{"id":"66c33a05-a769-435a-9821-62ebe36df29d","arxiv_id":"2607.09571","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"CHEFT recovers matter power to percent level and weighted tracers to ~3–5% by expressing the halo-halo spectrum as a sum of collapsed HEFT operators with probabilistic mass-dependent biases.","lead":"A hybrid halo model called CHEFT replaces the inaccurate linear 2-halo term with collapsed Hybrid Effective Field Theory operator templates measured from simulations, plus mass-dependent bias from probabilistic methods. This improves power-spectrum predictions for matter and mass-weighted tracers (SZ, CIB, HOD) across the 1-halo/2-halo transition without free bias parameters in the baseline.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"The predictive (no free bias) claim is load-bearing only for CHEFTmin; the headline 3–5% accuracy for CIB/HOD rests on a two-parameter effective Laplacian that Appendix B shows cannot restore full cross-mass coherence.","rationale":"The Reader correctly isolates the incomplete capture of cross-mass coherence as the weakest assumption and already notes that CHEFText introduces two fitted coefficients that slightly weaken the parameter-free rhetoric. My stress-test simply sharpens the same point: the abstract’s headline accuracy numbers for CIB/HOD are those of the extended model, not of the strictly predictive CHEFTmin. The matter and SZ results remain solid internal validations of the collapsed-operator idea, so the verdict stays CONDITIONAL rather than REJECT. No independent concern (resolution dependence, FoF definition, measured 1-halo, etc.) is more load-bearing than this one. The concrete test above would cleanly decide whether the effective Laplacian is a universal higher-derivative correction or a mild over-fit.","tokens_in":30335,"tokens_out":723,"duration_ms":9811,"concrete_test":"Freeze the two Laplacian coefficients (c0,c1) obtained from the joint SZ+CIB+HOD fit, then re-evaluate CHEFText on an independent mass-weighting scheme never used in the calibration (e.g. α=0.4 pure power-law or a different HOD with Mmin shifted by 0.5 dex). If the residual on that new auto- and cross-spectrum rises above ~5% in the transition regime, the effective Laplacian is absorbing tracer-specific freedom rather than a universal correction, and the predictive claim for weighted tracers weakens.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that CHEFT is a predictive model with no free bias parameters holds for CHEFTmin (operators {1,δ_L,δ_L^{2},s^{2}} + probabilistic b_i(M)). That model already reaches percent-level matter recovery (after mild mass-conservation enforcement) and ~2% on SZ×matter. The abstract’s stronger ~3–5% claim for weighted tracers, however, is achieved only by CHEFText, which replaces the probabilistic Laplacian bias by an effective rescaling α(M)=c0+c1 log10 M with two coefficients fitted jointly to the same SZ/CIB/HOD spectra being predicted (Eq. 49 and App. B5). Appendix B demonstrates that even freely fitted second-order (or third-order) bias vectors inside the same collapsed basis still fail to reproduce the off-diagonal structure of P_hh(k|M1,M2), especially for widely separated masses; the residual is precisely the source of the remaining CIB/HOD errors. Thus the few-percent accuracy advertised for the most interesting tracers is not a pure prediction of the probabilistic-bias CHEFT construction; it is an effective absorption of missing cross-mass physics by two free parameters. Because the 1-halo term is also measured rather than modelled, the paper is a clean proof-of-concept for the 2-halo piece, but the “no free parameters” rhetoric does not fully cover the accuracy numbers that appear in the abstract.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper introduces CHEFT, a hybrid halo-model construction in which the 2-halo term is built from Hybrid EFT operator spectra measured after collapsing particles to halo centres, thereby removing 1-halo contributions from the templates. Halo bias coefficients as a function of mass are taken from an independent probabilistic peak-background-split measurement rather than fitted to the spectra under test, yielding a baseline model (CHEFTmin: operators {1, δ_L, δ_L², s²}) with no free bias parameters. The 1-halo term is measured directly from the simulation so that validation isolates the 2-halo piece. On the matter field the reconstruction reaches percent-level accuracy across the 1-halo/2-halo transition once mild mass-conservation constraints are imposed. For mass-weighted mock tracers (SZ-, CIB- and HOD-like) the baseline model achieves ~5–10% accuracy in power, improving to ~3–5% when an effective Laplacian bias rescaling with two free coefficients is added (CHEFText). Appendix B documents residual failures of the finite operator basis on the off-diagonal structure of P_hh(k|M1,M2).","tokens_in":30717,"tokens_out":1605,"duration_ms":31227,"significance":"If the results hold, CHEFT is a useful and modular advance for multi-probe large-scale structure modelling: it keeps the halo-model separation of profiles, mass weighting and centre clustering while replacing the inaccurate linear 2-halo closure with simulation-calibrated non-linear templates. Strengths that should be credited explicitly include (i) external grounding of bias functions via probabilistic PBS rather than fitting to the power spectra under test, (ii) a clean isolation of the 2-halo contribution by measuring the 1-halo term, (iii) an honest and quantitative Appendix B that falsifies the claim that free bias amplitudes alone restore full cross-mass coherence, and (iv) validation across several astrophysically motivated mass weightings. The approach is well matched to joint analyses of galaxies, SZ, CIB and weak lensing, and the planned emulator path is clearly signposted.","major_comments":[{"comment":"Abstract and §4.3 / App. B5: The abstract’s stronger ~3–5% accuracy claim for weighted tracers is achieved only by CHEFText, in which the Laplacian bias is replaced by α(M)=c0+c1 log10 M with two coefficients fitted jointly to the same SZ/CIB/HOD auto- and cross-spectra being predicted (Eq. 49; c0=1.036, c1=−0.072). The baseline “no free bias parameters” statement is correct for CHEFTmin, but the abstract and §5 should state more explicitly that the headline few-percent numbers for CIB/HOD include this two-parameter effective correction, and should report the CHEFTmin residuals for those tracers side-by-side so that the pure predictive accuracy is not conflated with the calibrated extension.","section":"Abstract, §4.3, App. B5"},{"comment":"§4.2 and Appendix B: Even when bias vectors are freely fitted to Phh(k|M,M) and Phm(k|M) (and even with third-order operators or scale-dependent noise), the reduced χ² on the full Phh(k|M1,M2) matrix remains far from unity, with the largest residuals in cross-correlations of widely separated masses (Figs B1–B3). This is the structural origin of the remaining CIB/HOD errors. The paper correctly identifies the limitation, but the central claim that the second-order collapsed basis “captures a large fraction of the relevant non-linear clustering physics” should be qualified by a quantitative statement that multi-mass tracers remain limited at the few-to-ten-percent level until higher-derivative, exclusion or stochastic terms that restore cross-mass coherence are included.","section":"§4.2, Appendix B"},{"comment":"§3.1–3.2 and Fig. 4: Percent-level matter recovery is obtained only after enforcing the mass-conservation integrals I_i^m=0 via a compensating low-mass contribution (Eq. 48). Without that enforcement the reconstruction is at the 2–5% level, and the paper correctly notes that an analogous constraint cannot be imposed model-independently for weighted tracers. The target accuracy floor quoted for SZ/CIB/HOD should therefore be tied to the unconstrained matter residual, not to the constrained one, so that the comparison is fair.","section":"§3.1–3.2, Fig. 4"}],"minor_comments":[{"comment":"§2.5: The dependence of the CHEFT basis on halo definition and mass resolution is acknowledged but not quantified. A short resolution or FoF-vs-SO comparison (even at fixed volume) would strengthen the claim that the collapse procedure is robust on scales k R_min ≪ 1.","section":"§2.5"},{"comment":"§2.9: Only the z=0 snapshot of a single 512 h⁻¹ Mpc box is used. This is acceptable for a proof-of-concept, but the text should flag more clearly that cosmic-variance and redshift dependence of the CHEFT templates remain untested.","section":"§2.9"},{"comment":"Fig. 1 caption and §2.5: “most-bound particle” is used as the halo centre; a one-sentence note on sensitivity to centre definition (e.g. centre-of-mass vs most-bound) would help reproducibility.","section":"Fig. 1, §2.5"},{"comment":"Eq. (26) and surrounding text: the mean subtraction ⟨O_i⟩ and the shot-noise subtraction via randomised catalogues are described, but the number of random realisations (stated as 10 only in App. A) should be given in the main methods section.","section":"§2.5, App. A"},{"comment":"Typographical: “there is is a non-zero shot-noise” (§2.5); “Int. Const.” label in Fig. 4 is cryptic; several figure legends use “lin” without defining the linear-bias halo-model curve in the caption.","section":"§2.5, Fig. 4"},{"comment":"References: the Web-Halo Model of Brieden et al. (2026) and related 2-halo improvements (Mead & Verde 2021; Nishimichi et al. 2019) are cited; a one-sentence quantitative comparison of residual accuracy in the transition regime would help place CHEFT relative to those approaches.","section":"§1, §5"}],"recommendation":"minor_revision","confidential_remarks":"Solid methods paper, appropriate for MNRAS. The free-parameter framing of CHEFText is the only point that could generate reader confusion; once the abstract/§5 wording is tightened the contribution is clear and the honest Appendix B is a genuine strength rather than a liability. I do not see a load-bearing error that would require major revision or rejection."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The real novelty is the collapse step: weight particles by the usual second-order Lagrangian operators, then move every particle inside a resolved halo to the halo centre before measuring the operator spectra. That cleanly strips the 1-halo piece so the templates can sit inside the standard halo-model 2-halo integral without double-counting. They then take the mass-dependent bias coefficients from an independent probabilistic peak-background-split measurement rather than fitting them to the spectra under test. That combination is new and useful.\n\nWhat works: on the matter field the construction recovers the power spectrum at the percent level once the mild mass-conservation constraints are imposed (Fig. 4). For SZ-like weights the baseline already does well, especially in the cross with matter. Appendix B is honest: even freely fitted bias vectors inside the same collapsed basis still fail to reproduce the full off-diagonal P_hh(k|M1,M2) matrix, especially for widely separated masses. That residual is exactly why CIB- and HOD-like weights (which draw from a broader intermediate-mass range) sit at 5–10 % rather than a few percent.\n\nThe soft spot is proportional, not fatal. The abstract’s stronger ~3–5 % claim for the weighted tracers is achieved only after promoting the Laplacian to an effective rescaling α(M)=c0+c1 log10 M fitted jointly to the same SZ/CIB/HOD spectra. So the pure predictive (no free bias) statement holds for CHEFTmin; the headline accuracy for the most interesting tracers is an effective absorption of missing cross-mass physics. The 1-halo term is also measured rather than modelled, so this is a clean proof-of-concept for the 2-halo piece, not a finished emulator. Citations look solid and the math is transparent.\n\nThis is for people who actually build multi-probe halo models (SZ, CIB, HOD + lensing). Worth a serious referee; I would bring it to reading group and expect to cite the collapse construction.","headline":"Clean collapse trick that makes HEFT usable as pure 2-halo templates; the no-free-bias claim is real for the baseline, while the abstract’s best numbers for CIB/HOD rest on a two-parameter effective Laplacian.","tokens_in":31370,"tokens_out":535,"would_cite":true,"duration_ms":6227,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Collapsing particles to halo centres turns nonlinear HEFT into a predictive 2-halo model with no free bias parameters.","keywords":["halo model","Hybrid Effective Field Theory","CHEFT","2-halo term","halo bias","large-scale structure","power spectrum","probabilistic bias"],"falsifier":"Measure the full shot-noise-subtracted cross-mass coherence matrix of halo centres in an independent simulation (or at higher resolution) and check whether the CHEFT prediction with fixed probabilistic biases recovers the off-diagonal entries for widely separated mass bins at the few-percent level; persistent large residuals would falsify the claim that the present operator basis is sufficient.","tokens_in":31187,"feed_emoji":"🌌","tokens_out":1015,"duration_ms":10055,"temperature":0.7,"pith_summary":"Standard halo models treat the 2-halo term with linear bias times the linear matter power spectrum, and that fails badly on the intermediate scales where 1-halo and 2-halo contributions meet. Pure Hybrid Effective Field Theory captures those nonlinearities but mixes intra-halo structure into the templates, so it cannot be dropped cleanly into the halo-model split. This paper builds collapsed HEFT (CHEFT): the same Lagrangian operators are measured after every particle in a halo is moved to the halo centre, stripping out 1-halo power while keeping the nonlinear inter-halo clustering. Halo bias coefficients as a function of mass come from the probabilistic bias method, so the model has no free bias parameters. On matter it recovers the power spectrum to about a percent across the transition; on mass-weighted tracers that mimic the SZ effect, the CIB, or HOD galaxies it reaches a few percent once a simple effective Laplacian term is restored. The result is a modular halo model that keeps the astrophysical interpretability of profiles and mass functions while using simulation-calibrated nonlinear templates for halo-centre clustering.","feed_headline":"Collapse haloes, keep the nonlinear 2-halo term","feed_subtitle":"CHEFT recovers matter power to ~1% and mass-weighted tracers to a few percent with no free biases","key_machinery":"Collapsed HEFT (CHEFT): the second-order Lagrangian operator fields of HEFT are rebuilt after every particle belonging to a resolved halo is displaced to that halo’s centre (field particles stay put). The resulting operator auto- and cross-spectra become the templates that multiply the mass-dependent bias coefficients in the 2-halo term.","core_discovery":"A collapsed HEFT basis, with particles inside each halo moved to the halo centre before operator spectra are measured, supplies nonlinear templates for the 2-halo term that are free of 1-halo contamination. Combined with mass-dependent Lagrangian bias coefficients taken from probabilistic bias, the construction yields a predictive halo-halo power spectrum with no free bias parameters and recovers the matter power spectrum at the percent level across the 1-halo/2-halo transition; mass-weighted tracers reach ~3–5 % once an effective Laplacian contribution is included.","pith_inferences":["If the residual cross-mass incoherence is largely stochastic or exclusion-driven, a compact noise model or halo-exclusion counterterm may restore percent-level accuracy without enlarging the deterministic operator basis.","The same collapse idea could be applied to higher-order statistics (bispectra, marked power spectra) to keep 1-halo and 2-halo contributions cleanly separated.","Because the effective Laplacian calibration appears largely probe-independent in the tests shown, a single mass-dependent correction may suffice for a wide class of mass-weighted observables."],"forward_implications":["The 1-halo term can be modelled independently with astrophysical profiles while the 2-halo term remains simulation-calibrated and free of free bias parameters.","Multi-probe analyses that combine weak lensing or galaxy clustering with SZ, CIB or X-ray maps can use a single coherent description of the transition regime.","Emulators of the CHEFT operator spectra and bias functions would turn the method into a cosmology- and redshift-dependent predictive tool.","Once the 2-halo accuracy is fixed, the dominant remaining theoretical uncertainty for these observables is the modelling of halo profiles, occupation statistics and their covariances."],"fun_headline_variants":["Collapse particles: clean nonlinear 2-halo templates in CHEFT","Hybrid HEFT supplies predictive halo-halo power with no free biases","Collapsed HEFT recovers matter power to percent level across transition","Mass-dependent biases plus collapsed operators for weighted tracers","CHEFT joins halo model with HEFT templates free of 1-halo terms"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The finite second-order set of collapsed operators, together with bias coefficients measured at one smoothing scale, is assumed to capture how different halo masses stay coherent with one another; Appendix B shows that even freely fitted biases inside the same basis still fail for widely separated masses.","fun_headline_variants_meta":{"raw":{"variants":["Collapse particles: clean nonlinear 2-halo templates in CHEFT","Hybrid HEFT supplies predictive halo-halo power with no free biases","Collapsed HEFT recovers matter power to percent level across transition","Mass-dependent biases plus collapsed operators for weighted tracers","CHEFT joins halo model with HEFT templates free of 1-halo terms"]},"model":"grok-4.5","effort":"low","cost_usd":0.003632,"raw_usage":{"total_tokens":1258,"prompt_tokens":883,"num_sources_used":0,"completion_tokens":91,"cost_in_usd_ticks":36320000,"prompt_tokens_details":{"text_tokens":883,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":284,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":883,"tokens_out":91,"duration_ms":4926,"temperature":1.0,"reasoning_tokens":284,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T02:02:55.624413+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure the full shot-noise-subtracted cross-mass coherence matrix of halo centres in an independent simulation (or at higher resolution) and check whether the CHEFT prediction with fixed probabilistic biases recovers the off-diagonal entries for widely separated mass bins at the few-percent level; persistent large residuals would falsify the claim that the present operator basis is sufficient.","supporting_citations":[],"review_version":1}