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A new open-source clusterization library reproduces established heavy-ion cluster finders and adds a stable-cluster tracking step that recovers nuclei lost by transport models.

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2026-08-03 19:10 UTC pith:M2UABM45

load-bearing objection A genuinely useful open-source clusterization library with real algorithmic improvements (DSU MST, two-pass SA, sMST tracking), but the sMST validation is only circumstantial and the binding-energy criterion is never defined. the 4 major comments →

arxiv 2512.02084 v5 pith:M2UABM45 submitted 2025-12-01 nucl-th hep-ph

Modifications in clusterization procedures for heavy-ion collisions: minimum spanning tree, simulated annealing, coalescence

Viktar Kireyeu This is my paper
classification nucl-th hep-ph
keywords heavy-ion collisionsclusterizationminimum spanning treesimulated annealingcoalescenceQMD transport modelsbinding energy criterionstable cluster tracking
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that a single open-source library, CCL, can replace the separate clusterization modules tied to individual transport codes without losing physics. On the same set of simulated events, its DSU-based MST reproduces the full-graph MST output, and its two-pass simulated annealing chain matches established observables at 600 MeV per nucleon while cutting computing time. The main new mechanism is sMST, a stable-cluster tracking step that uses binding energy and per-baryon collision times to keep registered clusters alive and reattach baryons lost to artificial dissolution; enabling it drastically raises mid-rapidity deuteron and helium-3 yields. The paper also reports that MST-style cluster finding and coalescence applied to the identical baryon set produce different helium-3 spectra, with the sMST result closer to measured rapidity data.

Core claim

The central claim is that all major clusterization approaches used in heavy-ion transport simulations—minimum spanning tree, simulated annealing, coalescence, and a hybrid of the last two—can be implemented in one open library and validated on exactly the same events. The DSU-based MST gives identical results to the full-graph MST at lower cost; the modified two-pass simulated annealing chain reaches SACA-like agreement with data while reducing computational time; and the new sMST tracking algorithm repairs the artificial dissolution of previously stable clusters during QMD evolution, substantially improving mid-rapidity deuteron and helium-3 yields. For helium-3, the sMST result matches the

What carries the argument

The load-bearing object is the binding-energy-per-nucleon filter, E_bind(C) < E_cut with E_cut = -4 MeV, computed from the four-momenta of constituents in the cluster rest frame, which is reused inside the SA chain, the sMST tracking step, and the mixed coalescence procedure. Alongside it, the sMST tracking algorithm maintains a persistent list of stable clusters, removing a cluster only if a constituent disappears or collides after registration, and applying a preferential-growth / controlled-dissociation update rule to decide whether a new candidate replaces overlapping stored clusters.

Load-bearing premise

The whole filtering and tracking chain assumes that the cluster rest-frame binding energy per nucleon, with the chosen threshold E_cut = -4 MeV, genuinely separates physically bound nuclei from accidental groupings; the paper does not write the formula or validate it against known nuclear binding energies.

What would settle it

Compute the binding-energy-per-nucleon spectrum for identified deuterons, tritons, helium-3, and helium-4 using the same four-momentum formula and compare the peak positions to the empirical binding energies. If the formula labels obviously bound nuclei as unbound (or vice versa) by more than a few MeV, the E_cut filter and every conclusion built on it lose their physical basis.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Cluster finding for heavy-ion simulations can be done without building the full graph, giving identical MST results at lower computational cost.
  • A two-stage simulated annealing chain that treats unstable MST clusters one at a time reaches SACA-like agreement with data while reducing runtime.
  • Enabling the sMST tracking step restores mid-rapidity deuteron and helium-3 yields that otherwise drop, with the helium-3 yield matching measured data better than spin-isospin coalescence on the same baryons.
  • At early times, cluster-finding parameters should be chosen according to the system evolution rather than fixed for the whole reaction.
  • Applying the binding-energy cut to coalescence candidates suppresses yields too strongly, but a mixed coalescence-plus-binding-energy procedure offers a way to tune parameters for MST-based approaches.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper's entire filtering chain rests on an E_bind formula that is never written out; validating that formula against empirical nuclear binding energies would be a direct check of whether the 'stable' clusters are truly bound.
  • The same-baryon-set comparison between MST and coalescence for helium-3 suggests a clean experimental discriminator between formation mechanisms, provided both procedures are calibrated to identical acceptance.
  • The sMST tracking rule could be adapted to other transport models that do not propagate correlations, and its sensitivity to the 'collision after registration' criterion could be studied by varying that rule.
  • The momentum-proximity checks used in the mixed procedure hint that the default MST chain could be extended with relative-momentum cuts, which the paper suggests but does not build into the default algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper presents a new open-source clusterization library (CCL) for heavy-ion transport simulations, implementing MST-based cluster finding, a two-pass simulated annealing chain, a stable-cluster tracking algorithm ('sMST'), a 'box-like' coalescence procedure, and a 'mixed' coalescence+binding-energy method. The library is applied to PHQMD events and compared with established implementations (PHQMD MST, SACA, UrQMD coalescence) and with ALADiN and NA49 data. The central claims are: (i) CCL reproduces established MST/SACA results on the same events; (ii) sMST tracking 'drastically improves' the stability and yield of mid-rapidity clusters; and (iii) for 3He, sMST matches NA49 data better than coalescence applied to the same baryon set. The paper also reports a first comparison of MST-based versus coalescence 3He yields on identical events.

Significance. If the claims hold, CCL would be a valuable open resource: the field suffers from closed-source, model-specific clusterization tools, and a modular, well-tested library with a direct comparison on identical events is genuinely useful. The authors also provide several concrete algorithmic contributions (DSU-based MST, a two-pass SA chain, an online tracking method that does not require freeze-out time). The paper is honest about some limitations, such as the need for time-dependent SA parameters at low energies. However, the central validation currently rests on two fragile pillars: the binding-energy formula is never defined, and the sMST tracking is validated only by comparison to data on a single event sample without any ground-truth test. The 'better than coalescence' conclusion is likewise based on a single coalescence parameter set. These are correctness-risk issues that can be addressed with additional definitions and controlled tests, but they currently prevent acceptance.

major comments (4)
  1. [Sec. 3.1.1] The binding energy per nucleon E_bind(C) is the central physical quantity of the paper: it drives the SA acceptance criterion, the E_cut=-4 MeV stability cut in Sec. 3.2, the sMST stability filter in Sec. 4, and the 'mixed' procedure in Sec. 5. Yet it is never written down. The reader cannot reproduce any result, nor can the physical content of 'bound' clusters be assessed. Please provide the explicit formula, including how the cluster rest frame is defined and how the four-momenta are combined (e.g., sum of four-momenta, invariant mass, subtraction of constituent masses). This is a load-bearing omission.
  2. [Sec. 4, Fig. 4] The claim that sMST 'drastically improves mid-rapidity cluster stability' and 'recovers lost clusters' is not validated against any ground truth. The only evidence is the comparison of d and 3He rapidity spectra with tracking on/off on one PHQMD event sample. The update rule has an inherent asymmetry: a candidate p replaces overlapping stored clusters iff A(p)>A(s_max), otherwise it is discarded. In a dense mid-rapidity environment this rule can merge distinct objects and inflate cluster yields; the only physical filter is the negative-binding-energy test, which is undefined (see above). No false-positive rate, no synthetic-event test, and no comparison with an independent tracking method (e.g., aMST or collision-history-based reconstruction) are provided. Please add at least one controlled test with known cluster content and quantify over-merging and under-recovery.
  3. [Sec. 5.2, Fig. 7] The conclusion that sMST describes NA49 3He data 'better than coalescence' is based on a single coalescence parameter set (M1, as stated for Fig. 6). Table 3 lists other sets, and M4 is explicitly described as chosen to better describe the data; indeed, in the mixed procedure of Fig. 9, the M4 set with reduced Δr=2.5 fm reproduces the 3He shape much better than M1. Thus the claim is not robust to reasonable parameter choices. Please show the coalescence results for all parameter sets in the same comparison, or clearly state that the conclusion refers only to the default M1 set. Also include statistical uncertainties on the model curves, especially given the limited 50k-event statistics noted in the text.
  4. [Sec. 6, first bullet] The summary states that the MST-based clusterization overestimates ALADiN data even at t=200 fm/c, while the SA procedures with time-dependent parameters (S1 at t=50 fm/c, S2 at t=100 fm/c) achieve 'perfect' agreement. This means the ALADiN comparison is not a predictive, parameter-free test: the control parameters are adjusted per time step to match the data. The paper is partially transparent about this in Sec. 3.3, but the abstract's wording ('tested with complex observables') does not convey that the agreement involves parameter tuning. Please state this limitation explicitly in the abstract or in the conclusions, and specify which data points were used for tuning and which are genuinely predictions.
minor comments (6)
  1. [Abstract] There are several formatting/typo issues: '⟨Mimf⟩' and '⟨Zmax⟩' are rendered with missing spaces; 'same set of events' is fine but the abstract does not mention that the sMST tracking and the coalescence comparison use 50k events only.
  2. [Sec. 3.2] The threshold E_cut=-4 MeV is introduced without justification or a sensitivity study. Please provide a reference or a brief rationale, and consider adding a scan over E_cut to show that the conclusions are robust.
  3. [Sec. 4] The notation E^cut_bind (used in the text) is inconsistent with E_cut used in Sec. 3.2. Please unify.
  4. [Fig. 2] The bottom panel label reads '⟨∑ E_bind⟩' but the text refers to '⟨E_bind⟩'; the figure should match the text.
  5. [Sec. 3.1.3] The steps mode formula in Sec. 3.1.2 uses 'ℓ' for temperature level index, but later in Sec. 3.1.3 the stagnation counter and step definitions would benefit from a concrete pseudo-code or a reference to the code repository.
  6. [Sec. 5.2] The statement 'the final result must be the sum of kinetic deuterons and those found by (s)MST or formed via coalescence' is important, but Fig. 6 does not show the sum of coalescence and kinetic deuterons (only coalescence alone, and sMST+kinetic). A plot of the coalescence+kinetic sum would make the comparison more direct.

Circularity Check

0 steps flagged

No significant circularity: the paper's central comparisons are external benchmarks against PHQMD MST, SACA, UrQMD coalescence, and ALADIN/NA49 data.

full rationale

The validity of the main claims rests on comparisons with existing closed-source implementations (PHQMD MST, SACA, UrQMD built-in coalescence) on the same events and with experimental data (ALADIN, NA49). The CCL MST results are checked directly against the PHQMD full-graph MST, the CCL SA routine against SACA, and the CCL coalescence against the UrQMD built-in implementation; these are independent external benchmarks, not restatements of CCL parameters. The explicit statement that the M4 set was 'chosen to better description of available data' (Sec. 5.2) is transparent fitting, not a disguised prediction, and does not support the paper's central sMST-vs-coalescence comparison, which is anchored to NA49 data. Self-citations to refs. [9], [10], and [12] are contextual (code provenance and background) and are not load-bearing for the derivation. The unstated binding-energy formula and user-chosen E_cut threshold in Sec. 3.2/4 are a physical-validation gap, but not circularity, since the sMST stability filter's output is ultimately tested against external NA49 yields. No equation was found that is equal to its input by construction, and no fitted parameter is renamed as a prediction.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The paper's results depend on a handful of user-chosen thresholds (radii, momentum cuts, E_cut, SA schedule) and on the physical assumption that the four-momentum-based binding energy identifies real nuclei. No new physical entities are introduced.

free parameters (5)
  • Clusterization radii r_clust = 2.5, 3.5, 4.0, 9.5 fm
    Chosen by hand for different parameter sets (T1-T3, S1-S2, M1-M4) in Tables 1-3; not derived from first principles.
  • Momentum thresholds delta_p = 0.285-0.55 GeV/c
    Used in MST momentum checks and coalescence; values are tuned to data or taken from prior work (Table 3).
  • SA control parameters (Tmax, Tmin, steps, Pnew, smin, sden) = Tmax=1, Tmin=1e-15, steps 500/4000, Pnew 0.1-0.9, smin=50, sden=2
    Hand-chosen to reduce computation time (Table 1); no optimization or justification beyond performance.
  • Binding energy cut E_cut = -4 MeV
    User-defined stability threshold for 'stable' clusters in SA and tracking (Section 3.2).
  • Coalescence parameter set M4 = delta_r/delta_p combinations
    Explicitly 'the mix of all previous parameters chosen to better description of available data' (Section 5.2), i.e., fitted to NA49.
axioms (4)
  • domain assumption The binding energy per nucleon computed from four-momenta in the cluster rest frame correctly identifies physically bound nuclei.
    Invoked in Sections 3.1.1, 3.2, 4, and 5.2; the formula is never written, but all SA and tracking stability criteria depend on it.
  • domain assumption QMD-based transport (PHQMD) propagates the phase-space correlations needed to form final-state clusters.
    Section 1 states 'Only QMD-based approaches will be used as base models' because BUU models lack correlations; all results rest on this.
  • domain assumption Clusters found by coordinate-space proximity (MST) at late times correspond to final-state fragments.
    Used throughout Sections 2 and 4; the paper compares such clusters directly to experimental data.
  • domain assumption The 'lost cluster' phenomenon in QMD is an artifact that can be corrected by tracking stable clusters.
    The entire sMST algorithm (Section 4) is built on this premise, citing [12].

pith-pipeline@v1.3.0-alltime-deepseek · 14549 in / 7788 out tokens · 77713 ms · 2026-08-03T19:10:39.175235+00:00 · methodology

0 comments
read the original abstract

A new open-source cluster finding library ''Common Clusterization Library'' (CCL) is proposed to describe the clusters production when applied to the transport codes. The new library was applied to the Parton-Hadron-Quantum-Molecular Dynamics approach to be comparable with the established and well known MST and SACA implementations on the exactly same set of the events. The presented procedures were tested with rapidity density distributions and complex observables like $\langle M_{imf} \rangle$ and $\langle Z_{\text{max}} \rangle$ vs $Z_{bound}2$ at the energies of ALADiN and NA49 experiments. An improvement to the simulated annealing chain is proposed to reduce the computational time. The new stable clusters tracking algorithm for the ''lost'' cluster recovering is presented. The results of the ''box-like'' coalescence procedure and a mixed method which incorporates the coalescence algorithm steps and the negative binding energy criteria are presented. The difference between the Helium-3 found by the MST-based cluster finding procedure and the coalescence algorithm applied on the exactly same set of events and baryons is shown for the first time.

Figures

Figures reproduced from arXiv: 2512.02084 by Viktar Kireyeu.

Figure 1
Figure 1. Figure 1: Upper panel: ⟨Mim f⟩ vs Zbound2; Lower panel: ⟨Zmax⟩ vs Zbound2; Black solid lines – PHQMD MST at t = 50 fm/c. Red dashed lines – PHQMD MST at t = 100 fm/c. Orange dash-dotted lines – CCL MST at t = 50 fm/c. Blue dotted lines – CCL MST at t = 100 fm/c. ALADiN experimental data (black circles) are taken from [7]. decades ago another procedure was proposed to be applied on top of the MST clusters – the Simul… view at source ↗
Figure 3
Figure 3. Figure 3: ⟨Mim f⟩ (top panel), ⟨Zmax⟩ (middle panel) and ⟨Ebind⟩ (bottom panel) as a function of Zbound2. Black solid lines and orange dash-dotted lines are PHQMD SACA at t = 50 and t = 100 fm/c. Red dashed lines and blue dot￾ted lines – CCL SA at t = 50 and t = 100 fm/c. Black circles – ALADiN experimental data taken from [7]. 4. Tracking As it was discussed in [12], the QMD dynamics propagates single baryons and t… view at source ↗
Figure 5
Figure 5. Figure 5: Rapidity density distribution. Black solid lines and orange dash [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Rapidity density distribution of deuterons. Black solid lines are [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Rapidity density distribution of 3He. Black solid lines are coales￾cence with spin-isospin coupling cut. The red dashed lines shows the ”sMST” results. Black circles – NA49 experimental data[13]. As on the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Rapidity density distribution of deuterons (top panel) and [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Freeze-out model of light nuclei formation in heavy-ion collision transport

    nucl-th 2026-05 unverdicted novelty 6.0

    A hybrid freeze-out model combining transport dynamics and thermal cluster production is proposed for light nuclei in intermediate-energy heavy-ion collisions.

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