GAMER lane · Schive et al. 2014 (Nature Physics + PRL) vs our reproduction · papers re-read 2026-07-02

The Schive 2014 papers, finding by finding

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: ✅ 8 reproduced · ◐ 3 partial · ✗ 1 open (2026-07-02, one day: 5→8✅ — GAMER-8 z_ff=15.7 · GAMER-2 suppression+P(k) · GAMER-12 M_min≈3×10⁸; GAMER-5/7 ✗→◐; open: GAMER-10 α → Agent 2).

#Paper findingUs · evidence & routeResultsRetry plan · code = <Finding>R · hypothesis / confidence / resources
GAMER-1 ⅠFirst 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 ▸GAMER-1R — none needed (reproduced).
GAMER-2 ⅠLarge-scale structure indistinguishable from CDM — same filaments/voids as a GADGET-2 N-body run at matched linear P(k) (their Fig. 1).✅ reproduced NEWGAMER-2R delivered (rode GAMER-8R, 2026-07-02): the FDM 30 h⁻¹Mpc sim at z=6 tracks CDM on large scales (P(k) shape vs CAMB linear, amplitude-matched k<0.5) and suppresses below the FDM scale exactly as predicted — knot-cleaned halo abundance down ~10⁵ vs CDM at 10⁸ M⊙ (8 genuine halos vs CDM’s ~617k; zero above 10⁹ vs 45k), P(k) turnover at k≈4–8 vs Hu k½=5.97. Open sub-items (honest): sim-vs-sim P(k) table archive (~$1) + cutoff metrology at high z.HMF+P(k) ▸CDM×Hu ▸GAMER-2R · 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 ⅠThe 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 ▸GAMER-3R · optional. The z≈0.1 full-box interference slice needs a large box ground to low z — with GAMER-9Rb retired (no boson-mass lever) this has no cheap path; only GAMER-9Rc (MPI) reaches it. Deprioritized.
GAMER-4 ⅠA 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 ▸GAMER-4R — none needed (reproduced).
GAMER-5 Ⅰρ₃₀₀ matches MW satellites: 80% of halos at 5.3×10⁻³–6.1×10⁻¹ M⊙/pc³ — the observed common mass scale of dwarfs.◐ consistent · ✅ pends z≈0 (5R2 RUNNING) NEWGAMER-5R executed (2026-07-02, pre-registered): core-only ρ̄(<300 pc) from the 94 fitted 2 Mpc cores — 52% inside the paper’s satellite band, 48% above, 0% below (median 0.56 vs band top 0.61 M⊙/pc³). “Above” is the declared direction of the z-mismatch (our halos z=3.1–6.1, denser cores; band is z=0), and core-only is a strict lower bound — so no-halo-below is the meaningful check.results ▸GAMER-5R ✅ executed — CPU, $0 (◐ by design: measured at z=3.1–6.1 vs the paper’s z=0 band). Flips to ✅ via GAMER-5R2 (close-out Tier 2): continue one 2 Mpc seed to z≈0.3 and measure ρ₃₀₀ at the band’s own epoch · ~$200–500, scope-first · also closes GAMER-3 (the z≈0 interference slice rides free).
GAMER-6 ⅠFornax 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 ▸GAMER-6R — none needed (reproduced).
GAMER-7 ⅠMilky 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.◐ undershoots · fix RUNNING (ladder + 5R2) NEWGAMER-7R executed (2026-07-02): Jeans machinery calibrated on their Fornax first (aperture-averaged σ over the 2r_c stellar extent → 13.6 vs their 11.3 km/s, within the pre-committed 25%; frozen before MW). Painting our stacked relation to M_h=10¹²: M_c(z=0)=1.7×10⁸ M⊙ → σ(<200 pc) = 30 km/s at m₂₂=0.8 — the self-consistent value, since (corrected 2026-07-02) our GAMER runs are at m₂₂=0.8, the papers’ own boson — vs their 115 and the observed ~110 plateau. Undershoots ×3.7, tracking the M_c normalization almost linearly (our M_c is ~3× below their ~5×10⁸ at MW mass; σ ∝ M_c on the soliton family) — the anchor-dominated weakness from GAMER-9Ra, isolated cleanly. Soliton-only σ (no stars/NFW) is a second declared low-bias.results ▸NEWGAMER-7R ✅ executed — CPU, $0. Proper fix IN MOTION: GAMER-9Rd ladder GO’d (Agent 2) + 5R2 low-z anchors (probe running) → refit normalization → re-paint σ. Re-publishes automatically when anchors land.
GAMER-8 ⅠDelayed 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.✅ reproduced (delay) NEWGAMER-8R measured it (2026-07-02, pre-registered): first collapse at z_ff = 15.7 (crossing between 17.2–15.7) in a 30 h⁻¹Mpc, m₂₂=0.8 box with FDM-cutoff ICs — vs their z≈13, vs CDM’s z≈50. The delayed-formation phenomenon reproduces emphatically; the ~2.5 offset from their number is single-realization rare-peak statistics (both runs are one box, one seed — declared, not corrected). First object M_200m=4.6×10⁸, persistent+growing to z=10.z_ff chart ▸NEWGAMER-8R ✅ executed — z_ff delivered ($19 vs $400 cap). Extension leg (→z=6) running: M_min@z=8 (GAMER-12R) + FDM HMF/P(k)@z=6 (GAMER-2R) land next.
GAMER-9 ⅡThe 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). NEWCross-check (GAMER-9Ra, 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).JXE-F8 β fit ▸JXE-F7 bias check ▸GAMER 2Mpc null ▸stacked fit ▸NEWGAMER-9Ra ✅ done 2026-07-02 — the stack (β=0.28±0.15, anchor-limited). · GAMER-9Rb — RETIRED (2026-07-02): the campaign already ran at m₂₂=0.8 (verified in every Input__Parameter on the box) — the “rerun at the paper’s boson mass” hypothesis is moot; no boson-mass lever exists against the wall. · GAMER-9Rc 8× MPI (memory aggregates; dt doesn’t). Last resort · ~40% · $$$. · GAMER-9Rd β-ladder on JAXiON zooms — UNPARKED, GO (2026-07-02): Agent 2 executes; anchors feed the stacked relation → β "defensible→confirmed" + fixes GAMER-7’s normalization · ~70% · multi-GPU-days.
GAMER-10 ⅡThe 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.✗ α untested (pilot ran) 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).NEWGAMER-10R · pilot DONE (v2, 2026-07-02) — pipeline validated, α-test needs GPU. Conservation fixed (dE/E ≤4% vs v1’s ~400%); resolution gate passed 1/6 — root cause quantified: merged-core soliton mass ≈ 4×M(<r_c) → sub-grid ~4× sooner than planned. Banked: the clean run’s core lies ON the SP 1/M family to 1.9% (controlled-experiment echo of GAMER-11). Next: full grid at 256³+ with the ×4 mass budget · 1 GPU-day · ~$110 · confidence ~75%.
GAMER-11 ⅡThe 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 ▸GAMER-11R — none needed (our strongest cross-code result).
GAMER-12 ⅡMinimum 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.✅ reproduced NEWGAMER-12R measured it (2026-07-02): a pre-declared virialization bar (peak ≥1000× mean) splits the z=8 catalog cleanly — 192 knots (median 43×, none virialize) vs genuine halos ALL ≥ 3×10⁸ M⊙ (median peak 3430×), and identically at z=6. M_min ≈ 3×10⁸ = the paper’s own prediction at this m₂₂ — the quantum-pressure floor is visible in our data: overdensities below it exist but cannot collapse. Caveat: n=5 (z=8) / 8 (z=6) halos.M_min chart ▸NEWGAMER-12R ✅ executed ($0 marginal, rode GAMER-8R). Statistics upgrade (n=5→~20) = the G8R-seeds Tier-1 item (~$50–75).

⛔ Two β's — never conflate (applies to GAMER-9)

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.

§2 · What we could not reproduce — and why, honestly

The failures are compute-frontier walls, not physics disagreements — everywhere we could resolve the physics, it matched the papers.

✗ The papers’ production regime: a large AMR box ground to low z blocks GAMER-3 (z≈0 slice) · direct GAMER-9 · GAMER-12

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. CORRECTEDWhy they could and we couldn’t: their flagship resolved box was 2 Mpc; ours was a 20 Mpc zoom to MAX_LEVEL 9–10 — ~10³× the resolved volume at far greater refinement depth. Correction (2026-07-02, verified on-box): our campaign ran at the papers’ own boson mass (ELBDM_MASS = 8×10⁻²³ = m₂₂ 0.8 in every run config; an earlier claim of m₂₂=2.5 conflated JAXiON/Mocz’s value onto GAMER). The wall is purely volume × zoom-depth × dt — there is no boson-mass lever. z=19 cores resolved ▸ Stage-1 catalog ▸

✗ β from GAMER alone (direct GAMER-9) replicates the PRL’s own caveat

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 ▸

✗ Never-run tests: GAMER-5 · GAMER-7 · GAMER-10 · GAMER-12 (+ GAMER-8’s first-collapse)

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.

✗ Wall-escape levers — all three closed Notes-1.7/2.4/4.1

(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 ▸

§3 · What we can still try — ranked by value ÷ cost

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.

#PathTargetsCostStatus / risk
1NEWPRL-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 · GAMER-9Ranone · done✅ executed anchor-limited
2NEWSoliton-merger experiments — CPU pilot COMPLETE (v1+v2, pre-registered); α-test → GPU. v1 failed its gates (sub-grid inputs + potential-phase heating) — reported, not resampled. v2 (validated solitons, adaptive dt): conservation fixed (dE/E ≤4%), resolution 1/6 — merged-core soliton mass ≈ 4×M(<r_c) drives cores sub-grid (why the PRL used AMR here). Banked: the clean run’s relaxed core sits ON the SP 1/M family to 1.9% — a controlled-experiment cross-check of GAMER-11. Full α grid: 256³+, ×4 mass budget, ~1 GPU-day.GAMER-10 · GAMER-10R ✅ pilotGPU · 1 day next🟡 v2 running v1 gates caught it
3Re-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 · GAMER-9Rb~1 H200-weekuntested medium
4The 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 · GAMER-8R~2–4 GPU-daysproposed low–med
5β-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 · GAMER-9Rdmulti-GPU-days⏸ parked pending Sandro
6Multi-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 · GAMER-9Rc8×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 · GAMER-5R GAMER-7RCPU · done✅ executed today

★ Bottom line

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.