{"id":"512d3da6-61e7-4677-bcc8-d41341145c44","arxiv_id":"2512.07020","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Self-interacting scalar field dark matter produces non-universal core-halo scaling relations that depend on interaction strength, sign, and halo evolutionary stage, extending beyond standard fuzzy dark matter.","lead":"This preprint runs 3D simulations of merging wave-like dark matter structures to show how particle self-interactions change the size and density of galaxy cores. Repulsive interactions produce bigger, lower-density cores while attractive ones increase density and can trigger collapse, altering expected scaling laws.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Merger-only simulations may not capture how continuous cosmological assembly alters core scaling with interaction strength and stage","rationale":"The reader's weakest assumption directly identifies the generalization gap from merger simulations to cosmological histories. With the full text now available, the simulation methodology appears standard and internally consistent for the GPP system, but the absence of cosmological context remains the single most load-bearing uncertainty for the non-universality claim. No other technical inconsistencies (e.g., in soliton fitting or energy definitions) rise to the same level.","tokens_in":1726,"tokens_out":328,"duration_ms":24122,"concrete_test":"Re-run a subset of the repulsive and attractive cases with an added uniform background density or slow mass infall calibrated to match typical halo growth rates; recompute the core mass-size-energy scalings at equivalent post-merger times and check whether the interaction-dependent deviations from universality persist or are washed out.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that core-halo scaling relations for mass, size, and energy are non-universal and depend on self-interaction sign/strength plus evolutionary stage. This rests on 3D GPP soliton-merger runs across scattering lengths. For the dependence on stage to be general, the discrete merger sequences must adequately sample the range of assembly histories that occur in realistic halos (continuous accretion, tidal fields, multiple generations of mergers). The paper's controlled initial conditions and isolated evolution leave open whether the reported stage dependence is an artifact of the merger setup rather than a robust feature of cosmological SFDM halos.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper uses three-dimensional Gross-Pitaevskii-Poisson simulations of multiple soliton mergers to study self-interacting scalar field dark matter halos across repulsive and attractive regimes. It reports that repulsive self-interactions produce more massive, extended cores with lower central densities while attractive interactions raise central densities and can trigger collapse above a critical mass; the mass-radius relation remains consistent with analytical soliton solutions; and core-halo scaling relations for mass, size, and total energy are non-universal, depending on interaction strength/sign and halo evolutionary stage.","tokens_in":1873,"tokens_out":538,"duration_ms":22202,"significance":"If the central claims hold, the work demonstrates that self-interactions provide a tunable mechanism for regulating SFDM core properties, extending core-halo relations beyond the non-interacting fuzzy dark matter limit and offering implications for supermassive black hole seeding and galactic-core observables. The numerical confirmation of analytical mass-radius relations across interaction strengths is a concrete strength.","major_comments":[{"comment":"The central claim that scaling relations depend on evolutionary stage rests on discrete soliton-merger sequences. Because the simulations employ isolated initial conditions without continuous accretion or tidal fields, it is unclear whether the reported stage dependence generalizes to realistic cosmological assembly histories; this directly affects the load-bearing assertion that the relations are non-universal in a cosmologically relevant sense.","section":"Simulation setup and results sections"},{"comment":"The paper states that the mass-radius relation is 'well described by analytical predictions' even with self-interactions, yet no quantitative measure (e.g., fractional residuals, reduced chi-squared, or explicit comparison to the interaction-dependent soliton solution) is provided to substantiate the level of agreement across the scanned scattering lengths.","section":"Results on mass-radius relation"}],"minor_comments":[{"comment":"Notation for the scattering length and its sign convention should be defined once in the methods and used consistently; occasional switches between 'positive' and 'repulsive' labels reduce clarity.","section":"Throughout"},{"comment":"Figure captions for the core-halo scaling plots should explicitly state the number of merger realizations per scattering length and whether error bars represent standard deviation across runs or fitting uncertainty.","section":"Figures showing scaling relations"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a reasonable fit for a cosmology or astrophysics journal focused on dark-matter phenomenology, but the limited scope of the merger-only setup may warrant a brief discussion of planned follow-up with full cosmological initial conditions."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their constructive and detailed review of our manuscript. We have carefully considered each major comment and provide point-by-point responses below, along with the revisions we plan to implement.","responses":[{"response":"We agree that the simulations rely on isolated soliton-merger sequences with fixed initial conditions and lack continuous accretion or tidal fields. This controlled setup was chosen to isolate the effects of self-interactions on core-halo relations during successive mergers. We acknowledge that this does not fully capture the complexities of cosmological assembly histories. In the revised manuscript, we will add an expanded discussion of this limitation in the conclusions and methods sections, explicitly stating the scope of our claims regarding evolutionary-stage dependence and noting that future work with cosmological initial conditions would be valuable to test broader applicability. We maintain that the demonstrated non-universality within this regime remains a robust result.","revision_made":"yes","referee_comment":"[Simulation setup and results sections] The central claim that scaling relations depend on evolutionary stage rests on discrete soliton-merger sequences. Because the simulations employ isolated initial conditions without continuous accretion or tidal fields, it is unclear whether the reported stage dependence generalizes to realistic cosmological assembly histories; this directly affects the load-bearing assertion that the relations are non-universal in a cosmologically relevant sense."},{"response":"We thank the referee for this observation. The manuscript includes visual comparisons between simulated core properties and analytical soliton solutions, but we did not include quantitative metrics such as residuals or goodness-of-fit measures. In the revised version, we will add explicit quantitative comparisons, including fractional residuals and root-mean-square deviations between the simulated mass-radius data and the interaction-dependent analytical predictions across the range of scattering lengths studied. These will be presented in a new figure or table in the results section to rigorously support the level of agreement.","revision_made":"yes","referee_comment":"[Results on mass-radius relation] The paper states that the mass-radius relation is 'well described by analytical predictions' even with self-interactions, yet no quantitative measure (e.g., fractional residuals, reduced chi-squared, or explicit comparison to the interaction-dependent soliton solution) is provided to substantiate the level of agreement across the scanned scattering lengths."}],"tokens_in":1375,"tokens_out":478,"duration_ms":33265,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper's main point is that self-interactions break the universality of core-halo scaling relations in scalar field dark matter. The relations for core mass, size, and energy depend on the sign and strength of the interaction as well as the halo's stage in its merger history.","headline":"Self-interactions in SFDM make core-halo scalings non-universal and dependent on interaction details and halo stage, though merger simulations raise questions about broader applicability.","tokens_in":2405,"tokens_out":135,"would_cite":false,"duration_ms":39286,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"SFDM soliton-merger simulations derive non-universal core-halo scalings from GPP energy minimization; no RS J-cost, φ-ladder or 8-tick structure invoked","alignment":"orthogonal","rationale":"The paper's central machinery consists of numerical GPP integrations of soliton mergers, Gaussian ansatz energy minimization (E = K + W + U_SI) yielding mass-radius relations, and empirical power-law fits to M_c/M vs. invariant Ξ. These are standard hydrodynamic/quantum-pressure calculations in the SFDM literature and do not employ cosh-cost reasoning, ratio-symmetric J(x), golden-ratio identities, φ-ladder spacings, or parameter-free constant derivations. The domain (astrophysical halo assembly) lies outside the RS forcing chain from distinction to spacetime/constants.","tokens_in":57951,"confidence":"high","tokens_out":183,"duration_ms":36879,"cache_read_input_tokens":32896,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Self-interactions make core-halo scaling relations in scalar field dark matter depend on interaction strength, sign, and halo evolutionary stage rather than being universal.","keywords":["scalar field dark matter","self-interacting dark matter","soliton cores","core-halo relations","Gross-Pitaevskii-Poisson","fuzzy dark matter","dark matter halos"],"falsifier":"A survey of galactic cores that finds mass-size-energy relations independent of any measurable proxy for interaction strength or halo age would falsify the claim that self-interactions control the scalings.","tokens_in":2630,"feed_emoji":"🌌","tokens_out":835,"duration_ms":41829,"temperature":0.7,"pith_summary":"The paper uses three-dimensional simulations of soliton mergers in the Gross-Pitaevskii-Poisson system to examine how self-interactions change the inner structure of scalar field dark matter halos. Repulsive interactions produce more massive and extended cores with lower central densities, while attractive interactions raise central densities and can cause collapse past a critical mass. The mass-radius relation of the cores still follows analytical soliton predictions, but the broader scaling relations linking core mass, size, and total energy vary with the strength and sign of the self-interaction and with how far the halo has evolved. This extends earlier results for non-interacting fuzzy dark matter by showing that self-interactions provide a built-in regulator for core properties. A reader would care because the findings tie directly to observable galactic cores and to the possible role of these cores in seeding supermassive black holes.","feed_headline":"Self-interactions alter core scaling in scalar dark matter","feed_subtitle":"Simulations show core mass and size relations depend on interaction strength, sign, and halo stage rather than remaining universal.","key_machinery":"Three-dimensional Gross-Pitaevskii-Poisson simulations of multiple soliton mergers that incorporate a constant scattering length to control the strength and sign of self-interaction and track core evolution inside forming halos.","core_discovery":"Using three-dimensional Gross-Pitaevskii-Poisson simulations of multiple soliton mergers across repulsive and attractive regimes, the authors show that repulsive self-interactions yield more massive and extended cores with lower central densities than the free case, while attractive interactions increase central densities and drive collapse beyond a critical mass. The solitonic core mass-radius relation remains consistent with analytical predictions even when self-interactions are present, and the core-halo mass relation is extended accordingly. Scaling relations among core mass, size, and total energy are not universal but depend sensitively on self-interaction strength and sign as well as,","pith_inferences":["Measurements of core densities and sizes in nearby galaxies could directly constrain the allowed range of self-interaction strengths.","The reported dependence on evolutionary stage implies that recently assembled halos should exhibit systematically different core scalings than relaxed systems, offering a testable signature in large-scale simulations.","Similar non-universal scalings may appear in other self-interacting dark matter models if soliton-like cores form, suggesting a broader class of regulated core structures."],"forward_implications":["Repulsive self-interactions produce more massive and extended cores with lower central densities than non-interacting fuzzy dark matter.","Attractive self-interactions raise central densities and trigger core collapse once a critical mass threshold is crossed.","The core mass-radius relation remains consistent with analytical soliton solutions across interaction regimes.","The core-halo mass relation extends beyond the free fuzzy dark matter case when self-interactions are included.","Self-interactions supply a natural regulator for core properties that affects supermassive black hole formation and galactic-core observables."],"fun_headline_variants":["Repulsive self-interactions produce massive extended cores","Attractive interactions raise densities before core collapse","Core-halo scaling depends on interaction sign and halo stage","Mass-radius relation holds under self-interacting scalar dark matter"],"cache_read_input_tokens":64,"weakest_assumption_plain":"That the outcomes of soliton-merger simulations with fixed scattering length in the Gross-Pitaevskii-Poisson system generalize to realistic cosmological halo assembly histories and that the analytical soliton solutions continue to hold when self-interactions are added.","fun_headline_variants_meta":{"raw":{"variants":["Repulsive self-interactions produce massive extended cores","Attractive interactions raise densities before core collapse","Core-halo scaling depends on interaction sign and halo stage","Mass-radius relation holds under self-interacting scalar dark matter"]},"model":"grok-4.3","cost_usd":0.012134,"raw_usage":{"total_tokens":5312,"prompt_tokens":702,"num_sources_used":0,"completion_tokens":60,"cost_in_usd_ticks":121337000,"prompt_tokens_details":{"text_tokens":702,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4550,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":702,"tokens_out":60,"duration_ms":45712,"temperature":1.0,"reasoning_tokens":4550,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-17T00:00:40.934990+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A survey of galactic cores that finds mass-size-energy relations independent of any measurable proxy for interaction strength or halo age would falsify the claim that self-interactions control the scalings.","supporting_citations":[],"review_version":1}