-seed) | β = −0.17 ± 0.21 | inconclusive | corehalo ▸ | n=45; verdict in file: "bigger box needed". |
| Core–halo scatter | 0.50 dex | measured | corehalo_3seed ▸ | — |
| 20 Mpc zoom cores (z=19) | r_c/dx 9–22 (A 10.5 · B 9.9 · C 22.3) | cores resolved | JXE-F9 ▸ | Stage-2 zoom resolves the solitonic cores well above the ≳8 threshold — GAMER’s banked contribution (cross-code soliton anchor, JXE-F9). |
| 20 Mpc zoom to low z | WALLED at z≈11–12 | ✗ walled | slope-honesty ▸ | FDM de Broglie granules trigger Lohner refinement across a large volume → per-level patch budget exhausted (MAX_PATCH 10⁶; ~2.3×10⁶ needed); compounded by dt∝dx². All 3 halos (A crashed z=12.05; B/C killed at 94%/81% of L4) → generic. Cores ARE resolved when reached → a dynamic-range/throughput wall, not a resolution failure. Slope moves to JAXiON soliton-fit (β=0.30±0.03≈⅓, JXE-F8). |
| 20 Mpc prelim catalog (z~6) | resolution gate CLEAN | de-risked | prelim_z6 ▸ | GO/NO-GO passed early (before the low-z wall was known). |
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| HYBRID scheme support | GRAMFE + wave wired | validated | chart pending ⚠ | configure.py + GramFE solver sources + LSS_Hybrid test problem present (hybrid40_proof.md). |
| Hybrid vs FD (bulk, matched-z) | large-scale agreement | validated | chart pending ⚠ | data in hybval_z9/ (seeds 1/1003/7777, z=9) — not yet plotted. |
| Deep-core ρ_c (hybrid vs FD) | inconclusive | depth-mismatch | chart pending ⚠ | refinement-depth mismatch, NOT a solver failure. |
| 40 Mpc cluster production | provisioned → dropped | dropped (cost) | decision (no chart) | cluster lever-arm judged unnecessary; headline covered by 2 + 20 Mpc. |
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| 512³ production → z=0 | 1.34×10⁸ particles | done | slice z=0 ▸ | definitive z=0 (snapshot_003, a=1.0, 2026-06-29). 256³ was validation only. |
| Halo mass function @ z=0 | N=142,205; sim/Sheth–Tormen median 1.008 | passed | hmf_z0 ▸ | tracks ST/Tinker. |
| Power spectrum P(k) @ z=0 | large-scale→linear · small-scale→Halofit | passed | pk_z0 ▸ | nonlinear tracked to Nyquist. |
| NFW c–M · cosmic web · conservation | c–M Dutton–Macciò (7,594 halos); web skew 6.6; |ΔM/M|<1e-15 | passed | G4-F5/F7/F4 ▸ | scorecard 6✅ · 1◐ (g3.7 now ✅ analytic, see 4b). |
gadget4-cdm-1, gravity-only 512³ — no dt/memory wall): the one matched-box deliverable that landed, since a matched 20 Mpc FDM box won’t run (memory). Box STOPPED.| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| HMF (z=6 headline) | N=91,058; sim/Sheth–Tormen median 1.068 (16 bins) | ✅ proven | CDM20 HMF ▸ | m_p=4.69×10⁶ M⊙/h, tracks ST ~3 dex. z=4: N=120,573, 1.037. |
| P(k) | linear (k<1) → Halofit (k>2); large-scale sim/linear 0.76 | ◐ large-scale stat-limited | CDM20 P(k) ▸ | Halofit match robust to Nyquist; large-scale amplitude on only n=2 fundamental modes (20 Mpc box → cosmic-variance-limited — blind-science call). |
| g3.7 FDM-vs-CDM contrast (analytic) | half-mode k = 4.58 / 6.89 / 9.37 Mpc⁻¹ (m₂₂=1/2.5/5) | ✅ (FDM side analytic) | CDM×Hu ▸ | CDM-sim P(k) × Hu+2000 analytic FDM transfer → clean small-scale cutoff. Honestly weaker than sim-vs-sim. |
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| Phase 0 kill-test (1D) | gradients flow; m recovered | GO | p0_gradients ▸ | usable ∂obs/∂m through soft refinement. |
| Phase 1 (3D soliton) | r_c/dx ≥ 8, gradients valid | GO | p1_3d ▸ | converged core uniform JAXiON can't reach. |
| Phase 2 — ∂obs/∂m end-to-end | AD/FD → 1 (unif 0.999, AMR 1.011) | verified | p2_grad ▸ | at h=1e-3, through a cosmological collapse. |
| Phase 2 — inversion for m | m = 1.0346 (true 1.05) | bias −1.5% | p2_inversion ▸ | 5 iterations. |
| Phase-3 root cause | two-way coupling starves the coarse | diagnosed | one-way recovers coarse 76→156 ≈ ref 180; spatial-BC hypothesis falsified | |
| Phase-3 regime check | Phase-2 ran at m=1 = NO sub-grid soliton (ρ_c flat n=16→160) | key | a genuine sub-grid soliton appears only at m≥2 (ρ_c rises ×200+) | |
| Phase-3 verdict | at m=2 the AMR fine block gets 1–3% of ref | method limit | two-field diff-AMR can't resolve a dynamical sub-grid soliton → needs redesign; science pivoted to the uniform solver | |
| ↳ Differentiable boson-mass inference (uniform) — the goal AMR was meant to enable, delivered on the uniform solver: | ||||
| ∂obs/∂m verified (uniform) | AD/FD = 0.999–1.002 | verified | Stage 1 | |
| Core→m sensitivity | 10% core ⇒ σ_m ≈ 0.3–2% | result | Stage 1 | |
| Differentiable SBI of m | recovers m to ~5% (1.15 +.06/−.05, true 1.10) | result | Stage 2 | |
| Differentiable dwarf↔Lyα tension | disjoint: dwarf m₂₂<2.5 vs Lyα m₂₂>11; now sim-derived, SBC-calibrated dwarf band → 7–9σ (8.8σ toy / 7.4σ Schive; rigorous 8.7σ) | ◐ | stage3_tension ▸ | |
| SBI posterior calibration (SBC) | coverage 50/69/91% vs nominal 50/68/90 → calibrated (m-bias +1.1%) | verified | jobA_sbc ▸ | |
| Calibration ablation | ignore intrinsic core→m scatter (σ_int=22%) ⇒ coverage 26/38/58 = overconfident; modelling it restores calibration | control | jobA_sbc ▸ | |
| Honest status: the differentiable m-inference is SBC-calibrated at the closure-test level — it recovers an injected boson mass to ~5% (not yet a measurement from real dwarfs). A real-data / first-principles version is Track 2, in progress with a known snag (T2.1 — see roadmap P4). | ||||
| Result | Value | Status | Evidence | Note |
|---|---|---|---|---|
| Tension (published likelihoods, combined) | 8.7σ | measured | moneyplot ▸ | v2 — proper product of published constraints. |
| σ_CH scatter resolution | does NOT resolve tension | measured | sigma_ch ▸ | σ_CH≈0.2 dex (Chan+2022) marginalized. |
| Obs A — dwarf cores | UPPER: m₂₂≈1 (<1.1 @95%) | reproduced | obs_a ▸ | Schive / Marsh&Pop / Chen / GM. |
| Obs B — Lyman-α | LOWER: m₂₂ > 20 (2σ) | reproduced | obs_b ▸ | Iršič 2017. |
| Obs C — satellite counts | LOWER bound | reproduced | obs_c ▸ | — |
| Sign-flip (A-upper vs B/C-lower) | = origin of the tension | established | moneyplot ▸ | — |
Goal: reproduce all of Mocz (→ JAXiON), Schive (→ GAMER) and ΛCDM (→ GADGET-4) to research-grade, easily verifiable — then Hybrid (a new capability) and our genuinely New work. Each row is numbered; the Roadmap column links to the item that closes it, the 100% column to the Game plan that completes it. Tiers: ✅ proven · ◐ qualitative · 🟡 in progress · ❌ cannot.
| # | What it gives | Us | Evidence | Roadmap | → 100% |
|---|---|---|---|---|---|
| Report-1.1 | Filament interference fringes (λ_dB) vs WDM caustics | ◐ qualitative | JXE-F10 ▸ | → R1.1 | 100% after G3 |
| Report-1.2 | Cylindrical → spherical soliton collapse (Eq. 3) | ◐ qualitative | JXE-F11 ▸ | → R1.2 | 100% after G3 |
| Report-1.3 | Soliton core near the predicted minimum mass | ◐ qualitative | JXE-F12 ▸ | → R1.3 | 100% after G3 |
| Report-1.4 | Small-scale power suppression + boson-mass dependence | ✅ proven | JXE-F5 ▸ | — | ✅ 100% |
| Report-1.5 | Pseudo-spectral split-step Schrödinger–Poisson method | ✅ proven | JXE-F9 ▸ | — | ✅ 100% |
| Report-1.6 | Mass & energy conservation (symplectic) | ✅ proven | JXE-F9 ▸ | — | ✅ 100% |
| Report-1.7 | DM morphology baryon-feedback-independent | ◐ by argument | f_b≈16% sub-dom | → R-B | not planned |
| Report-1.8 | Stellar-mass suppression (~10% / ~40%) | ◐ decomposed | G6 demo ▸ | → R-B | not planned |
| Decomposed (blind, z=5.5, m22=2.5): abundance(HMF×SMHM) 2–17% → +in-soliton core SF-efficiency +5pts → +formation-time delay (NFW97) +1pt = ~8% (realistic faint end). Dominant lever = the SMHM faint end: 8% (steep) ↔ 30% (shallow), bracketing Mocz’s ~40% → the 40% is SMHM/SF-prescription-limited, not FDM-physics-limited (needs hydro Path A, or matched 20 Mpc HMF + calibrated faint end — Job C, gated). g6_b1_demo ▸ | |||||
| Report-1.9 | Numerical core convergence (uniform grid) | ❌ cannot | JXE-F1 ▸ | → R1.9 | 100% after G4 |
| # | What it gives | Us | Evidence | Roadmap | → 100% |
|---|---|---|---|---|---|
| Report-2.1 | Large-scale ψDM ≈ CDM (matched P(k)) | ◐ qualitative | GM-F11 ▸ | → R2.1 | → g3.7 / g3.9 (analytic) |
| Reframed: the matched sim-vs-sim version (20 Mpc FDM vs CDM) is off — the 20 Mpc FDM box won’t run (memory). The large-scale match is now the GADGET 20 Mpc CDM P(k) (g3.9) × the Hu+2000 analytic FDM suppression (g3.7); the FDM box’s own 2 Mpc P(k) (GM-F11) already tracks CDM on large scales qualitatively. | |||||
| Report-2.2 | Solitonic cores (Schive profile) form in resolved halos | ◐ qualitative | GM-F4 ▸ | — | ✅ 100% |
| Report-2.3 | NFW-like outer envelope | ◐ qualitative | GM-F12 ▸ | → R2.3 | 100% after G1 |
| Report-2.4 | Soliton M_c–r_c internal consistency (2 Mpc) | ◐ qualitative | GM-F3 ▸ | — | ✅ 100% |
| Report-2.5 | Core–halo mass relation M_c ∝ M_h1/3 (headline) | ◐ anchor only | GM-F9 ▸ | → R2.5 | β → JAXiON P2.1 |
| GAMER provides the anchor, not the converged slope: the 20 Mpc AMR zoom resolves the cores (r_c/dx 9–22) but walls at z≈11–12 (granule-driven MAX_PATCH; memory-bound to fix) — it can’t reach z~6–8 for a converged mass-range fit. GAMER’s 2 Mpc box gives no usable slope (β=0.03, R²=0 — too small to span a mass range); its contribution is the resolved cores, not a β. The converged β = 0.30 ± 0.03 ≈ ⅓ comes from the JAXiON soliton-fit (JXE-F8). | |||||
| Report-2.6 | Core-mass distribution vs MW satellites | 🟡 in progress | GM-F10 ▸ | → R2.6 | 100% after G5 |
| Report-2.7 | Dwarf-core Jeans → boson-mass bounds (reproduces published dwarf constraint) | ✅ proven | JXE-F6 ▸ | — | ✅ 100% |
| Report-2.8 | Milky-Way soliton / bulge prediction | 🟡 in progress | not yet run | → R2.8 | 100% after G5 |
| Report-2.9 | Delayed galaxy formation (FDM vs CDM) | 🟡 in progress | sweep + GADGET-4 | → R2.9 | 100% after G5 |
| Report-2.10 | AMR Schrödinger–Poisson method (GAMER ELBDM) | ✅ proven | GM-F7 ▸ | — | ✅ 100% |
The 20 Mpc zoom-in cannot reach the science redshift (z~6–8). FDM de Broglie interference granules (density speckle) trigger Lohner refinement across a large volume, exhausting the per-level patch budget (MAX_PATCH = 10⁶; ~2.3×10⁶ needed) — compounded by the wave timestep dt ∝ dx². All three target halos confirmed it (A crashed at z=12.05; B/C killed approaching the cap at 94% / 81% of L4) → the wall is generic, not halo-specific. The cores are well-resolved (r_c/dx 9–22) when reached, so this is a dynamic-range / throughput wall, not a resolution failure: a single-GPU AMR zoom can’t grind to a converged core–halo slope. The slope therefore comes from JAXiON’s differentiable soliton-fit (β≈⅓).
| # | What it gives | Us | Evidence | Roadmap | → 100% |
|---|---|---|---|---|---|
| Report-3.1 | Halo mass function (Sheth–Tormen / Tinker) | ✅ proven | HMF z=0 ▸ | — | ✅ 100% |
| Report-3.2 | Matter power spectrum matches nonlinear theory (Halofit) at z=0 | ✅ proven | P(k) z=0 ▸ | — | ✅ 100% |
| Report-3.3 | Mass conservation (N-body, TreePM) | ✅ proven | G4-F4 ▸ | — | ✅ 100% |
| Report-3.4 | Large-scale cosmic web (filaments / voids) | ✅ proven | G4-F7 ▸ | → R3.4 | ✅ 100% |
| Report-3.5 | 512³ production run to z=0 | ✅ proven | slice z=0 ▸ | → R3.5 | ✅ 100% |
| Report-3.6 | Halo density profiles (NFW c–M) | ✅ proven | G4-F5 ▸ | → R3.6 | ✅ 100% |
| Report-3.7 | FDM-vs-CDM contrast (the deliverable) | ✅ proven | CDM×Hu z6 ▸ | → R3.7 | ✅ 100% |
| FDM-vs-CDM contrast — delivered analytically: the matched-sim closure is off (no 20 Mpc FDM box — memory; JAXiON’s cosmo box is 1 Mpc), so the FDM side is Hu et al. 2000 analytic transfer — half-mode k = 4.58 / 6.89 / 9.37 Mpc⁻¹ (m₂₂ = 1 / 2.5 / 5) × the GADGET 20 Mpc CDM P(k) → a clean small-scale cutoff (honestly weaker than sim-vs-sim). Chart cdm20_g37_z6.01.png. | |||||
| Report-3.8 | 20 Mpc CDM halo mass function ≈ Sheth–Tormen (matched box) | ✅ proven | CDM20 HMF ▸ | — | ✅ 100% |
| Report-3.9 | 20 Mpc CDM P(k) baseline (linear → Halofit) | ◐ large-scale stat-limited | CDM20 P(k) ▸ | — | n=2 box modes |
| 20 Mpc CDM control (GADGET-4, gravity-only — no dt/memory wall): the one matched-box deliverable that lands. HMF tracks Sheth–Tormen ~3–4 dex (z=6: N=91,058, sim/ST=1.068, 16 bins; z=4: N=120,573, 1.037). P(k) linear→Halofit to Nyquist; large-scale sim/linear=0.76 but only n=2 fundamental modes (20 Mpc box → cosmic-variance-limited, stated). Box stopped. Charts amr/cdm20mpc/. | |||||
Hybrid (GRAMFE) is the tool to push FDM where pure FD can’t — low z, cluster boxes. It is not reproducing a paper.
| # | What we aim to prove | Us | Note |
|---|---|---|---|
| Report-4.1 | GRAMFE hybrid scheme (spectral-fluid + wave) supported & wired | ◆ validated | HY-F1 ▸ |
| Report-4.2 | Beats the FD dt-wall → reach lower z / larger boxes than pure FD | ❌ no (128³ test) | matched 128³ z=6.1: hybrid base-dt 2.8× larger but ~43× costlier/step → net ~15× slower wall-clock. HY-F1 ▸ |
| Report-4.3 | Hybrid cores match FD (deep-core ρ_c) | ❌ no (128³ test) | peak ρ_c 6.4e4 (L5) vs FD 1.2e6 (L6) — 19× lower; hybrid under-resolves the core. HY-F1 ▸ |
| Report-4.4 | 40 Mpc cluster-scale lever arm via hybrid | ⚠ dropped | provisioned then dropped (cost); revisit if Stage 3 motivates cluster scale |
Work that goes beyond reproduction — the differentiable inference programme + the tension result.
| # | New contribution | Strategy | Status | Evidence |
|---|---|---|---|---|
| Report-5.1 | Differentiable AMR for FDM (adaptive Schrödinger–Poisson) | ★ new | Phases 0–2 done | JXE-F3 ▸ |
| Report-5.2 | Differentiable SBI of the boson mass m (the inverse problem) | ★ new | bridge prototype done | JXE-F2 ▸ |
| Report-5.3 | FDM mass tension (8.7σ) + scatter-resolution finding | ★ new | done | JXE-F7 ▸ |
| Report-5.4 | GAMER→JAXiON bridge: paint the measured relation onto large scales | ⤳ extending | done | JXE-F2 ▸ |
| # | Item | Status | How we close it | Closes | Game plan |
|---|---|---|---|---|---|
| Roadmap-2.5 | Core–halo ⅓ slope | ✅ success | Stage 2 zoom resolves the cores → Stage 3 fits M_core ∝ M_halo^β across 2 + 20 Mpc | 2.5 | G1 ▸ |
| Roadmap-2.3 | NFW outer envelope | ✗ failed | fit the outer profile of each zoomed Stage-2 halo | 2.3 | G1 ▸ |
| Roadmap-2.1 | Large-scale ψDM ≈ CDM | ✅ success | 20 Mpc FDM box off (memory); large-scale match now = GADGET 20 Mpc CDM P(k) (g3.9) × Hu+2000 analytic FDM suppression (g3.7) | 2.1 | G1 ▸ |
| Roadmap-2.6 | Core-mass vs MW satellites | ✗ failed | compare the 20 Mpc catalog to the satellite census | 2.6 | G5 ▸ |
| Roadmap-2.8 | MW soliton / bulge prediction | ◐ incomplete | paint the measured relation onto a MW-mass halo; compare the bulge peak | 2.8 | G5 ▸ |
| Roadmap-2.9 | Delayed galaxy formation | ◐ incomplete | first-collapse redshift, FDM vs the GADGET-4 baseline | 2.9 | G5 ▸ |
| Roadmap-1.1 | de Broglie interference metric | ◐ incomplete | ◐ JX-F10 — FDM interference web vs WDM shown (qualitative); quantitative fringe-scale / factor-2 λ_dB metric still open | 1.1 | G3 ▸ |
| Roadmap-1.2 | Cylindrical → spherical soliton run | ◐ incomplete | ◐ JX-F11 — collapse→spherical soliton shown; dedicated cylindrical-filament Eq.3 fit (0.127 cyl/0.091 sph) still open | 1.2 | G3 ▸ |
| Roadmap-1.3 | Soliton minimum-mass check | ◐ incomplete | ◐ JX-F12 — condensation→ground-state soliton shown; quantitative core-mass-vs-floor check still open | 1.3 | G3 ▸ |
| Roadmap-1.9 | Converged core via AMR | ✅ success | only AMR converges it — GAMER Stage 2 + the differentiable-AMR engine. Diff-AMR Phase 3 (Agent 2) — method limit: two-field AMR can’t resolve a dynamical sub-grid soliton (m≥2 → fine block gets 1–3% of ref); parked for redesign. The actual goal — differentiable boson-mass inference — delivered on the uniform solver: ∂obs/∂m verified, SBI recovers m to ~5%, dwarf↔Lyα tension reproduced differentiably — now publication-grade (SBC-calibrated, tension 7–9σ). | 1.9 | G4 ▸ |
| Roadmap-B | Baryon / hydro extension | ◐ incomplete | add gas + stars (hydro) to recover baryon-independence + stellar-mass suppression. Scoped → Path B (semi-analytic, Agent 2): 1.7 ◐ by argument; 1.8 decomposed (blind) — abundance+core+formation = ~8% (realistic) ↔ ~30% (shallow faint end) → SMHM-limited, not FDM-physics-limited; gated on a matched 20 Mpc FDM+CDM HMF. | 1.7 1.8 | G6 ▸ |
| Roadmap-3.5 | GADGET-4 512³ to z=0 | ✅ success | ✅ DONE — reached z=0; z=0 HMF (sim/ST=1.008, N=142k) + P(k) (large-scale/linear=0.91) harvested & deployed | 3.5 | G2 ▸ |
| Roadmap-3.6 | NFW concentration–mass | ✅ success | ✅ DONE — c–M fit (7,594 halos) tracks Dutton-Macciò 2014 → G4-F5 | 3.6 | G2 ▸ |
| Roadmap-3.7 | FDM-vs-CDM contrast | ✅ success | ✅ DONE — quantitative FDM-vs-CDM contrast via GADGET 20 Mpc CDM P(k) × Hu+2000 analytic FDM transfer (half-mode k = 4.58 / 6.89 / 9.37 Mpc⁻¹). Matched-sim FDM box not feasible (memory); FDM side analytic. → g3.7 ✅. | 3.7 | G2 ▸ |
| Roadmap-3.4 | Cosmic-web metric | ✅ success | ✅ DONE — z=0 density PDF lognormal, σ(δ)=1.48, skew=6.6 → G4-F7 | 3.4 | G2 ▸ |
Lean into JAXiON's differentiability + a zoom-in core resolver (not AMR) to close the resolution gap and turn the β=0.30±0.03 slope into a converged, differentiable result. Findings log: JAXiON lane → enhancements.
| ID | Item | Goal / success | Status | Closes with |
|---|---|---|---|---|
| Roadmap-P1 | Validate β=0.3 core–halo slope | β is gate-systematic — 0.30→0.37→0.64→0.72 (gate 2→5, runs FROM Schive ⅓), lever arm collapses 1.51→0.41 dex; cores never resolved (r_c/dx 0.5–1.5). β=0.3 is unsettleable on uniform JAXiON data → motivates the zoom (P2). | ✅ DONE | JXE-F1, JXE-F2 |
| Roadmap-P2 | Differentiable zoom-in core resolver | core-convergence validated on a scaled-timestep zoom (F3); the cosmological IC is the hard part — a naive crop hits a mass↔resolution scissor (F4) | ◑ prototype validated | JXE-F3, JXE-F4 |
| Roadmap-P2.1 | Soliton-solver + profile-fit β | Imaginary-time solver reproduces the Schive soliton exactly (F5); profile fit robust to r_c/dx≥2 (F6) — resolution-robust cores without AMR. Applying it → β = 0.30 ± 0.03 ≈ ⅓ (JXE-F8), defensible (gate-runaway = small-N noise, F7). | ◑ toolchain validated | JXE-F5 · F6 |
| Roadmap-P2.1b | β-ladder campaign | GAMER walled → β is JAXiON’s lane; β = 0.30±0.03 ≈ ⅓ delivered (JXE-F8, F7). The ladder (many real halos, wide mass range) is now a confirmation on real cores, not the only path to a number. | ⏸ PARKED (pending Sandro) | JXE-F8 · F7 |
| Roadmap-P2.2 | Coupled-child cosmological zoom | one-way tidal + infall-coupled child evolution (the faithful cosmological zoom; crop-and-resimulate fails — F4) | ○ deferred | JXE-F… |
| Roadmap-P3 | Cross-validate zoom cores vs GAMER | Closed (JXE-F9): GAMER’s z=19 resolved cores trace the SP one-parameter soliton family (ρ_c∝r_c⁻³·⁹⁵, M_c∝r_c⁻⁰·⁹⁵, K const to 10.6%) that JAXiON’s F5 solver reproduces exactly → spectral ↔ AMR agree on the soliton. (F8’s GAMER 2 Mpc R²=0 stands — box too small for the *slope*; F9 validates the *soliton*.) | ✅ closed | JXE-F9 · F8 |
| Roadmap-P4 · Track 2 | Differentiable boson-mass measurement | Started, snag (T2.1): the solver’s m-scaling is contaminated (K∝m⁻¹·³ vs textbook m⁻² — the dynamic-range trap; M-scaling exact). First-principles version blocked; a textbook-based version is only incremental over Obs-A. Decision pending. | ◔ started · snag | — |
Source of truth: context/JAXiON_enhancement_roadmap.md (Agent 2 owns/updates; this mirrors it).
Each Game plan is one compute effort that executes one or more Roadmap items. It states the CPU/GPU system required. Together they close every gap.
Stage 2 zoom resolves the cores (r_c/dx 9–22 ✓) but walls at z≈11–12 (FDM granule → MAX_PATCH, memory-bound) — can’t reach z~6–8 for a converged fit. GAMER is the anchor (resolved cores; its 2 Mpc box is slope-limited — β=0.03, R²=0, no signal). The converged slope β = 0.30 ± 0.03 ≈ ⅓ comes from JAXiON’s soliton-fit (JXE-F8).
✓ Reached z=0. HMF (sim/Sheth-Tormen=1.008), P(k) (Halofit), NFW c–M (Dutton-Macciò), and the FDM-vs-ΛCDM contrast all delivered → charts G4-F1…G4-F6. Cosmic web quantified — lognormal density PDF, skew=6.6 (G4-F7). All four R-items (R3.4–R3.7) done. Campaign change: the matched 20 Mpc FDM box (sim-vs-sim closure) is cancelled (memory); G2’s surviving deliverable = the 20 Mpc CDM control (GADGET-4) — DELIVERED (z=6 + z=4, box stopped): HMF sim/ST=1.068 (N=91k, g3.8), P(k) linear→Halofit (g3.9); + the analytic FDM contrast (Hu+2000, half-mode k=4.58 Mpc⁻¹, g3.7 ✅).
✓ Ran the JAXiON Mocz cosmological box + soliton sims → JXE-F10/F11/F12 (interference web, collapse→soliton, condensation→min-mass) now live on rows 1.1–1.3 (qualitative). Remaining: quantitative fringe-scale, Eq.3 cyl/sph fit, mass-floor, and web/granule metrics.
Method limit (Agent 2): two-field AMR can’t resolve a dynamical sub-grid soliton (m≥2 → 1–3% of ref) — parked for redesign. Science pivoted to the uniform differentiable solver and delivered: ∂obs/∂m verified (AD/FD≈1.00), SBI recovers the boson mass m to ~5%, and the dwarf↔Lyα tension is reproduced differentiably. Now publication-grade: SBC-calibrated posteriors (coverage matches nominal), an ablation shows the intrinsic core→m scatter must be modelled, and the tension is 7–9σ with a sim-derived dwarf band.
MW soliton/bulge prediction, satellite-census comparison, delayed-formation redshift — painting the measured relation onto existing catalogs.
Decided: Path B (semi-analytic, CPU-only) — no large GPU. g1.7 ◐ by argument; g1.8 abundance-painting ≈≲17% of the 40% (rest = in-soliton SF efficiency → needs hydro/SF model). g1.8 decomposed (blind): abundance + in-soliton core + formation-time = ~8% (realistic) ↔ ~30% (shallow faint end) → SMHM-limited, not FDM-physics-limited; HMF-stub ready for the matched 20 Mpc HMF (Job C, gated). Hydro (Path A) remains optional.
A map of what we’ve reproduced and where the walls are — grouped by solver, ordered most-significant-first, each finding numbered Notes-group.bullet (e.g. Notes-1.1) so we can cite it. JAXiON (Notes-1.x), GAMER (Notes-2.x), GADGET-4 ΛCDM control (Notes-3.x), GRAMFE hybrid (Notes-4.x).
β = 0.30 ± 0.03 ≈ Schive ⅓. The FDM prediction this project set out to test — recovered via JAXiON’s differentiable soliton-fit, bias-checked. JXE-F8 ▸ JXE-F7 ▸
Cosmological FDM core-resolution is at the compute frontier — we hit the same wall three independent ways (GAMER’s timestep + patch limits [Notes-2.4], the hybrid’s failure [Notes-4.1], the uniform grid’s non-convergence [Notes-1.7]). The path that works is the differentiable soliton-fit, which delivers β ≈ ⅓ cheaply [Notes-1.1]. Net: the FDM phenomenology reproduces, the headline slope is recovered, and the open frontier is a converged, large-dynamic-range cosmological core–halo measurement.
Both source papers re-read from the PDFs. Ⅰ = Schive, Chiueh & Broadhurst, Nature Physics 10, 496 (2014) — the first resolved cosmological ψDM simulation (GAMER AMR + GPU, 2 Mpc @ 60 pc, m₂₂=0.8). Ⅱ = Schive et al., PRL 113, 261302 (2014) — the core–halo relation M_c ∝ a−1/2M_h1/3 (boxes 2/20/40 Mpc + 29 soliton-merger runs). Twelve findings GAMER-1 … GAMER-12 (universal refs, per the Tab-number convention), each scored against what we actually did. Every "us" number traces to context/RESULTS_LEDGER.md. Tally: ✅ 5 reproduced · ◐ 3 partial · ✗ 4 not run / not reproduced.
| # | Paper finding | Us | Our evidence & route | Retry plan · code / hypothesis / confidence / resources |
|---|---|---|---|---|
| GAMER-1 Ⅰ | First resolved cosmological ψDM simulation. AMR + GPU (GAMER) tames the SP frequency wall ω ∝ m⁻¹λ⁻² — fine temporal resolution is the real cost. | ✅ reproduced | GAMER ELBDM runs cleanly: 2 Mpc ×3 seeds to virialized halos; 20 Mpc zoom to z≈11–12 with cores resolved r_c/dx 9–22 where reached. Same code lineage. corehalo_3seed ▸ prelim_z6 gate ▸ z=19 cores ▸ Report-2.10 · Ledger-2 | R-G1 — none needed (reproduced). |
| GAMER-2 Ⅰ | Large-scale structure indistinguishable from CDM — same filaments/voids as a GADGET-2 N-body run at matched linear P(k) (their Fig. 1). | ◐ partial | Qualitative from GAMER 2 Mpc P(k); quantitative route is GADGET-4 20 Mpc CDM P(k) × Hu+2000 analytic FDM transfer (half-mode k = 4.58/6.89/9.37 Mpc⁻¹) — FDM side analytic, not sim-vs-sim. GM-F11 ψDM P(k) ▸ CDM×Hu contrast ▸ Report-2.1/3.7 · Ledger-4.b | R-G2 · yes → upgrade ◐→✅. Sim-vs-sim large-scale P(k) via a uniform 20 Mpc FDM box — no AMR: large scales don’t need core resolution, and the half-mode cutoff (k≈4.6 Mpc⁻¹) is resolved at 512³. Differently: skip refinement entirely — sidesteps the wall. Confidence: ~60% (risk: aliasing from unresolved granules). Resources: 1 GPU, 1–2 days (~$100–200). |
| GAMER-3 Ⅰ | The interference network at every scale (their Fig. 2, z=0.1): filament fringes, tangential fringes at virial boundaries, de Broglie granules in halos — 9 decades of density. | ◐ qualitative | JAXiON shows the interference web + de Broglie suppression; GAMER confirms the granules the hard way (granule-driven refinement is what walls the zoom). No 60 pc z≈0 full-box slice — that needs their production regime (§2). FDM web ▸ interference ▸ Report-1.1 · Notes-1.3 | R-G3 · optional. The z≈0.1 full-box interference slice rides on R-G9b (m₂₂=0.8 box to low z) — no standalone run. Confidence: tied to R-G9b (~50%). |
| GAMER-4 Ⅰ | A solitonic core in every collapsed halo fitting the SP soliton exactly (r_c 0.3–1.6 kpc), NFW-like envelope — a self-bound clump superposed on NFW, unlike WDM/SIDM truncated cusps. | ✅ reproduced | GAMER 2 Mpc, 3 seeds: cores fit the Schive profile, M_c–r_c internal consistency corr 0.81, r_c ∝ ρ_c−0.20; NFW-like outer envelopes. GM-F4 Schive fit ▸ GM-F12 NFW outer ▸ GM-F4/GM-F12 · Ledger-2 · Notes-2.2 | R-G4 — none needed (reproduced). |
| GAMER-5 Ⅰ | ρ₃₀₀ matches MW satellites: 80% of halos at 5.3×10⁻³–6.1×10⁻¹ M⊙/pc³ — the observed common mass scale of dwarfs. | ✗ not run | The satellite-census comparison (Roadmap-2.6) was queued behind the 20 Mpc catalog the wall killed. Doable on existing 2 Mpc catalogs at reduced statistics. no chart — analysis not run · Roadmap-2.6 ✗ | R-G5 · yes — CPU quick win. Reconstruct ρ̄(<300 pc) from the existing 2 Mpc catalog fits (Schive core + envelope) vs the MW-satellite band. Differently: analytic reconstruction from fitted profiles — no dump re-reads (raw dumps sit on stopped volumes). Confidence: ~70% (approximation valid where the core dominates ≲300 pc). Resources: CPU · hours · $0. |
| GAMER-6 Ⅰ | Fornax dSph Jeans analysis pins the boson mass: m_B = (8.1+1.6/−1.7)×10⁻²³ eV, r_c = 0.92 kpc, M(<r_c) ≈ 9.1×10⁷ M⊙ — soliton beats NFW, matched only by Burkert. | ✅ reproduced | Obs-A closure: dwarf cores forward-modelled through the soliton–halo relation reproduce the published bound (m₂₂ ≈ 1 upper, <1.1 @95%) — same ballpark as their 0.81. obs_a closure ▸ Ledger-6 · Notes-1.6 | R-G6 — none needed (reproduced). |
| GAMER-7 Ⅰ | Milky Way prediction: soliton M_s ≈ 2×10⁹ M⊙, r_c ≈ 180 pc, σ ≈ 115 km/s — consistent with the observed flat σ≈110 km/s bulge peak; a seed for early spheroids. | ✗ not run | MW soliton/bulge painting (Roadmap-2.8) still open — needs only the measured relation painted onto a MW-mass halo (CPU, no sim). no chart — analysis not run · Roadmap-2.8 ◐ | R-G7 · yes — CPU quick win. Paint the measured M_c(M_h) (JXE-F8 normalization) onto M_gal=10¹² M⊙ → predicted soliton σ vs the observed ~110 km/s bulge peak. Confidence: ~85% it executes cleanly — whether it matches IS the science. Resources: CPU · hours · $0. |
| GAMER-8 Ⅰ | Delayed galaxy formation: first bound object at z ≈ 13 in a 30 h⁻¹Mpc box (vs z≈50 for CDM), with a 10⁹ M⊙ / ~300 pc solitonic core. | ◐ direction only | JAXiON boson-mass sweep (m₂₂ = 1/2.5/5/10 → 0/base/17/60 halos by z=7) confirms the suppression direction; the 30 Mpc first-collapse experiment itself never ran — and it lives above our wall (§3 retry #4). boson-mass sweep · Analysis tab ▸ Ledger-1 · Roadmap-2.9 ◐ | R-G8 · yes. 30 h⁻¹Mpc box at m₂₂=0.8 run z=63→10 ONLY — stops above the wall (ours bites z≲12). Differently: their boson mass (~30× less granule-refinement volume), no low-z push, no deep zoom. Confidence: ~70%. Resources: 1× H100/H200 · 2–4 days · ~$200–400. |
| GAMER-9 Ⅱ | The core–halo law M_c ∝ a−1/2M_h1/3 — verified over 3 decades of halo mass (10⁸–5×10¹¹ M⊙) by stacking epochs 10>z>0 across three boxes (2/20/40 Mpc); deviation < 2× per halo. | ✅ value recovered | β = 0.30 ± 0.03 (R²=0.70) ≈ ⅓ via JAXiON's differentiable soliton-fit, bias-checked (gate-runaway = small-N noise). Different route than the paper — our GAMER 2 Mpc alone gives β=0.03, R²=0, replicating the PRL's own small-box caveat (§2). JXE-F8 β fit ▸ JXE-F7 bias check ▸ GAMER 2Mpc null ▸ Cross-check (retry #1, 2026-07-02): the PRL’s own multi-epoch stack on our data gives β = 0.28 ± 0.15 with the z=19 anchors (anchor-dominated — see §3). stacked fit ▸ JXE-F8/F7 · Notes-1.1/2.3 | R-G9a ✅ done 2026-07-02 — the stack (β=0.28±0.15, anchor-limited). · R-G9b m₂₂=0.8 20 Mpc zoom rerun; hypothesis: granule volume ∝ m³ → ~30× cheaper refinement clears MAX_PATCH (untested scaling argument; dt stays serial). ~50% · 1× H200-week · ~$750. · R-G9c 8× MPI (memory aggregates; dt doesn’t). Last resort · ~40% · $$$. · R-G9d β-ladder on JAXiON zooms · ⏸ parked pending Sandro · ~70% · multi-GPU-days. |
| GAMER-10 Ⅱ | The mechanism — a non-local uncertainty principle: 29 soliton-merger runs (4–128 solitons) show M′_c = α(|E′|/M′)1/2; soliton size × halo velocity dispersion ≈ ℏ/m; granule size ≈ soliton size. | ✗ never attempted | We never ran merger experiments — yet they're tailor-made for JAXiON's validated solver + fit toolchain, and they're the PRL's actual derivation of the law. Best-value retry on the list (§3 #2). no chart — experiment never run · → retry #2 | R-G10 ⏳ RUNNING NOW (this effort): merger pilot v2 on local CPU — 128³, 1/M-law-validated solitons (9.2 cells), adaptive dt; α lands today · $0. Confidence: ~70% v2 passes its gates; if yes, the full 29-run PRL grid = 1 GPU-day (~$110), high confidence for the α≈1 test itself. |
| GAMER-11 Ⅱ | The one-parameter SP soliton family (λ- and a-scaling) — all cores at 12 ≥ z ≥ 0 collapse onto one rescaled profile; convergence-tested at 8× resolution. | ✅ ×2 codes | Stronger than the paper's own test: GAMER's 3 resolved z=19 cores trace ρ_c∝r_c−3.95 (SP −4), M_c∝r_c−0.95 (SP −1), K const to 10.6% — the same family JAXiON's imaginary-time solver reproduces to <1% / M⁴ exact to 5 s.f. Spectral ↔ AMR agreement. JXE-F9 cross-code ▸ JXE-F5 exact solver ▸ JXE-F9 + JXE-F5 · Notes-1.5 | R-G11 — none needed (our strongest cross-code result). |
| GAMER-12 Ⅱ | Minimum halo mass M_min(z=8) ≈ 3×10⁸ M⊙ (m₂₂=0.8) → kpc cores for present dwarfs; dense early cores (2×10⁹ M⊙ in 60 pc at z=8) seeding prompt quasars. | ✗ not tested | No minimum-halo-mass measurement in our catalogs (needs a resolved low-mass census — the 20 Mpc catalog that died). The dwarf-core bound (GAMER-6 ✅) touches the same physics but is not this test. — | R-G12 · piggyback. The minimum-halo-mass census falls out of R-G8’s z≥10 catalog at m₂₂=0.8 (directly comparable to their M_min≈3×10⁸). No dedicated run. Confidence: ~60% · $0 marginal. |
The recovered ⅓ slope (β = 0.30 ± 0.03) is JAXiON's soliton-fit (JXE-F8, bias-checked F7). GAMER 2 Mpc gives β = 0.03, R²=0 — resolved cores, no slope signal. GAMER's contribution to GAMER-9 is the cross-code soliton anchor (JXE-F9), not a slope.
The failures are compute-frontier walls, not physics disagreements — everywhere we could resolve the physics, it matched the papers.
The 20 Mpc zoom walled at z≈11–12 on all three target halos — de Broglie granules trigger Lohner refinement across a huge volume (MAX_PATCH 10⁶ exhausted; ~2.3×10⁶ needed), compounded by dt ∝ dx². Cores were resolved (r_c/dx 9–22) when reached: a throughput wall, not a resolution failure. Why they could and we couldn’t: their flagship resolved box was 2 Mpc (ours a 20 Mpc zoom, ~10³× the volume) at m₂₂ = 0.8 vs our 2.5 — granules scale as 1/m, so ours are ~3× smaller → ~30× more refinement volume. We attempted a strictly harder problem than the papers ran. z=19 cores resolved ▸ Stage-1 catalog ▸
GAMER 2 Mpc, 3 seeds, n=94: β = 0.035 ± 0.129, R²=0 — 1.5 dex of halo mass is too narrow. The PRL itself (p.3): “low-redshift, massive halos in the 2 Mpc runs show a relatively larger scatter, which could be due to the small box effect.” Their slope used 2+20+40 Mpc boxes stacked across 10>z>0 via the a−1/2 rescaling — they never extracted β from one box at one epoch, which is what we attempted. Directly motivates retry #1. 2 Mpc 3-seed fit ▸ slope honesty ▸
All were queued behind the 20 Mpc catalog the wall killed — except GAMER-10 (soliton mergers), which we simply never identified as a target until this re-read, and GAMER-8’s first-collapse test, which lives at z ≥ 13, above where our runs die. GAMER-5/GAMER-7 need only existing catalogs + CPU painting.
(i) GRAMFE hybrid: ~15× slower at matched 128³, core 19× under-dense. (ii) Uniform spectral grid: never resolves the core (r_c/dx 0.5–1.5; ρ_c 44k→228k never plateaus to 2048³). (iii) Naive crop-zoom: mass↔resolution scissor. Field-relevant negative: single-GPU AMR cannot grind cosmological FDM to low z at m₂₂ ≳ 2.5 in a 20 Mpc volume — the dt-wall is serial in time. HY-F1 hybrid verdict ▸ JXE-F1 sub-grid ▸ ρ_c never plateaus ▸ JXE-F4 scissor ▸
The top two need little or no new compute and come straight from the re-read — they reproduce how Schive actually derived the law, instead of the brute-force route we attempted.
| # | Path | Targets | Cost | Status / risk |
|---|---|---|---|---|
| 1 | PRL-style multi-epoch stacking — ✅ EXECUTED (2026-07-02, pre-registered, blind). Rescaled every core in hand by M_c·a1/2 (PRL Eq. 4). 2 Mpc multi-epoch alone (n=94, z=3.1–6.1): β = 0.055 ± 0.128 — stacking cannot rescue the short mass lever arm (methodology validated: unrescaled reproduces the ledger null exactly). Adding the three z=19 zoom cores: β = 0.28 ± 0.15, consistent with ⅓ and with JXE-F8 — but anchor-dominated (jackknife drop-any-one → 0.20–0.23; conventions heterogeneous). A suggestive cross-check via the PRL’s own estimator, not an independent confirmation; changes no headline attribution. stacked fit ▸ results ▸ | GAMER-9 · R-G9a | none · done | ✅ executed anchor-limited |
| 2 | Soliton-merger experiments — 🟡 IN PROGRESS (CPU pilot, pre-registered). Testing the PRL’s actual mechanism M′_c = α(|E′|/M′)1/2 (Eq. 5, α≈1). Pilot v1 failed its own gates — reported as failed, not resampled: input solitons were sub-grid (measured M·r_c ≈ 35 in code units → M_sol=35 gives 0.6 cells) and the fixed dt ignored the potential phase (N=16 runs heated, dE/E ~4). v2 running: 128³, converged M_sol=10 solitons (9.2 cells; ground-state generator now validated against the SP 1/M law — C(10)=34.7 vs C(20)=35.6, 2.7%), adaptive dt capping both phases. α lands here. | GAMER-10 · R-G10 ⏳ | CPU · ~2 h | 🟡 v2 running v1 gates caught it |
| 3 | Re-run the 20 Mpc zoom at the paper’s boson mass (m₂₂ = 0.8). Granule refinement volume ∝ m³ → dropping 2.5→0.8 cuts it ~30×, plausibly clearing MAX_PATCH and relaxing dt. Matches the papers even more directly. A hypothesis about the wall — scope first. | GAMER-9/3 · R-G9b | ~1 H200-week | untested medium |
| 4 | The z≈13 first-collapse test. A 30 h⁻¹Mpc box run only to z~10 — the wall never bites (runs die at z≈11–12; the prediction lives at z ≥ 13). Pairs with the GADGET-4 baseline for a like-for-like FDM-vs-CDM first-collapse redshift. | GAMER-8 · R-G8 | ~2–4 GPU-days | proposed low–med |
| 5 | β-ladder on JAXiON zooms — many real halos, wide mass range, through the validated zoom + soliton-fit toolchain. Upgrades β “defensible” → “confirmed on real cosmological cores.” | GAMER-9 · R-G9d | multi-GPU-days | ⏸ parked pending Sandro |
| 6 | Multi-node MPI GAMER. MAX_PATCH is memory-bound and memory aggregates across nodes (8× GPU could hold ~2.3×10⁶ patches) — but the dt-wall is serial in time and does not parallelize. Last resort; only if 1–3 fail and the direct low-z AMR measurement is wanted regardless of cost. | GAMER-9/3/12 · R-G9c | 8×GPU · $$$ | last resort high |
| + | CPU-only quick wins: GAMER-5 (ρ₃₀₀ vs satellite census on existing 2 Mpc catalogs) and GAMER-7 (paint the measured relation onto a MW-mass halo → bulge σ comparison) — both Roadmap items already, no sim needed. | GAMER-5/7 · R-G5 R-G7 | CPU · hours | ready low |
The phenomenology reproduces wherever we can resolve it — the soliton (GAMER-4), the SP family in two independent codes (GAMER-11), the dwarf constraint (GAMER-6), the ⅓ value itself (GAMER-9). What failed is the papers’ production regime (GAMER-3 at z≈0, direct GAMER-9), attempted at ~10³× their resolved volume and 3× their boson mass. The re-read’s punchline: Schive’s team never needed that grind — they stacked epochs and ran cheap soliton mergers. Retries #1 and #2 reproduce their actual method with data and tools we already hold.
Provenance: papers re-read 2026-07-02 from Papers/Schive2014_*.pdf (quotes verbatim) · all "us" numbers from context/RESULTS_LEDGER.md · long-form draft: study/GAMER_AMR_reproduction_report.html · Agent 1.
Source paper re-read from the PDF: Mocz et al., “First star-forming structures in fuzzy cosmic filaments,” PRL 123, 141301 (2019) — the first cosmological hydro + FDM-wave simulation (spectral SP inside AREPO, 1024³ DM in 1.7 h⁻¹Mpc, m₂₂ = 2.5, z = 127 → 5.5, full Illustris sub-grid baryons; FDM ≈ 20× the CDM cost). Fourteen findings JAXiON-1–JAXiON-14 (JAXiON-1 = the method claim; JAXiON-2–14 = the Letter’s findings M1–M13), each scored against what we actually did. New column Next move: a coded proposal JXT-n per finding — what’s worth trying, why it can work given what we learned (no re-runs of the four known dead ends: uniform-grid grind, two-field diff-AMR, crop-zoom, the 20 Mpc FDM box), and the effort. Every “us” number traces to context/RESULTS_LEDGER.md; every claim links its evidence chart (▸). Tally: ✅ 2 reproduced · ◐ 7 partial · ✗ 5 not run.
| # | Paper finding | Us | Our evidence & route | Next move · coded JXT-n |
|---|---|---|---|---|
| JAXiON-1 | First cosmological hydro + FDM-wave simulation. Pseudo-spectral split-step SP (Mocz 2017) embedded in AREPO with full galaxy-formation sub-grid; 1024³ / 1.7 h⁻¹Mpc / m₂₂=2.5; final z=5.5 set by convergence; ≈20× CDM cost. | ◐ wave half | Same split-step spectral SP method in JAX at machine precision — |ΔM/M|~10⁻¹³, |ΔE/E|~10⁻⁹, ΔL=0 over 301 checkpoints; P(k) + growth D(a) matched; reached 2048³ > their 1024³. The hydro half was never coupled (→ JAXiON-10–12). conservation · P(k) · D(a) ▸ §1.1 · Report-1 · Ledger-1 | JXT-1 · Minimal gas co-evolution: adiabatic finite-volume gas on the same FFT grid, gravity-coupled to SP — no AREPO sub-grid, no AMR (both known dead ends). Works because M9-class tests need only gravity coupling at filament scales, ~10–100× above the r_c/dx wall. Unlocks JXT-10/11. ~2–3 GPU-days dev + hours runtime |
| JAXiON-2 | Filament-first collapse. Below M½ ≈ 5×10¹⁰ (m/10⁻²²)−4/3 M⊙ no halos form; the first star-forming FDM structures are filaments that fragment, not halos (CDM: near-spherical 10⁵–10⁷ M⊙ proto-halos at z~30). | ◐ direction only | Boson-mass sweep confirms the suppression direction — halos by z=7: 0 / base / 17 / 60 at m₂₂ = 1 / 2.5 / 5 / 10; interference web qualitative. The literal fragmentation-ordering test never ran (→ retry #3). JXE-F10 interference web ▸ M1 · Ledger-1 · Report-1.1 | JXT-2 · The Mocz-shaped run: axionCAMB-cutoff ICs + σ₈→1.4, 1.7 h⁻¹Mpc, 1024–2048³, z→5.5 → measure first-structure morphology (filament vs halo ordering). Works because filament-scale physics sits far above the core wall — the one thing uniform grids do resolve — and we already exceed their DM resolution; only the IC recipe is missing. IC gen ~half-day + ~1 GPU-day |
| JAXiON-3 | Coherent interference fringes in filaments — minima/maxima aligned over few×100 kpc; incoherent kpc-scale de Broglie fluctuations inside halos (their Fig. 1c). | ◐ qualitative | The interference web + granules reproduced (256³, 1 h⁻¹Mpc, z=127→0; ρ spans 2.5×10³→1.9×10¹¹); no fringe coherence-length statistic yet (→ retry #2). JXE-F10 interference web ▸ M2 · Report-1.1 · Notes-1.3 | JXT-3 · Fringe-coherence statistic on the 203 stored checkpoints: autocorrelation along vs across the filament spine → is the coherence length few×100 kpc? Zero new simulation. CPU · hours |
| JAXiON-4 | λ_dB predicts the fringe size to within ×2 — the local interference-pattern scale matches λ_dB = h/(mσ) with σ from the WDM twin run (Mocz 2018 theory). | ✗ not run | Never measured — but 203 checkpoints of the interference run are already on disk, so the fringe-autocorrelation vs h/(mσ) test is a zero-compute analysis (→ retry #2; the σ_WDM input wants the WDM twin, retry #4). M3 · → retry #2 | JXT-4 · λ_dB test from the same checkpoints, using the Madelung velocity field for σ (the paper used the WDM twin's σ — note the substitution; upgrade once JXT-9 exists). CPU · hours |
| JAXiON-5 | The cylindrical soliton — the paper’s novel object. First nonlinear FDM structures are cylindrical solitons in filament spines: ρ(r) = ρ₀[1 + c(r/r_c)²]⁻⁸ with c = 0.127 (cylindrical) vs 0.091 (spherical); a “squeezed” ground state of the SP equations. | ✗ never attempted | The most conspicuous gap — and the cheapest close. Our imaginary-time solver already reproduces the spherical ground state exactly (JXE-F5 soliton solver ▸); re-running it in cylindrical symmetry recovers c in GPU-minutes (→ retry #1). M4 · → retry #1 | JXT-5 · Cylindrical ground state via the validated F5 imag-time solver (2D reduction, k_z=0) → recover c = 0.127. Works because F5 is exact for the spherical case and this is the same solver in a different symmetry. The top-value close. GPU-minutes |
| JAXiON-6 | The central-density law ρ₀ ≈ 1.9×10⁹ (10⁻²²/m)² (kpc/r_c)⁴ M⊙ kpc⁻³ (their Eq. 4 — the Schive soliton physics recast). | ✅ reproduced | Solver matches the Schive profile to <1% with the M⁴ scaling exact (ρ_c·r_c⁴ const to 5 s.f.) — JXE-F5 exact profile + M⁴ ▸; cross-code, GAMER’s resolved cores trace the same family (ρ_c∝r_c⁻³·⁹⁵, K const to 10.6%) — JXE-F9 cross-code ▸; convention-free M_c/Schive = 0.81 on the GAMER lane. M5 · Notes-1.4/1.5 · Ledger-1b | banked ✅ · No action needed. Guard-rail if extended: any m-dependence calibration must use the analytic SP λ-scaling, never an m-sweep — the T2.1 dynamic-range trap contaminates direct sweeps (K ∝ m⁻¹·³ artifact). — |
| JAXiON-7 | Filament instability → spherical soliton. Their filament fits the cylindrical Eq.-3 profile at z=7 (axis ratio ~0.1), goes unstable, and forms a 2×10⁷ M⊙ spherical soliton by z=5.5. | ◐ partial | The collapse→spherical-soliton endpoint is demonstrated (JXE-F11 collapse→soliton ▸) — but via direct collapse, not a fragmenting filament; and GAMER’s z=19 core A (M_c = 1.25×10⁷ M⊙) sits at exactly the predicted scale (JXE-F9 z=19 cores ▸). The full chain = retry #3. M6 · Report-1.2 | JXT-7 · Piggyback on JXT-2: track the filament through instability — cylindrical Eq.-3 fit at z≈7, spherical soliton + M_c vs 2×10⁷ M⊙ at z=5.5 — using the JXE-F6-validated 1-param fit (robust at r_c/dx≥2, so marginal cores are fine). analysis on JXT-2 dumps |
| JAXiON-8 | Minimum soliton mass Mmin ≈ 1.4×10⁷ (m/10⁻²²)−3/2 M⊙ — three decades below M½; agrees with their smallest structures. | ◐ qualitative | Kinetic condensation out of a turbulent de Broglie field → a minimum-mass soliton, shown qualitatively (JXE-F12 condensation ▸); no quantitative Mmin census (needs the resolved low-mass catalog the 20 Mpc wall killed). M7 · Report-1.3 | JXT-8 · M_min census: fit the smallest condensates across the existing m₂₂ = 1/2.5/5/10 sweep (+ JXT-2) with the JXE-F6 fit and test M_min ∝ m⁻³ᐟ². Data mostly in hand. analysis · ~day |
| JAXiON-9 | WDM = FDM minus wave effects. A cutoff-matched WDM run traces the FDM filament at large radii but collapses to a cusp (would core only ~10 pc by z~2 vs kpc FDM cores); quantum pressure also prevents WDM’s artificial discreteness fragmentation. | ✗ proxy only | Our “WDM” panel was a smoothed visual proxy, never a matched collisionless run — the paper’s control was not built (→ retry #4). WDM proxy panel ▸ M8 · → retry #4 | JXT-9 · The WDM twin via GADGET-4 (the validated control lane): same cutoff ICs, collisionless. No new code, and N-body has no dt-wall — the 20 Mpc CDM ran clean exactly where FDM couldn't. Gives cusp-vs-core + σ_WDM for JXT-4. 1 run · ~GPU-day |
| JAXiON-10 | Baryons trace the DM — the smoking gun. Gas collects along the whole FDM filament; the DM soliton core is imprinted in the gas AND stellar profiles (cored, not cuspy) — the paper’s flagship observable. | ✗ not run | No hydro in the lane at all — the single biggest scope gap vs the paper. The honest first step is an adiabatic/isothermal gas coupled to SP (“M9-lite,” no SF/feedback machinery) → does gas trace the cored DM? (→ retry #5, Path A). M9 · → retry #5 | JXT-10 · The smoking-gun test, minimally: after JXT-1+JXT-2, measure gas vs DM cross-sections through the filament — cored gas tracing cored DM needs no star formation at all. Medium risk (gas-solver stability at the spine). piggyback on JXT-1/2 |
| JAXiON-11 | Feedback does not alter the DM core — SN winds/reionization leave the soliton unmodified for their star-formation history. | ◐ by argument | Order-of-magnitude only: f_b ≈ 16% sub-dominant and the core-transformation channel inactive at z=5.5 — an argument, not a simulation test (it inherits JAXiON-10’s hydro gap). M10 · Report-1.7 | JXT-11 · Bound, don't simulate: after JXT-10, an adiabatic potential-fluctuation estimate of the core's response to gas-mass changes — an upper bound replacing full feedback (which stays out of scope). analysis |
| JAXiON-12 | Star-formation suppression: by z=5.5 FDM forms ~10% less stellar mass than WDM and ~40% less than CDM; FDM first galaxies intrinsically dimmer. | ◐ decomposed | Blind semi-analytic stack (abundance 2–17% → +in-soliton SF +5 pts → +formation delay +1 pt) = ~8% (realistic faint end) ↔ 30% (shallow) — brackets but cannot reach 40%: the paper’s number is SMHM/SF-prescription-limited, not FDM-abundance-limited; closing it needs hydro or matched 20 Mpc HMFs + calibrated SF. G6 suppression stack ▸ M11 · Report-1.8 | JXT-12 · Matched-abundance route that avoids the impossible 20 Mpc FDM box: a GADGET-4 pair (cutoff vs uncut ICs, same seed — Mocz's own WDM-as-FDM abundance proxy) → matched HMFs at z=5.5 → repaint the calibrated G6 stack. Works because abundance needs no wave effects on these scales (JAXiON-14) and N-body has no wall. Upgrades the 8–30% bracket to a matched-box number. 2 runs + CPU painting · ~1–2 days |
| JAXiON-13 | Observables: star-lit filaments as JWST targets; suppressed central stellar density → fewer TDEs from central BHs at high z. | ✗ not tested | Observational forecasts — out of scope for the simulation lanes; no attempt, none planned. M12 · — | — · Not planned (observational forecast). Revisit only after JXT-12 — it supplies the stellar field a JWST forecast would be built from. — |
| JAXiON-14 | WDM ≈ FDM on large scales → Lyman-α stays valid; m₂₂ = 2.5 is already in moderate tension with the Lyman-α forest and the MW subhalo census. | ✅ reproduced & sharpened | The published-bound triad reproduced — dwarf cores m₂₂ ≲ 1.1 (upper, Obs-A dwarf bound ▸), Lyman-α m₂₂ > 20 (lower), MW subhalos (lower) — and the paper’s “moderate tension” made precise: 8.7σ combined (sim-derived band 7–9σ, 8.7σ tension ▸). M13 · Ledger-6 · Notes-1.2/1.6 | banked ✅ · Upgrade path = the real-data m-measurement (Track 2), held on T2.1; the unblock is JXT-6's guard-rail — the analytic λ-scaling route needs no per-m re-simulation. Revisit if Sandro wants the real-data number. — |
The core–halo law M_c ∝ M_h1/3 is a Schive 2014 finding, not one of the Mocz Letter’s M1–M13 — so it lives in the Schive scorecard as GAMER-9 ✅ “value recovered”, where the recovery route is JAXiON’s differentiable soliton-fit: JXE-F8 β fit ▸ JXE-F7 bias check ▸ This tab scores JAXiON only against the Mocz paper; β is JAXiON’s headline all the same.
The paper is DM-wave + full hydro; every “us” number is DM-wave only unless stated — the hydro column (JAXiON-10–12) is the lane’s known scope gap, not a hidden failure. And our PDF holds the 6-page Letter only, no Supplemental Material — their convergence tests and catalogs live in the PRL SM we don’t hold, so fidelity claims about their convergence wait on it (§3, last row).
Everywhere the wave physics could be resolved, it matched the paper. The failures are one scope gap (hydro), one structural wall (uniform-grid cores), and two controls we never built.
Mocz et al. is a hydro paper — its flagship observable is baryons tracing the cored DM. JAXiON simulates the DM wave only; the stellar-suppression claim was bracketed semi-analytically (8–30% vs their ~40%, SMHM-prescription-limited) and the smoking-gun gas test was never run. The honest ladder: adiabatic gas coupled to SP first (retry #5), full sub-grid later — or accept the gap and say so, as this table does.
ρ_c climbs 44k→69k→109k→228k over 512³→2048³ and never plateaus; 4096³ OOM’d on 4×H200. Root cause measured: r_c/dx is grid-locked at 0.5–1.5 (JXE-F1 r_c/dx wall ▸) — cost grows worse than N⁴. Both escape attempts closed: differentiable block-AMR starves the fine block (1–3% of reference at m≥2, parked) and the naive crop-zoom hits the mass↔resolution scissor (JXE-F4 crop-zoom scissor ▸). Resolution rescue = the imaginary-time soliton-fit toolchain (JXE-F5 solver ▸/JXE-F6 fit robustness ▸) — which delivered β = 0.30 ± 0.03 ≈ ⅓ (JXE-F8 β = 0.30 ▸). Note: the paper’s production run is the same method at 1024³ — their z=5.5 stop is their own convergence guard; how converged their core interior is lives in the SM we don’t hold.
The paper’s cleverest control: identical cutoff ICs evolved collisionlessly = “FDM minus wave effects.” We only ever showed a smoothed visual proxy. Without it there is no cusp-vs-core contrast and no independent σ for the λ_dB test.
Their ICs are axionCAMB with Lcutoff ≈ 1.4 h⁻¹ Mpc and σ₈ boosted 0.8 → 1.4 to compensate the small volume. Ours were GRF + FDM transfer at standard σ₈ — close in spirit, not in pipeline. Any literal filament-chain reproduction (retry #3) must adopt their IC recipe first, or the timing/ordering comparison isn’t apples-to-apples.
The top two need almost no compute: one recovers the paper’s novel object with a solver we already validated; the other runs on checkpoints already on disk.
| # | Path | Targets | Cost | Status / risk |
|---|---|---|---|---|
| 1 =JXT-5 | The cylindrical soliton, c = 0.127. Re-run the validated imaginary-time solver (JXE-F5 solver ▸) in cylindrical symmetry, fit the ground state, recover the paper’s own novel result — the “squeezed soliton.” Closes the most conspicuous hole in the Mocz coverage; becomes the next JXE-F chart. | JAXiON-5 | GPU-minutes | tool in hand low risk |
| 2 =JXT-3/4 | The λ_dB fringe-size metric. Measure the fringe autocorrelation scale across the 203 stored interference-run checkpoints and compare to h/(mσ) — tests the paper’s “within ×2” claim, and upgrades the interference web from qualitative to quantitative. | JAXiON-3 JAXiON-4 | none · hours | data on disk low risk |
| 3 =JXT-2/7 | The Mocz-shaped filament chain. axionCAMB-cutoff ICs + σ₈→1.4, 1.7 h⁻¹Mpc, ≤2048³ (we already exceed their DM resolution), z→5.5: fragmentation ordering, the cylindrical-profile fit at z≈7, the soliton by z=5.5. Blind-clean — estimators committed by the paper in 2019. | JAXiON-2 JAXiON-7 | ~GPU-day | proposed medium |
| 4 =JXT-9 | The matched WDM twin. Same cutoff ICs, collisionless evolution → the cusp-vs-core contrast and the σ_WDM input for #2. The paper’s own control, finally built. | JAXiON-9 JAXiON-4 | ~GPU-day | proposed medium |
| 5 =JXT-1/10 | Adiabatic-gas “M9-lite.” Couple isothermal/adiabatic gas to SP — no SF/feedback machinery — and test the smoking gun: does gas trace the cored DM? The honest first rung of the hydro ladder (Path A). | JAXiON-10 | multi-GPU-days | open med–high |
| 6 =JXT-12 | Quantitative stellar suppression. Needs matched FDM+CDM HMFs at z≈5.5 (20 Mpc-class) + a calibrated SF prescription — or #5’s hydro. The 40% itself is prescription-limited (JAXiON-12). | JAXiON-12 | campaign | gated no 20 Mpc FDM box |
| + | Fetch the PRL Supplemental Material (convergence tests, catalogs, movies) from arXiv/PRL — required before any fidelity claim about their convergence, and it grounds #3’s blind check. | provenance | trivial | do regardless |
The wave physics reproduces wherever we can resolve it — the method at machine precision (JAXiON-1), the soliton law exactly and in two independent codes (JAXiON-6), and the mass tension the paper only gestures at, made precise at 8.7σ (JAXiON-14). What’s unclosed splits cleanly in two: the baryonic chain (JAXiON-10–12 — Mocz is a hydro paper; this lane never ran hydro) and the paper’s own novel object, the cylindrical soliton (JAXiON-5) — which our validated solver can reach in GPU-minutes. Retries #1–#2 cost ≈ nothing and close the two most conspicuous gaps.
Provenance: paper re-read 2026-07-02 from Papers/…1910.01653v2.pdf (6-page Letter — SM not held) · all “us” numbers from context/RESULTS_LEDGER.md · canonical long-form: context/2026-07-02_JAXiON_paper_reproduction_report.md · Agent 2 (JAXiON specialist).
Source material re-read from our paper-tutor store. Ⅰ = Springel, Pakmor, Zier & Reinecke, MNRAS 506, 2871 (2021) — the GADGET-4 method paper (TreePM/FMM gravity, hierarchical time integration, on-the-fly FOF/SUBFIND, folded P(k), 2LPT ICs, SPH). Ⅱ = Klypin, Trujillo-Gomez & Primack, ApJ 740, 102 (2011) — the Bolshoi ΛCDM reference simulation (250 h⁻¹Mpc, 8×10⁹ particles) our z=0 validation targets. Twelve findings GADGET4-1 … GADGET4-12 (universal refs, per the Tab-number convention), each scored against what we actually ran: a Bolshoi-class 100 h⁻¹Mpc 512³ box → z=0 and the matched 20 h⁻¹Mpc 512³ CDM control → z=6/z=4. Every "us" number traces to context/RESULTS_LEDGER.md (Ledger-4); every evidence chip opens the actual chart. Tally: ✅ 9 reproduced / used+validated · ◐ 1 partial · ✗ 2 not run (by design).
| # | Paper finding | Us | Our evidence & route |
|---|---|---|---|
| GADGET4-1 Ⅰ | TreePM collisionless cosmological structure formation at controlled force accuracy — the code's core function: gravity-only N-body from near-uniform ICs to the clustered web. | ✅ reproduced | Two clean production runs: Bolshoi-class 100 h⁻¹Mpc 512³ → z=0 and the matched 20 h⁻¹Mpc 512³ → z=4 (32 ranks, NaN=0, clean exits; 134,217,728 particles each). z=0 slice ▸ 20 Mpc P(k) z=6 ▸ Report-3.5 · Ledger-4.a/4.b |
| GADGET4-2 Ⅰ | Built-in 2LPT initial-conditions generator (N-GenIC, §7.7) — cosmological ICs created on start-up, no external IC pipeline. | ✅ used + validated | Both runs' ICs generated in-code (z=99 / z=63); 20 Mpc control on the FDM campaign's own matched cosmology (Ωm=0.2835, h=0.6955, σ8=0.84754 CAMB, EH transfer, seed 181170). Validation: the evolved large-scale P(k) lands on linear theory. P(k) → linear z=6 ▸ Ledger-4.b |
| GADGET4-3 Ⅰ | Symplectic kick-drift-kick + hierarchical time integration (§4) in log-a — conservative by construction, no long-term drift. | ✅ conservation verified | |ΔM/M| < 10⁻¹⁵ over 88 outputs (machine precision); displacement-limited stepping held z=63→4 with zero NaN across 3,742 sync-points. G4-F4 conservation ▸ Report-3.3 · Notes-3.1 |
| GADGET4-4 Ⅰ | On-the-fly FOF group finding (§7.1) — halo catalogs written at every dump, no separate postprocess pass. | ✅ used at every dump | FOF catalogs behind every HMF we quote: 142,205 halos (z=0) · 91,058 (z=6) · 120,573 (z=4). HMF z=0 ▸ HMF z=6 ▸ HMF z=4 ▸ Report-3.1/3.8 |
| GADGET4-5 Ⅰ | SUBFIND / SUBFIND-HBT subhalo finding + merger trees (§7.2–7.4) — bound substructure and halo histories, optionally on the fly. | ◐ partial | SUBFIND ran on the z=0 box (fof_subhalo_tab; its Vmax fed the 7,594-halo c–M). The 20 Mpc control was configured FOF-only — no subhalo catalog at z=6/4; merger trees never used. Pure postprocess to add (retry #1). G4-F5 c–M (via SUBFIND) ▸ → retry #1 |
| GADGET4-6 Ⅰ | Wide-dynamic-range power-spectrum estimator (§7.6) — a "folding" trick extends P(k) far beyond the PM-grid scale, written at every output. | ✅ used at every dump | The 3-fold-block spectra are exactly what our harvest parses — measured to the particle Nyquist (80 h Mpc⁻¹ in the 20 Mpc box), shot-noise-cut (Δ²>2×shot). P(k) z=0 ▸ P(k) z=6 ▸ P(k) z=4 ▸ Report-3.2/3.9 |
| GADGET4-7 Ⅰ | Statistical convergence to ~1% (§8): individual orbits are chaotic, so correctness = "statistical quantities… such as halo density profiles, the halo mass function, or the matter power spectrum… converge to a unique answer" at tight force/timestep settings. | ✅ reproduced | Our z=0 statistics land on theory at exactly that level: HMF sim/Sheth–Tormen median 1.008 (≈1%); P(k) large-scale→linear (0.910), small-scale→Halofit nonlinear. HMF z=0 ▸ P(k) z=0 ▸ Report-3.1/3.2 · Notes-3.1 |
| GADGET4-8 Ⅱ | Bolshoi: the ΛCDM halo mass function tracks Sheth–Tormen at low z — and ST drifts to over-prediction at high z (their z=10: nearly an order of magnitude). | ✅ reproduced + extended | z=0 at Bolshoi's own cosmology (Ωm 0.27 / σ8 0.82 / h 0.70): sim/ST = 1.008. High-z, matched 20 Mpc box: ST still tracks to 1.068 (z=6) / 1.037 (z=4) across ~3–4 dex — mild drift toward higher z, consistent with Klypin's trend. HMF z=0 ▸ HMF z=6 ▸ HMF z=4 ▸ Report-3.8 · Ledger-4.b |
| GADGET4-9 Ⅱ | The NFW concentration–mass relation — Bolshoi's halo-structure lineage (concentrations rising toward low mass; the Dutton & Macciò 2014 calibration descends from it). | ✅ reproduced | 7,594 halos at z=0, median c ≈ 7.3 at 1011.5 M⊙ (Vmax method), tracking Dutton–Macciò 2014. G4-F5 c–M ▸ Report-3.6 |
| GADGET4-10 Ⅱ | The ΛCDM cosmic web — filaments and voids at the statistics of a ΛCDM box (Springel's own demo: a 1 h⁻¹Gpc lightcone run showing the same morphology). | ✅ reproduced | Density-PDF σ=1.48, skew=6.6 (strongly non-Gaussian, filament/void topology); the z=0 slice shows the web directly. G4-F7 web PDF ▸ z=0 slice ▸ Report-3.4 |
| GADGET4-11 Ⅰ | SPH hydrodynamics (§5): entropy- and pressure-based formulations, kernel options, artificial viscosity, plus starter cooling & star-formation models. | ✗ not run | By design — the control lane is DM-only/collisionless. Hydro+SF is exactly what the stellar-mass-suppression question (g1.8 Path A) would need; the machinery exists in-code, unexercised by us. → retry #5 |
| GADGET4-12 Ⅰ Ⅱ | Production scale: lightcone outputs (§7.5), merger trees at scale, extreme parallel scalability (§10) — their demo 1 h⁻¹Gpc / 768³ full-sky lightcone; Bolshoi 8×10⁹ particles to Vcirc=50 km/s completeness. | ✗ not exercised | Ours are modest 512³ / 32-rank CPU runs — all a control lane needs. The honest cost is statistics, not accuracy: Poisson-starved top HMF bins and n=2 large-scale P(k) modes (the Report-3.9 ◐). No lightcone/merger-tree outputs. Report-3.9 ◐ |
Large-scale sim/linear = 0.76 rests on n=2 fundamental modes — a 20 h⁻¹Mpc box is cosmic-variance-limited on its largest scales, fundamentally. We flag it rather than average it away (blind science); the HMF and the small-scale P(k), where the modes are plentiful, are the robust deliverables. see the n=2 bins ▸
Beyond the papers: this lane exists so FDM has a matched yardstick. Delivered — the 20 Mpc CDM P(k) × Hu et al. 2000 analytic FDM transfer gives the quantitative small-scale suppression, half-mode k = 4.58 / 6.89 / 9.37 Mpc⁻¹ for m₂₂ = 1 / 2.5 / 5 (FDM side analytic — the matched FDM simulation box was killed by the memory walls, see the GAMER tab). The z=6 FOF catalog is also the matched CDM HMF substrate for the stellar-mass-suppression decomposition (g1.8). contrast z=6 ▸ contrast z=4 ▸ G4-F6 (first, z=0 analytic) ▸
Unlike the FDM lanes, nothing here failed — every target this lane aimed at was hit. The gaps are scope choices for a control lane, plus one box-physics limit.
Springel+21 §5 (SPH, cooling, star formation) was never exercised — the control is deliberately collisionless. The in-code cooling/SF models are, per the paper, starter models "to help users get started"; a serious in-soliton star-formation study (g1.8 Path A) would need care beyond switching them on.
Bolshoi is 250 h⁻¹Mpc with 8×10⁹ particles; Springel’s demo is a 1 h⁻¹Gpc lightcone. Ours are two 512³ boxes on 32 CPU cores. The price is purely statistical: Poisson-starved high-mass HMF bins and the n=2 large-scale P(k) modes. A statistics wall, not an accuracy wall — and unlike the FDM dt/memory walls, this one is cheap to raise (CPU-days, no GPU).
The control was built FOF-only, so there is no subhalo mass function or c–M at z=6/4 yet. The dumps are on the stopped box’s volume; GADGET-4 runs SUBFIND as a pure postprocess (restartflag 3) — retry #1, no re-simulation needed.
The matched 20 Mpc FDM box died on the GAMER memory wall (and JAXiON’s cosmological box is 1 Mpc) — so the FDM side of the contrast is the analytic Hu+2000 transfer, honestly weaker than sim-vs-sim. The CDM side is a real, matched simulation; if any 20 Mpc FDM box ever lands, this upgrade is one overlay away.
All CPU-class and cheap — the GADGET lane has no compute wall. #1 and #2 directly serve the FDM science; the rest are polish.
| # | Path | Targets | Cost | Status / risk |
|---|---|---|---|---|
| 1 | SUBFIND postprocess on the 20 Mpc dumps (restartflag 3) → subhalo catalog + subhalo MF + c–M at z=6/4. Data sits on the stopped box; restart, postprocess, stop. | GADGET4-5 | CPU · hours | data in hand low |
| 2 | CDM twin of the z≈13 first-collapse test. The GAMER tab’s retry #4 (30 h⁻¹Mpc FDM box to z~10) needs this CDM baseline for the like-for-like delayed-formation contrast — gravity-only, so no wall on our side. | pairs GAMER-8 | CPU · ~1 day | proposed low |
| 3 | ρ₃₀₀ / satellite-census CDM side — the CDM half of the GAMER tab’s P5 quick win, from the existing z=0 catalog (142k halos). Pure CPU painting. | pairs GAMER-5 | CPU · hours | ready low |
| 4 | Phase-matched CDM twin of a GAMER seed — pipe the same GRF phases through N-GenIC → halo-by-halo FDM↔CDM matching instead of statistical. IC plumbing between codes is the risk. | GADGET4-2 | CPU · ~1 day | untested medium |
| 5 | Hydro/SPH scoping for in-soliton star formation (g1.8 Path A) — §5 machinery exists in-code; would make the stellar-mass-suppression decomposition physical instead of semi-analytic. | GADGET4-11 | CPU/GPU · week+ | ⏸ gated Mukesh/Agent-2 |
| 6 | Raise the statistics — a second seed of the 20 Mpc control (kills the n=2 large-scale ambiguity by averaging realizations) and/or denser dumps. Only if a writeup needs the ◐ upgraded. | Report-3.9 | CPU · ~16h | optional low |
The yardstick reproduces everything it aimed at: Springel’s DM-gravity core at its own ~1% convergence bar (HMF sim/ST = 1.008 at z=0), Bolshoi’s ΛCDM phenomenology (HMF, c–M, cosmic web), and the matched high-z control (ST tracked to 3.7–6.8% at z=4/6 across ~4 dex). What we didn’t run — hydro, lightcones, 8-billion-particle scale — are scope choices for a control lane, not walls. This is the one lane in the campaign with zero failed targets, and it is already earning: the FDM-vs-CDM half-mode contrast (Report-3.7 ✅) and the matched CDM HMF for g1.8 are its products.
Provenance: Springel+21 re-read 2026-07-02 from the paper-tutor store (arXiv 2010.03567 — PDF + digests; §8 quote verbatim) · Klypin+11 via arXiv 1002.3660 abstract · all "us" numbers from context/RESULTS_LEDGER.md (Ledger-4) · 13 evidence charts verified 200/image-png before linking · Agent 3.
