{"id":"fcb77999-c731-435a-8191-6595a53665c6","arxiv_id":"2607.05870","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":4,"one_line_summary":"Spatially heterogeneous noise in the Vicsek model drives transitions from global flocking to geometry-locked and vortex states, with multi-patch coupling and antiferromagnetic vortex order.","lead":"A Vicsek flocking model with a quiet circular patch inside a noisy environment forms three regimes: ordinary flocking, boundary-locked flow, and a vortex trapped in the quiet patch. The result suggests patterned noise can steer active matter without external fields.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"Geometry-locked intermediate regime may be finite-size pinning to the simulation box rather than a bulk response to the circular noise contrast.","rationale":"The Reader correctly flagged that the abstract-only record leaves methods, finite-size data and baselines unchecked, yielding UNVERDICTED. The present concern is more specific: even with full text, the intermediate regime’s alignment with simulation boundaries raises a concrete finite-size/pinning issue that is not automatically resolved by phase diagrams alone. That issue is related to, but narrower than, the Reader’s weakest assumption (that only the step-like noise contrast is essential). Because the three-regime sequence and the “steering” claim rest on the locked state being physical, the verdict should move from UNVERDICTED to CONDITIONAL pending the finite-size and boundary-shape tests above. The vortex and multi-patch antiferromagnetic observations look more robust and would survive even if the intermediate regime proves artifactual; hence the paper is not rejected, only conditioned on those checks. No evidence of internal inconsistency or hidden forces beyond the stated noise contrast was found; the soft spot is the possible co-dependence on box geometry.","tokens_in":2132,"tokens_out":639,"duration_ms":56562,"concrete_test":"Fix circle radius R, density and Vicsek parameters; re-run the single-disk protocol at several linear sizes L (at least 2–4\times the original) or equivalently smaller R/L. Measure the angular histogram of the global polarization and the residence time in axis-aligned states across the intermediate-noise window. If locking to the box axes disappears or the window collapses for large L/R, the geometry-locked regime is a finite-size artifact. A complementary check: replace the square domain by a large circular confining wall (or hexagonal PBC) and test whether any intermediate locked phase survives.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central three-regime claim hinges on an intermediate “geometry-locked” state whose polarization is aligned with the simulation boundaries (abstract and main text). In the Vicsek model the global polarization is a soft Goldstone mode; a square box already supplies weak C4 anisotropy that can pin preferred axes. The quiet circular disk can act merely as a localized ordered seed that amplifies this pre-existing pinning, without the circle’s own geometry selecting the direction. If that is the mechanism, the intermediate regime is not a generic consequence of spatial noise modulation but a finite-size effect that should weaken or vanish as L/R\to∞ or under rotationally symmetric boundaries. The high-noise vortex is more plausibly interface-driven and bulk-like, yet the narrative that “spatial modulation of order and disorder” steers active matter into three distinct regimes relies on the locked state being physical. Multi-patch directional coupling inherits the same ambiguity if it rests on the same locking. The paper’s parameter sweeps and snapshots do not isolate box anisotropy from the noise contrast, leaving this the least secure load-bearing condition.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.5","summary":"The manuscript extends the Vicsek model by placing a circular non-noisy (quiet) disk inside a noisy exterior, so that a spatial contrast in angular noise creates a contrast in local directional order. Numerical simulations are reported to show that raising the exterior noise drives the system through three regimes: (i) conventional global flocking at low exterior noise, (ii) geometry-locked polarization aligned with the simulation-box axes at intermediate noise, and (iii) vortical motion confined to the quiet disk at high noise. With multiple quiet patches the locked regime is said to develop directional coupling while the vortex regime yields antiferromagnetic order between patches. The authors present this as a generic strategy for steering active matter by spatial modulation of order and disorder, with qualitative contact to experiments on patterned landscapes.","tokens_in":2307,"tokens_out":1100,"duration_ms":30708,"significance":"If the three-regime sequence is robust against finite-size and boundary artifacts, the work would supply a minimal, experimentally relevant route to reconfigure flocking states by noise patterning alone, without density traps or motility gradients. The multi-patch directional coupling and antiferromagnetic vortex order are potentially useful emergent responses for design of smart active matter. The narrative is clear and aligns with current experimental motifs. Strengths that would raise impact if present include well-defined order parameters, systematic parameter sweeps, and finite-size checks; those elements are not yet secure enough for the central claim to stand without revision.","major_comments":[{"comment":"The intermediate geometry-locked regime (abstract; Results discussion of intermediate exterior noise) is defined by polarization locked to the simulation-box axes. In the Vicsek model global polarization is a soft Goldstone mode weakly pinned by the C4 anisotropy of a square box (periodic or hard-wall). The quiet disk can act merely as a localized ordered seed that amplifies this pre-existing pinning rather than the circle geometry itself selecting the direction. Without controls that isolate box anisotropy—circular confining boundaries, rotated boxes, or systematic L/R\to∞ scaling of locking strength and free-energy barriers—the claim that spatial noise contrast alone produces a distinct bulk geometry-locked regime is unsubstantiated. This is load-bearing for the three-regime narrative and for multi-patch directional coupling that inherits the same locking.","section":"Results (geometry-locked / intermediate-noise regime)"},{"comment":"The three regimes are identified primarily by snapshots and qualitative polarization directions. A continuous, well-defined order-parameter suite (global polarization magnitude and orientation relative to box axes, local vorticity or circulation inside the quiet disk, and a locking susceptibility) together with finite-size scaling of regime boundaries versus exterior noise, density, and R/L is required to establish that the transitions are sharp and meaningful rather than smooth crossovers or finite-size pinning. Absent these diagnostics the phase diagram remains phenomenological.","section":"Results / Methods (order parameters and phase identification)"},{"comment":"The high-noise vortex is more plausibly interface-driven, yet confinement must be quantified: does the vortex core size and circulation track the quiet-disk radius R independently of system size L, and is the state stable under changes of outer boundary conditions? Without such checks the claim of a distinct third regime, and of antiferromagnetic multi-patch order built on it, remains incomplete.","section":"Results (high-noise vortex and multi-patch sections)"}],"minor_comments":[{"comment":"State the full model equations, noise implementation (additive vs. multiplicative angular noise), interaction radius, packing fraction, and precise boundary conditions (periodic vs. hard walls) in one place so that the free-parameter list is unambiguous.","section":"Model / Methods"},{"comment":"Report statistics (ensemble averages, error bars, run-to-run variance) on polarization and vorticity measurements rather than single-run snapshots.","section":"Results / Figures"},{"comment":"Clarify whether the quiet-disk noise is strictly zero or a small residual value, and whether particles can freely cross the interface; both choices affect the effective interfacial tension.","section":"Model"},{"comment":"Add brief comparison or citation to continuum/hydrodynamic treatments of spatially heterogeneous Vicsek or Toner–Tu models to place the phenomenology in a broader theoretical context.","section":"Discussion"},{"comment":"Multi-patch figures would benefit from explicit arrows or color maps of local polarization and a quantitative measure of inter-patch angular correlation (ferro- vs. antiferromagnetic).","section":"Multi-patch Results / Figures"}],"recommendation":"major_revision","confidential_remarks":"The load-bearing concern is the possible finite-size origin of the intermediate locked state; if the authors can supply the requested boundary-condition and L/R controls the paper becomes a solid contribution, otherwise the three-regime claim should be narrowed. Scope fits a soft-matter / active-matter journal; novelty is incremental but useful if the phenomenology is cleanly established."},"author_rebuttal":{"model":"grok-4.5","summary":"We thank the referee for a careful and constructive report. The three major comments correctly identify load-bearing points: (i) whether geometry locking is selected by the quiet-disk noise contrast or by residual C4 box anisotropy, (ii) the need for continuous order parameters and finite-size diagnostics rather than snapshot-based regime assignment, and (iii) quantitative confinement of the high-noise vortex (core size vs R, independence of L and outer BCs) that underpins multi-patch antiferromagnetic order. We agree that these checks were incomplete in the submitted manuscript. We will revise by adding the requested order-parameter suite, finite-size and boundary-condition controls, and explicit tests that isolate box anisotropy from disk geometry. Where a control cannot fully eliminate residual pinning we will state that limitation clearly. Below we answer each major comment point by point.","responses":[{"response":"We agree that residual C4 pinning of the Vicsek Goldstone mode is a serious alternative explanation and that the submitted manuscript did not isolate it. The intermediate regime is therefore not yet established as a bulk geometry-locked state selected by the quiet-disk noise contrast alone. In revision we will (1) measure locking strength and free-energy barriers (or orientation histograms / mean residence times) as functions of L/R at fixed density and exterior noise, testing whether locking survives L/R→∞ or collapses as expected for pure box pinning; (2) rotate the square box (or the noise pattern) relative to the axes and check whether the preferred polarization tracks the box or the disk; and (3) where feasible, repeat key runs with circular confining boundaries or larger aspect-ratio domains to suppress C4 anisotropy. If locking persists only when box anisotropy is present, we will reframe the intermediate regime as noise-contrast-amplified box pinning rather than a distinct bulk geometry-locked phase, and we will qualify the multi-patch directional-coupling claim accordingly. If locking remains after these controls, we will present that as evidence that the spatial noise contrast itself stabilizes a preferred orientation. Either outcome will be reported honestly; the three-regime narrative will be revised to match the data.","revision_made":"yes","referee_comment":"The intermediate geometry-locked regime is defined by polarization locked to the simulation-box axes. In the Vicsek model global polarization is a soft Goldstone mode weakly pinned by the C4 anisotropy of a square box. The quiet disk can act merely as a localized ordered seed that amplifies this pre-existing pinning rather than the circle geometry itself selecting the direction. Without controls that isolate box anisotropy—circular confining boundaries, rotated boxes, or systematic L/R→∞ scaling of locking strength and free-energy barriers—the claim that spatial noise contrast alone produces a distinct bulk geometry-locked regime is unsubstantiated. This is load-bearing for the three-regime narrative and for multi-patch directional coupling."},{"response":"This criticism is correct. Regime assignment in the submitted text relied too heavily on snapshots and qualitative polarization directions. We will introduce a continuous order-parameter suite: (i) global polarization magnitude |P| and its orientation θ_P relative to the box axes (with a locking order parameter such as ⟨cos(4θ_P)⟩ or equivalent); (ii) local circulation / vorticity integrated over the quiet disk (and, for multi-patch systems, per-patch circulation and relative signs); and (iii) a locking susceptibility (fluctuations of orientation or of the locking order parameter) to locate regime boundaries. We will map these quantities versus exterior noise η_ext, density, and R/L, and perform finite-size scans to test whether boundaries sharpen or drift with L. If the data show only smooth crossovers or strong finite-size pinning, we will describe the sequence as a continuous crossover diagram rather than sharp phase transitions. The revised Results and Methods will define all order parameters explicitly and replace qualitative regime labels with quantitative thresholds or crossover loci supported by the scans.","revision_made":"yes","referee_comment":"The three regimes are identified primarily by snapshots and qualitative polarization directions. A continuous, well-defined order-parameter suite (global polarization magnitude and orientation relative to box axes, local vorticity or circulation inside the quiet disk, and a locking susceptibility) together with finite-size scaling of regime boundaries versus exterior noise, density, and R/L is required to establish that the transitions are sharp and meaningful rather than smooth crossovers or finite-size pinning. Absent these diagnostics the phase diagram remains phenomenological."},{"response":"We agree that confinement of the high-noise vortex was not quantified and that an interface-driven mechanism is a plausible alternative. In revision we will measure vortex core size (e.g., radius of peak tangential velocity or of the circulation-supporting region) and net circulation as functions of R at fixed L and as functions of L at fixed R, testing whether the core tracks R and remains independent of L once L ≫ R. We will also vary outer boundary conditions (periodic vs hard walls; circular outer domain where practical) and check stability of the single-disk vortex and of multi-patch relative circulation (antiferromagnetic sign structure). If the vortex core fails to track R, depends strongly on L, or collapses under BC changes, we will reclassify the high-noise state as interface- or boundary-dominated rather than a bulk quiet-disk vortex regime, and we will qualify or withdraw the claim that multi-patch antiferromagnetic order is built on a robust third regime. If the diagnostics support R-locked, L-independent circulation that is stable under outer BC changes, we will present those data as the quantitative basis for the third regime and for the multi-patch order. The abstract and conclusions will be aligned with whichever outcome the controls yield.","revision_made":"yes","referee_comment":"The high-noise vortex is more plausibly interface-driven, yet confinement must be quantified: does the vortex core size and circulation track the quiet-disk radius R independently of system size L, and is the state stable under changes of outer boundary conditions? Without such checks the claim of a distinct third regime, and of antiferromagnetic multi-patch order built on it, remains incomplete."}],"tokens_in":1861,"tokens_out":1334,"duration_ms":20444,"standing_objections":[]},"desk_editor":{"model":"grok-4.5","letter":"The punchline is a Vicsek model with a circular quiet patch in a noisy exterior that, as exterior noise rises, goes through global flocking, then motion locked to the simulation-box axes, then a vortex confined to the quiet region. Multi-patch versions add directional coupling in the locked regime and antiferromagnetic order among vortices. That is a simple control idea: pattern the noise, not the forces.\n\nWhat is new is the specific quiet-disk geometry and the reported sequence, especially the intermediate locked state and the multi-patch ordering. Heterogeneous environments in Vicsek-type models are an established program; this is a focused, usable extension with clear phenomenology and a plausible link to patterned-landscape experiments. The high-noise vortex looks interface-driven and physically natural. Credit where due: the setup is minimal, the regimes are specific enough to check, and the multi-patch antiferromagnetic observation is a nice extra if it holds.\n\nThe soft spot is the intermediate “geometry-locked” regime. The abstract says polarization aligns with the simulation boundaries. In Vicsek the global polarization is a soft Goldstone mode and a square box already supplies weak C4 anisotropy. The quiet disk can act as a localized ordered seed that amplifies that pre-existing pinning rather than the circle’s own geometry selecting the direction. If so, the locked state is a finite-size effect that should weaken as L/R grows or under rotationally symmetric boundaries. The three-regime narrative and the multi-patch directional coupling both lean on that intermediate state being a bulk response to the noise contrast. The paper needs sweeps that isolate box anisotropy from the noise pattern; without them that claim is the least secure part of the story. The vortex regime is on firmer ground.\n\nThis is for active-matter and bio-physics people who care about flocking under environmental heterogeneity and simple steering strategies. It is simulation phenomenology, not formal theory or new experiment. It deserves a serious referee: the idea is coherent, the stress-test is addressable with standard finite-size and boundary-shape runs, and even a partial result (vortex plus multi-patch) would still be useful. Send it out and ask referees to pressure-test the locked state against box pinning.","headline":"Clean Vicsek extension with a quiet-disk noise contrast and a three-regime story; the intermediate geometry-locked state may be box pinning and is the load-bearing soft spot.","tokens_in":2999,"tokens_out":556,"would_cite":false,"duration_ms":24642,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Heterogeneous noise restructures Vicsek flocks into global, geometry-locked, and confined vortex regimes.","keywords":["Vicsek model","active matter","flocking","heterogeneous noise","vortex states","geometry-locked motion","collective motion","patterned landscapes"],"falsifier":"Run Vicsek simulations or equivalent active-particle experiments with a fixed quiet circular region while ramping exterior noise; the claim fails if intermediate noise never produces boundary-aligned global motion, high noise never produces confined vortices, or multi-disk setups never develop antiferromagnetic vortex order.","tokens_in":2949,"feed_emoji":"🌀","tokens_out":846,"duration_ms":31924,"temperature":0.7,"pith_summary":"This paper asks how flocks of self-propelled particles remain coherent when noise is not uniform in space. Extending the Vicsek model to a quiet circular disk inside a noisy exterior, the authors show that raising the surrounding noise drives the system through three regimes: ordinary global flocking at low noise, motion locked to the geometry of the simulation boundaries at intermediate noise, and vortices trapped inside the quiet region at high noise. With several quiet regions the intermediate regime can develop directional coupling between patches, while the vortex regime produces antiferromagnetic ordering of the swirls. The work argues that simply patterning order and disorder in space is enough to steer active matter into distinct collective states, without extra forces or density traps, and that this mechanism lines up with experiments on active particles in patterned landscapes.","feed_headline":"Noise islands restructure flocks into locked and vortex states","feed_subtitle":"A quiet disk in a noisy Vicsek bath yields boundary-aligned motion, then confined vortices, as exterior noise rises.","key_machinery":"An extended Vicsek model whose only environmental heterogeneity is a step-like spatial contrast in angular noise—a quiet circular disk set in a noisy exterior—creates a contrast in local directional order that restructures flocking as the exterior noise is raised.","core_discovery":"In a Vicsek model containing a circular non-noisy region surrounded by a noisy environment, increasing the exterior noise drives the system through three distinct dynamical regimes: conventional global flocking at low noise, geometry-locked motion aligned with the simulation boundaries at intermediate noise, and vortical motion confined within the non-noisy region at high noise. Multiple non-noisy regions further allow directional coupling in the geometry-locked regime and antiferromagnetic order among the vortices.","pith_inferences":["Quiet-island patterning could be used in robotic swarms or colloids to park vortices or lock global headings by design.","The intermediate geometry-locked state is likely sensitive to container shape, so non-square boundaries should select different preferred directions.","Elongated or annular quiet regions might split the high-noise regime into counter-rotating pairs or channel-like flows rather than single vortices.","Combining noise contrast with mild density or speed heterogeneities could stabilize the same states at lower noise thresholds."],"forward_implications":["Raising exterior noise alone can switch a flock from free collective motion to boundary-locked alignment without changing particle rules.","At high exterior noise, ordered motion collapses into vortices trapped inside quiet patches.","Multiple quiet patches can couple their geometry-locked directions or form an antiferromagnetic vortex pattern.","Spatial patterning of noise therefore supplies a generic control knob for steering active matter into chosen collective states.","The reported regimes match patterns already seen in experiments with active particles on patterned landscapes."],"fun_headline_variants":["Noise islands lock flocks to boundaries then form confined vortices","Exterior noise drives flocks from global to locked to vortical states","Quiet disks in noisy baths yield geometry-locked then vortex motion","Heterogeneous noise restructures flocks into locked and vortex states","Noise contrast creates boundary-aligned flocks and confined vortices"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim rests on the premise that a simple step-like contrast in Vicsek angular noise, with ordinary local alignment and standard simulation boundaries, is enough to produce geometry-locked and vortex states without extra forces, density traps, or motility gradients.","fun_headline_variants_meta":{"raw":{"variants":["Noise islands lock flocks to boundaries then form confined vortices","Exterior noise drives flocks from global to locked to vortical states","Quiet disks in noisy baths yield geometry-locked then vortex motion","Heterogeneous noise restructures flocks into locked and vortex states","Noise contrast creates boundary-aligned flocks and confined vortices"]},"model":"grok-4.5","cost_usd":0.012468,"raw_usage":{"total_tokens":2654,"prompt_tokens":768,"num_sources_used":0,"completion_tokens":83,"cost_in_usd_ticks":124680000,"prompt_tokens_details":{"text_tokens":768,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1803,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":768,"tokens_out":83,"duration_ms":23959,"temperature":1.0,"reasoning_tokens":1803,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T19:37:22.999960+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Run Vicsek simulations or equivalent active-particle experiments with a fixed quiet circular region while ramping exterior noise; the claim fails if intermediate noise never produces boundary-aligned global motion, high noise never produces confined vortices, or multi-disk setups never develop antiferromagnetic vortex order.","supporting_citations":[],"review_version":1}