{"id":"01aa6df2-7c1e-4975-a0ee-e670f84b67ad","arxiv_id":"2607.09569","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":7,"one_line_summary":"H-MOG recovers unsigned 3D jet magnetic orientation at ⟨|cos|⟩≃0.95–0.98 from W(z) and p(z), but the poloidal sense is unrecoverable because those observables are invariant under B→−B.","lead":"H-MOG reconstructs 3D magnetic field orientation in relativistic jets from jet width and linear polarization, recovering it at 95–98% accuracy across ten GRMHD models. It also proves the field sense is formally unrecoverable from those parity-even observables, so circular polarization or Faraday tomography is required.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The reader's weakest_assumption correctly flags the axisymmetrized 96^{3} cubes, but that choice is deliberate and acknowledged: the observables inverted are themselves dominated by the axisymmetric structure, and the scoring is against the same representation. It therefore does not reverse either the geometry-recovery claim or the formal non-identifiability of sense. No other load-bearing gap appears: the synthetic validation isolates the method, the library spans MAD/SANE and five spins, the prior is even by construction (h=0), and the failed recovery routes are diagnosed rather than papered over. The honest conclusion is that the argument stands; the reader's ACCEPT verdict needs no adjustment.","tokens_in":20527,"tokens_out":477,"duration_ms":6544,"concrete_test":"Re-run one MAD and one SANE reconstruction after replacing the axisymmetric mean cubes with full-φ native fields resampled onto a finer Cartesian lattice (e.g. 192^{3}) that better resolves the near-axis funnel; if ⟨|cos|⟩ remains ≳0.9 and signed ⟨cos⟩ stays near zero, the geometry/sense separation is robust to the resampling step.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claims hold under scrutiny. Proposition 1 is a short, correct invariance argument: W and p (and the retained even prior) are unchanged under B\to-B, so sense is non-identifiable from those data alone. The three recovery routes are tested and each fails for a named physical reason (projection/averaging for RM; near-axis coarse-graining for full 3D; non-monotonic spin–sense relation for the BZ prior). The high ⟨|cos|⟩ scores are measured against the same axisymmetrized Cartesian cubes that the forward model sees, so they correctly quantify recovery of the large-scale mean geometry the method is designed for; the paper states this limitation explicitly (Sect. 3.2, 6.3) and does not claim recovery of native non-axisymmetric turbulence. That modeling choice therefore does not undermine the stated claims.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper introduces H-MOG, a variational method that reconstructs the 3D magnetic field of a relativistic jet on a Cartesian lattice from two projected observables, the jet width W(z) and linear polarization degree p(z), regularized by a Hamiltonian prior and optimized with automatic differentiation. Applied to ten GRMHD models spanning MAD and SANE states and five black-hole spins, it recovers the unsigned field orientation at ⟨|cos|⟩ ≃ 0.95–0.98. Proposition 1 proves that W and p (and the retained even prior) are invariant under B → −B, so the poloidal sense is formally non-identifiable from these data. Three routes to break the degeneracy—an RM term, full 3D sampling, and a Blandford–Znajek spin prior—are tested and each fails for a distinct physical reason; the spin–sense relation in the simulated jets is shown to be non-monotonic and state-dependent. The authors conclude that recovering sense requires a parity-odd observable such as Faraday tomography or circular polarization.","tokens_in":20734,"tokens_out":966,"duration_ms":9932,"significance":"If the results hold, the paper cleanly separates what current VLBI/EHT linear-polarization and width data can determine (large-scale helical geometry) from what they cannot (poloidal sense). The formal invariance argument, the multi-model GRMHD campaign with reported snapshot scatter, the synthetic-jet validation across pitch and noise, and the explicit diagnosis of three failed recovery routes are all strengths. The finding that the spin–sense relation is not monotonic in these turbulent jets is an astrophysical result in its own right and cautions against silently imposing a BZ prior. The work is directly relevant to ongoing and next-generation EHT analyses of M87* and Sgr A*.","major_comments":[{"comment":"The high ⟨|cos|⟩ scores are measured against the same axisymmetrized, azimuthally averaged Cartesian cubes that the simplified forward model (ε ∝ |B|²) sees (Sect. 3.2). The paper states this limitation and does not claim recovery of native non-axisymmetric turbulence, so the central geometry claim remains sound for the large-scale mean field. A short, explicit statement in the abstract or conclusions that the reported accuracy is for the axisymmetric mean geometry would prevent over-reading by non-specialists.","section":null}],"minor_comments":[{"comment":"Table 1 and Table D.1 both report reconstruction statistics; a single consolidated table (or a clear pointer that D.1 is the complete version) would reduce redundancy.","section":null},{"comment":"In Sect. 2.3 the plane-of-sky angle is written χ = arctan(Bz/Bx) + π/2; a brief note on the branch choice and how it is handled under automatic differentiation would aid reproducibility.","section":null},{"comment":"Fig. 12 caption and text use “verso” for the mean poloidal sense; standard English “sense” or “sign” would be clearer for an international readership.","section":null},{"comment":"Appendix C and Figs. D.1–D.2 usefully document convergence; a one-sentence statement of the final data residual level (already sub-percent) in the main text of Sect. 2.4 would help readers who skip the appendix.","section":null},{"comment":"The frame-dragging term H_frame is correctly set to h = 0 for the main runs; stating the numerical value of h used in the failed Test 3 (Sect. 6.4) would make that experiment fully reproducible from the text alone.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is unusually clear about a negative result (the sign degeneracy) and diagnoses why three recovery routes fail. That honesty is a strength for A&A. The axisymmetrization step is the only modeling choice that could be over-read; the authors already flag it, so I do not see it as grounds for revision beyond a clarifying sentence. I recommend accept."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The useful takeaway is simple. From jet width and linear polarization alone you can recover the large-scale 3D helical geometry of a relativistic jet at high fidelity, but you cannot recover the poloidal sense, and the paper proves why.\n\nWhat is new is H-MOG: a lattice variational reconstructor (amplitude plus unit direction on a 96^{3} cube) regularized by an even Hamiltonian prior and optimized with automatic differentiation. It is not a parametric helix fit. They score it on the public Dhruv et al. library—ten models, MAD and SANE, five spins—and get ⟨|cos|⟩ ≃ 0.95–0.98 against the axisymmetrized truth cubes. Synthetic jets recover known pitch; noise and prior-weight sweeps show the geometry is data-driven, not prior-dictated. Proposition 1 is short and correct: W and p (and the retained prior) are invariant under B → −B, so sense is non-identifiable. The three attempted fixes—RM term, full 3D sampling, BZ spin prior—each fail for a distinct, diagnosed reason; the non-monotonic spin–sense relation in the MAD/SANE fields is itself a useful side result.\n\nThe soft spot is real but already stated: the “truth” fields are azimuthally averaged and resampled onto a uniform Cartesian cube, so the high scores measure recovery of the large-scale mean geometry the simplified forward model (ε ∝ |B|^{2}) can see, not native non-axisymmetric turbulence. That does not reverse the claims; it bounds them. No code is shipped, but the method is detailed enough to re-implement. Citations look standard and appropriate.\n\nThis is for people who work on EHT/VLBI jet magnetometry or GRMHD interpretation. It cleanly separates what current parity-even data can and cannot measure and supplies a practical free-field tool. I would send it to peer review without hesitation; the central argument holds.","headline":"Clean free-field reconstructor plus a formal non-identifiability proof: unsigned jet geometry is recoverable from W and p at high fidelity; poloidal sense is not, and three recovery routes fail for named physical reasons.","tokens_in":21351,"tokens_out":507,"would_cite":true,"duration_ms":5088,"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":"Jet width and linear polarization recover 3D magnetic geometry but never the field's sense of direction.","keywords":["relativistic jets","magnetic fields","GRMHD","linear polarization","variational reconstruction","sign degeneracy","Faraday rotation","circular polarization"],"falsifier":"Apply H-MOG to a GRMHD library that retains full non-axisymmetric structure and higher near-axis resolution, then check whether the unsigned alignment stays near 0.95–0.98 and whether any parity-even addition (or a parity-odd observable) can raise the signed alignment above chance.","tokens_in":21370,"feed_emoji":"🧲","tokens_out":702,"duration_ms":5117,"temperature":0.7,"pith_summary":"Every resolved image of a relativistic jet encodes its magnetic field, yet synchrotron intensity and linear polarization are blind to which way the field points along the jet axis: both depend only on even combinations of the field components. This paper introduces H-MOG, a variational method that reconstructs the full three-dimensional magnetic field on a lattice from two projected observables—the jet width profile W(z) and the linear polarization degree p(z)—regularized by a Hamiltonian prior and optimized by automatic differentiation. Applied to ten GRMHD simulations spanning MAD and SANE accretion states and five black-hole spins, the method recovers the unsigned field orientation at alignment 0.95–0.98, far above chance. The sense of the poloidal field, however, is not recovered; the paper proves it cannot be, because both observables are invariant under global field reversal. Three attempted routes to break that degeneracy—an added rotation-measure term, full non-axisymmetric sampling, and a Blandford–Znajek spin prior—all fail for distinct physical reasons. The result draws a clean observational boundary: geometry is measurable with present VLBI data, while sense requires a parity-odd observable such as Faraday tomography or circular polarization.","feed_headline":"Jet images recover magnetic geometry but never its sense","feed_subtitle":"Width and polarization fix 3D orientation at 95–98 percent; field direction requires a parity-odd observable","key_machinery":"H-MOG, a Hamiltonian-regularized variational inversion that reconstructs amplitude and unit direction of the magnetic field on a Cartesian lattice from projected W(z) and p(z), optimized by automatic differentiation; its even prior and data terms make the sign degeneracy exact (Proposition 1).","core_discovery":"From jet width and linear polarization alone, H-MOG recovers the unsigned three-dimensional magnetic geometry of relativistic jets at ⟨|cos|⟩ ≃ 0.95–0.98 across ten GRMHD models; the poloidal sense cannot be recovered because those observables are invariant under B → −B, and three physically motivated attempts to break the degeneracy all fail for identifiable reasons.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["H-MOG recovers unsigned jet B-geometry at 95-98% accuracy","Jet width and polarization fix 3D field orientation not sense","Magnetic polarity of jets remains hidden from W and p alone","Unsigned 3D field maps across GRMHD; B to -B invariance holds","Parity-odd data required to break jet magnetic sign degeneracy"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The truth fields used for scoring are axisymmetric mean fields after azimuthal averaging and resampling onto a uniform coarse Cartesian cube, so the high reported alignment measures recovery of large-scale mean geometry rather than the full native turbulent field.","fun_headline_variants_meta":{"raw":{"variants":["H-MOG recovers unsigned jet B-geometry at 95-98% accuracy","Jet width and polarization fix 3D field orientation not sense","Magnetic polarity of jets remains hidden from W and p alone","Unsigned 3D field maps across GRMHD; B to -B invariance holds","Parity-odd data required to break jet magnetic sign degeneracy"]},"model":"grok-4.5","effort":"low","cost_usd":0.005482,"raw_usage":{"total_tokens":1543,"prompt_tokens":848,"num_sources_used":0,"completion_tokens":97,"cost_in_usd_ticks":54820000,"prompt_tokens_details":{"text_tokens":848,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":598,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":848,"tokens_out":97,"duration_ms":7699,"temperature":1.0,"reasoning_tokens":598,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T02:04:22.439505+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Apply H-MOG to a GRMHD library that retains full non-axisymmetric structure and higher near-axis resolution, then check whether the unsigned alignment stays near 0.95–0.98 and whether any parity-even addition (or a parity-odd observable) can raise the signed alignment above chance.","supporting_citations":[],"review_version":1}