{"id":"51412cb0-7b01-4afc-aa0a-3f3d78f5207c","arxiv_id":"2606.19431","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A parity-breaking chiral extension of the FHP cellular automaton is constructed and shown to yield hydrodynamics with odd viscosity, verified through Poiseuille-flow simulations.","lead":"The authors modify the classic FHP lattice-gas cellular automaton by adding chiral collision rules and velocity rotations that mimic a magnetic field. The resulting discrete model produces macroscopic hydrodynamics that include odd viscosity, a transverse transport coefficient characteristic of odd fluids.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Velocity rotation on discrete triangular lattice may break 6-fold symmetry, allowing anisotropic corrections beyond odd viscosity in the hydro limit","rationale":"The reader's weakest assumption correctly flags the coarse-graining step. The more precise load-bearing point is the symmetry reduction induced by the discrete rotation, which directly threatens whether the coarse-grained equations contain only the desired odd term. This moves the verdict from UNVERDICTED to CONDITIONAL pending the explicit isotropy check; the reader's abstract-only limitation is thereby addressed without altering the core concern.","tokens_in":1685,"tokens_out":387,"duration_ms":20411,"concrete_test":"Recompute the linearized collision operator and the resulting viscosity tensor (Eq. for stress in § on hydro derivation) after applying the velocity-rotation map to the six discrete velocities; extract all independent components of the fourth-rank tensor and confirm that only the odd-viscosity coefficient is nonzero while the six even anisotropic coefficients remain below 1% of the shear viscosity. If any anisotropic coefficient exceeds that threshold the claim that the model yields 'a hydrodynamic model with odd viscosity' (without further terms) does not hold.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that the two modifications (chiral collisions + systematic velocity rotation) produce Navier-Stokes augmented solely by an odd-viscosity term after coarse-graining. On the FHP triangular lattice the velocity set is discrete; any rotation operation that is not an exact lattice automorphism necessarily reduces the symmetry group. If the Chapman-Enskog or moment expansion in the paper does not explicitly recompute the fourth-rank viscosity tensor after the rotation and verify that only the antisymmetric odd component survives while all anisotropic even components remain zero, the hydrodynamic model is under-specified. The Poiseuille simulations cannot by themselves rule out such hidden lattice artifacts because the flow geometry is aligned with a single axis.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The paper constructs a parity-breaking extension of the FHP lattice-gas cellular automaton on the triangular lattice by adding chiral two-body collisions and a systematic velocity-rotation step. It claims that systematic coarse-graining (via Chapman-Enskog or moment methods) produces the 2D Navier-Stokes equations augmented solely by an odd-viscosity term whose coefficient is derived analytically from the microscopic rules; the analytic transport coefficients are then checked against Poiseuille-flow simulations of the automaton.","tokens_in":1825,"tokens_out":487,"duration_ms":15791,"significance":"If the derivation is free of hidden fitting parameters and the hydrodynamic limit indeed contains only the isotropic odd-viscosity contribution, the work supplies a fully discrete, bottom-up microscopic realization of odd hydrodynamics. This is valuable for testing theories of chiral active matter and for exploring whether odd viscosity can be engineered from local parity-breaking scattering without continuous-space assumptions.","major_comments":[{"comment":"The central claim requires that the velocity-rotation operation, which is not a lattice automorphism of the FHP velocity set, leaves the fourth-rank even viscosity tensor isotropic. No section or equation is cited that recomputes the full viscosity tensor (including all anisotropic even components) after the rotation is introduced; the analytic derivation therefore remains incomplete on this load-bearing point.","section":"analytic derivation of transport coefficients"},{"comment":"Poiseuille-flow simulations are performed only for flow aligned with a single lattice axis. Because any residual anisotropic even-viscosity terms would be most visible under rotated forcing or in a different channel orientation, the existing numerical tests cannot rule out lattice artifacts that would appear in the hydrodynamic equations beyond the odd-viscosity term.","section":"Poiseuille-flow simulations"}],"minor_comments":[{"comment":"The abstract states that transport coefficients are 'verified analytically and via Poiseuille-flow simulations,' but the manuscript does not tabulate the numerical values extracted from the simulations alongside the analytic expressions for direct comparison.","section":null},{"comment":"Notation for the chiral collision operator and the rotation angle should be introduced with an explicit equation number in the model-definition section to allow readers to reproduce the microscopic rules.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments. We address each major comment below and indicate the revisions that will be made to strengthen the manuscript.","responses":[{"response":"We agree that the manuscript's analytic section derives the odd-viscosity coefficient but does not explicitly recompute the complete fourth-rank even-viscosity tensor after the velocity-rotation step is added. In the revised version we will carry out the full Chapman-Enskog (or moment) expansion of all transport coefficients, including verification that the even part remains isotropic, and will cite the relevant equations and results.","revision_made":"yes","referee_comment":"[analytic derivation of transport coefficients] The central claim requires that the velocity-rotation operation, which is not a lattice automorphism of the FHP velocity set, leaves the fourth-rank even viscosity tensor isotropic. No section or equation is cited that recomputes the full viscosity tensor (including all anisotropic even components) after the rotation is introduced; the analytic derivation therefore remains incomplete on this load-bearing point."},{"response":"We concur that simulations restricted to a single lattice alignment are insufficient to exclude possible residual anisotropy. The revised manuscript will include additional Poiseuille-flow runs with channel orientations rotated by 30 degrees relative to the lattice axes, together with quantitative comparison to the analytic transport coefficients, to confirm that no anisotropic even-viscosity terms appear.","revision_made":"yes","referee_comment":"[Poiseuille-flow simulations] Poiseuille-flow simulations are performed only for flow aligned with a single lattice axis. Because any residual anisotropic even-viscosity terms would be most visible under rotated forcing or in a different channel orientation, the existing numerical tests cannot rule out lattice artifacts that would appear in the hydrodynamic equations beyond the odd-viscosity term."}],"tokens_in":1359,"tokens_out":395,"duration_ms":19791,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's core contribution is a concrete extension of the FHP lattice gas: chiral two-body collisions plus a systematic velocity rotation on the triangular lattice, designed to generate odd viscosity at the hydrodynamic level.\n\nThis is new. Prior lattice-gas work stayed parity-even; here the rules are built to break it from the start, and the authors claim the transport coefficients follow directly from the automaton without extra fitting.\n\nThe simulations of Poiseuille flow are a reasonable first check, and the absence of free parameters in the construction is a plus for this style of model.\n\nThe soft spot is the symmetry issue raised in the stress-test note. Rotating velocities on a discrete six-direction lattice is not an automorphism, so the fourth-rank viscosity tensor could pick up anisotropic even components that survive coarse-graining. The abstract does not state that the full tensor was recomputed after the rotation, and single-axis Poiseuille flow would not catch off-axis artifacts. If the Chapman-Enskog section does not close this gap, the claim that the macro equations contain only standard NS plus odd viscosity is under-supported.\n\nThe work is aimed at people who build or use lattice gases for parity-odd hydrodynamics. It is coherent on its own terms and shows clear thinking about the microscopic origin of odd viscosity, so it deserves a serious referee even if revisions are needed on the symmetry analysis.","headline":"A chiral FHP automaton that produces odd viscosity from explicit parity-breaking rules, but the hydro limit after velocity rotation needs explicit checks for hidden anisotropy.","tokens_in":2296,"tokens_out":352,"would_cite":false,"duration_ms":17964,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A chiral version of the FHP cellular automaton produces hydrodynamic equations containing odd viscosity.","keywords":["cellular automata","lattice gas","odd viscosity","chiral fluids","hydrodynamics","parity breaking","FHP model"],"falsifier":"If Poiseuille-flow simulations of the automaton fail to produce the transverse velocity component predicted by the analytically derived odd-viscosity coefficient, the claim is falsified.","tokens_in":2603,"feed_emoji":"💧","tokens_out":650,"duration_ms":22191,"temperature":0.7,"pith_summary":"The authors modify the standard FHP lattice gas model by adding chiral two-body collision rules and rotating particle velocities in a way that mimics a background field. These changes break parity at the microscopic level. Upon coarse-graining the discrete dynamics, the resulting equations are the usual Navier-Stokes equations plus an additional term that encodes odd viscosity, a transport coefficient that acts perpendicular to the flow. The coefficients are derived directly from the automaton rules and then checked against direct simulations of flow through a channel. The construction therefore supplies an explicit particle-based route from parity-breaking scattering events to macroscopic odd-fluid behavior.","feed_headline":"Chiral automaton produces odd-viscosity hydrodynamics","feed_subtitle":"Parity-breaking collision rules and velocity rotations on a lattice yield Navier-Stokes equations with a transverse viscosity term, verified","key_machinery":"The chiral FHP automaton, defined by parity-breaking two-body collisions together with velocity rotations on the triangular lattice.","core_discovery":"Introducing chiral collision rules and systematic velocity rotations into the FHP automaton on the triangular lattice yields a hydrodynamic model whose transport includes a nonzero odd-viscosity coefficient. The coefficient is obtained analytically from the microscopic collision and propagation rules without additional fitting. Poiseuille-flow simulations of the discrete automaton reproduce the transverse effects predicted by the augmented Navier-Stokes equations.","pith_inferences":["The same rule-modification strategy could be applied to other lattice geometries or to three-dimensional automata to generate additional odd transport coefficients.","Because the model is fully discrete and deterministic, it offers a setting in which to test how odd viscosity interacts with lattice-scale fluctuations or boundaries.","The construction suggests a route to embed other parity-odd effects, such as those appearing in active or driven systems, directly into lattice gas rules."],"forward_implications":["The macroscopic equations recovered from the automaton contain the standard viscous terms plus a transverse odd-viscosity contribution whose magnitude is fixed by the chirality parameters.","Channel-flow simulations directly confirm that the analytically computed transport coefficients govern the observed flow profiles.","Parity breaking at the level of local particle collisions is sufficient to generate the macroscopic odd-viscosity effect.","The discrete model supplies a bottom-up particle description of odd fluids that does not presuppose continuum equations."],"fun_headline_variants":["Chiral automaton yields odd-viscosity flow","Parity-breaking lattice gas creates odd fluids","Chiral FHP model adds odd viscosity","Cellular automaton produces transverse viscosity"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"That coarse-graining the modified collision and propagation rules produces the Navier-Stokes equations with an added odd-viscosity term and requires no extra adjustments.","fun_headline_variants_meta":{"raw":{"variants":["Chiral automaton yields odd-viscosity flow","Parity-breaking lattice gas creates odd fluids","Chiral FHP model adds odd viscosity","Cellular automaton produces transverse viscosity"]},"model":"grok-4.3","cost_usd":0.002837,"raw_usage":{"total_tokens":1566,"prompt_tokens":647,"num_sources_used":0,"completion_tokens":51,"cost_in_usd_ticks":28374500,"prompt_tokens_details":{"text_tokens":647,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":868,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":647,"tokens_out":51,"duration_ms":8762,"temperature":1.0,"reasoning_tokens":868,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T18:44:47.625522+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"If Poiseuille-flow simulations of the automaton fail to produce the transverse velocity component predicted by the analytically derived odd-viscosity coefficient, the claim is falsified.","supporting_citations":[],"review_version":1}