{"id":"4308fc2e-b62b-4d8b-a518-ccde54c92f11","arxiv_id":"2607.03514","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"With fixed known initial phases, voxel-by-voxel Poisson likelihood on the galaxy number-counts field breaks the f(R)–bias degeneracy that power spectra cannot resolve, with voids and walls driving the gain.","lead":"Field-level analysis of the full 3D galaxy map, not just its power spectrum, can separate modified gravity from galaxy bias when initial phases are known. This matters because Stage-IV surveys will be limited by that exact degeneracy if they stick to two-point statistics.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.5","headline":"The fixed-phase idealisation is already the paper's own stated limit; no deeper internal flaw undercuts the controlled claim.","rationale":"The Reader correctly isolates the fixed-phase assumption as the weakest (and most load-bearing) idealisation and correctly grades the paper CONDITIONAL rather than ACCEPT. The controlled claim itself holds under the conditions the authors set: the phase-only test of §5.4, the void/wall attribution of §5.3, and the multi-seed/Poisson robustness of §6 all corroborate that non-Gaussian morphology supplies the extra information once phases are known. Because that idealisation is stated honestly and no deeper internal inconsistency was found, no verdict adjustment is warranted. The concrete test above simply makes the already-acknowledged limitation quantitative for future work.","tokens_in":31272,"tokens_out":530,"duration_ms":5327,"concrete_test":"Re-run the F6 full-field MCMC of §5.1 after replacing the fixed-phase COLA realisations with an ensemble of ~20 independent initial seeds (or a cheap BORG-style phase marginalisation if available) while keeping the same bias and Poisson setup; if the |f_R0|–eta degeneracy reappears at the level of the original P_g(k) contours, the practical value of the phase-driven break is confirmed to be limited to the idealised setting already claimed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is carefully scoped: with fixed and known initial phases, the full-field Poisson likelihood on n_g breaks the |f_R0|–eta degeneracy that P_g(k) cannot (Table 1, Fig. 2, §5.1). The authors themselves flag that pure-phase information will vanish once phases are marginalised (§5.4, §7), so the load-bearing idealisation is already transparent. Under that idealisation the pipeline is internally consistent: COLA + local bias + Poisson likelihood, fixed seed, N-normalisation that keeps N_tot constant, and explicit phase-only vs amplitude-only tests all support the reported tightening. No hidden inconsistency in the likelihood construction, cosmic-web attribution, or robustness suite appears to invalidate the controlled demonstration. The only residual technical softness is that the bias model is local-in-density and only eta is varied (N, \rho, ε fixed or retuned), but this is an acknowledged simplification, not a contradiction of the claim as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper develops a field-level Bayesian inference pipeline that evaluates a Poisson likelihood directly on the 3D galaxy number-counts field n_g, jointly constraining the Hu–Sawicki |f_R0| and the primary local bias parameter β. Dark-matter fields are generated with MG-extended COLA under fixed initial phases; galaxies are painted with a four-parameter non-linear bias model (only β free, N retuned to keep N_tot fixed). On controlled mocks the full-field analysis yields tighter, less degenerate posteriors than a Gaussian power-spectrum likelihood (Table 1, Fig. 2), isolates the contribution of Fourier phases (§5.4), attributes most of the gain to under-dense voxels via cosmic-web classification (§5.3), and demonstrates robustness to Poisson seeds, initial-condition realisations and number-count thresholding (§6).","tokens_in":31580,"tokens_out":1060,"duration_ms":15118,"significance":"If the controlled demonstration holds, the work supplies a concrete, reproducible illustration that non-Gaussian morphology and phase information can break the classic MG–bias degeneracy that limits two-point analyses. The explicit phase-only versus amplitude-only comparison, the voxel-level likelihood decomposition, and the suite of 100 Poisson + 5 IC robustness tests are genuine strengths that make the result falsifiable and useful for Stage-IV survey forecasts. The transparent scoping to fixed known phases (already flagged by the authors) keeps the claim honest while still charting a path toward BORG-style marginalisation and field-level emulators.","major_comments":[{"comment":"§5.4 and §7 correctly note that pure-phase information vanishes once initial phases are marginalised, yet the abstract and the final sentence of the conclusions still present the degeneracy-breaking result as a “powerful path forward for \tau next-generation surveys” without quantifying residual constraining power from non-Gaussian amplitudes alone. A short forecast (or at least a clear statement) of what survives after phase marginalisation is needed for the claim to remain load-bearing outside the idealised setting.","section":null},{"comment":"§2.3 and §3.1 fix ρ and ε at the Jasche & Lavaux (2019) values and only vary β (with N retuned). Because the exponential void-suppression term is precisely the piece that couples most strongly to the under-dense voxels identified as the main drivers in §5.3, the reported degeneracy breaking may be optimistic relative to a fully free local (or non-local) bias model. At minimum the authors should show one additional run in which ρ and ε are also free, or justify why the present restriction does not affect the central comparison.","section":null},{"comment":"The COLA implementation (§2.2) uses a modest number of time-steps and a linear-field screening approximation. Under-dense regions, which dominate the likelihood ratios in Tables 2–5, are exactly where chameleon screening is weakest and residual force errors are largest. A quantitative comparison of the FML-COLA density field against a full N-body MG run (or a published accuracy benchmark at the same resolution) for the void/wall voxels that drive the constraints would strengthen the claim that the reported |f_R0| posteriors are not resolution artefacts.","section":null}],"minor_comments":[{"comment":"Fig. 1 (right) correlation matrix and Fig. 3 power-spectrum ratios would benefit from explicit k-bin labels or a second x-axis in h Mpc^{-1} so that the scale dependence of the residual degeneracy is immediately readable.","section":null},{"comment":"Eq. (3) and the surrounding text use both n_g and n_g interchangeably; a single consistent notation for the expected galaxy count field would improve readability.","section":null},{"comment":"The Percival correction is cited (Percival et al. 2022) but the numerical value of the factor F applied to the 1024-realisation covariance is never stated; a one-line addition in §3.2.1 would aid reproducibility.","section":null},{"comment":"Several sentences in the abstract and introduction still contain concatenated words (“Wepresentafield-level\tldots”, “Non-linearstructureformation\tldots”); these are residual typesetting artefacts that should be cleaned.","section":null},{"comment":"Table 1 reports 95 % upper limits for the GR case and 68 % intervals for F6; a uniform confidence level (or an explicit note) would make the comparison cleaner.","section":null}],"recommendation":"minor_revision","confidential_remarks":"Solid, carefully scoped methods paper that belongs in MNRAS. The fixed-phase idealisation is already transparent, so the remaining issues are addressable with modest additional runs or clearer wording; I do not see grounds for rejection or major conceptual overhaul."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful takeaway is simple: with fixed known initial phases, the voxel-wise Poisson likelihood on the 3D galaxy counts field tightens both |f_R0| and β and kills the strong degeneracy that P_g(k) cannot resolve (Table 1, Fig. 2). They also show the information lives mainly in voids and walls, and that phases alone already help while amplitudes alone do not fully break the degeneracy.\n\nWhat is new is not field-level inference itself (BORG etc. already exist), but the controlled head-to-head on the specific MG–bias problem, plus the cosmic-web localisation and the explicit phase-only vs amplitude-only test. The pipeline is careful: same COLA seed for all models, N retuned so N_tot is fixed, Percival-corrected covariance, truncated Poisson for thresholding, 100 Poisson realisations and 5 IC realisations for robustness. The claim as scoped is solid.\n\nThe soft spot is exactly the one they flag: phases are known a priori. They state clearly that marginalising over them on real data will erase the pure-phase contribution that currently does the heavy lifting. The bias model is also simplified (local-in-density, only β free; ρ, ε fixed). That is an acknowledged limitation, not a hidden flaw. COLA + local bias is fine for a proof-of-concept; they already point to emulators and BORG-style phase sampling as next steps. Code/data are not public, which is a minor practical annoyance.\n\nThis is for people working on Stage-IV LSS gravity tests or field-level methods. It is not a finished survey pipeline, but it is a clear, honest demonstration that the information is there under ideal conditions and where it sits. I would send it to referees; the idealisation is transparent and the controlled result is worth having on the record. Worth citing when discussing how much of the FLI gain survives phase marginalisation.","headline":"Clean controlled demo that field-level Poisson on n_g breaks the f(R)–β degeneracy under known phases; the idealisation is already their stated limit.","tokens_in":32183,"tokens_out":505,"would_cite":true,"duration_ms":5338,"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":"Field-level analysis of the full galaxy map breaks the modified-gravity/bias degeneracy that power spectra cannot resolve.","keywords":["field-level inference","modified gravity","f(R) gravity","galaxy bias","large-scale structure","cosmic web","COLA","Fourier phases"],"falsifier":"Repeat the identical mock analysis after freely sampling the initial phases (or after replacing the fixed-phase COLA realisations with a full Bayesian reconstruction that marginalises over them) and check whether the |f_R0|–β degeneracy reappears at the power-spectrum level of width.","tokens_in":32174,"feed_emoji":"✨","tokens_out":930,"duration_ms":7709,"temperature":0.7,"pith_summary":"Power-spectrum analyses of galaxy clustering cannot cleanly separate the effects of modified gravity from those of galaxy bias, because both can raise or lower clustering amplitude on similar scales. This paper shows that comparing the full three-dimensional galaxy number-count field, voxel by voxel, recovers the missing non-Gaussian and Fourier-phase information and thereby breaks the degeneracy. On controlled mocks with known initial conditions, the field-level Poisson likelihood returns substantially tighter, unbiased constraints on both the Hu–Sawicki parameter |f_R0| and the leading bias parameter β than a power-spectrum analysis of the same data. Under-dense regions (voids and walls) supply most of the distinguishing power. The result is a concrete demonstration that next-generation surveys can test gravity more sharply once the entire map, rather than its two-point summary, is used.","feed_headline":"Full galaxy maps break the gravity-bias degeneracy power spectra cannot","feed_subtitle":"Voxel-by-voxel Poisson likelihoods on mocks tighten |f_R0| and β constraints and separate the two effects","key_machinery":"The full-field Poisson likelihood: each voxel is treated as an independent Poisson draw whose mean is the predicted galaxy count under a given (f_R0, β) model; the global log-likelihood is simply the sum over all voxels, thereby retaining both Fourier amplitudes and phases.","core_discovery":"When initial phases are fixed and known, a Bayesian Poisson likelihood evaluated on the three-dimensional galaxy number-count field jointly constrains |f_R0| and the primary bias parameter β more tightly than a Gaussian power-spectrum likelihood and, crucially, breaks the strong degeneracy between the two parameters that is inherent to two-point statistics.","pith_inferences":["Once initial phases must be marginalised, residual field-level gains will come mainly from non-Gaussian amplitude information rather than pure morphology, so hybrid likelihoods that keep higher-order moments may still outperform pure two-point analyses.","The finding that n_g = 1 voxels in voids/walls are the most informative suggests that carefully selected void and wall catalogues could serve as cheaper, partially field-level probes even before full map-level inference is routine.","Because the degeneracy-breaking is environment-dependent, any residual screening or assembly-bias mismodelling will appear first as spatially coherent residuals in under-dense regions, giving a practical diagnostic for model misspecification."],"forward_implications":["Stage-IV surveys can extract substantially tighter joint constraints on gravity and bias by analysing the three-dimensional galaxy field rather than power spectra alone.","Cosmic-web classifiers applied to the underlying density field can isolate which environments (especially voids and walls) drive gravity constraints.","Phase information alone already prefers the correct |f_R0|; combining it with amplitudes yields the tightest joint posteriors.","The same pipeline is modular and can incorporate field-level emulators, more complete bias models, weak lensing, and redshift-space distortions."],"fun_headline_variants":["Field-level maps break MG-bias degeneracy power spectra cannot","3D galaxy fields separate f(R) gravity from bias better than spectra","Fixed-phase voxel likelihoods disentangle |f_R0| and β","Galaxy number counts break two-point MG-bias degeneracy","Field-level inference tightens |f_R0| and β over power spectra"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The initial phases of the dark-matter density field are assumed known and fixed; the paper itself notes that marginalising over them on real data is expected to remove the pure-phase information that currently breaks the degeneracy.","fun_headline_variants_meta":{"raw":{"variants":["Field-level maps break MG-bias degeneracy power spectra cannot","3D galaxy fields separate f(R) gravity from bias better than spectra","Fixed-phase voxel likelihoods disentangle |f_R0| and β","Galaxy number counts break two-point MG-bias degeneracy","Field-level inference tightens |f_R0| and β over power spectra"]},"model":"grok-4.5","effort":"low","cost_usd":0.007812,"raw_usage":{"total_tokens":1932,"prompt_tokens":849,"num_sources_used":0,"completion_tokens":82,"cost_in_usd_ticks":78120000,"prompt_tokens_details":{"text_tokens":849,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1001,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":849,"tokens_out":82,"duration_ms":7466,"temperature":1.0,"reasoning_tokens":1001,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T01:56:48.636671+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Repeat the identical mock analysis after freely sampling the initial phases (or after replacing the fixed-phase COLA realisations with a full Bayesian reconstruction that marginalises over them) and check whether the |f_R0|–β degeneracy reappears at the power-spectrum level of width.","supporting_citations":[],"review_version":1}