{"id":"d281e89a-06d7-4f5b-b98e-14a4f1547e73","arxiv_id":"2608.06084","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Completion time in collective lattice search-and-capture is controlled by a late free-exploration tail, and maximum-cardinality matching reduces it by more than an order of magnitude relative to single-round assignment.","lead":"In a lattice simulation of persistent random walkers capturing stationary targets, the time to capture the last target has an optimal persistence rate, but the choice of assignment policy changes that time far more than the persistence setting does. The paper shows that these completion times are set by rare late-time events, and that global maximum-cardinality matching can shorten them by more than an order of magnitude.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The policy speedup is credible, but the headline mechanism that policies act mainly on the free-exploration tail is not established because Eq. (3) counts all churned, non-final assigned motion as free exploration.","rationale":"The reader's conditional verdict is appropriate. I agree with the reader's weakest_assumption: the kinematic rule in Sec. II.0.0.4 is the pivot on which the tail mechanism rests. The paper does provide independent support for the raw speedup: reported error bars, bootstrap caveats, the untruncated candidate-graph control at R=5, and the tie-breaking randomization control. Those controls address algorithmic and statistical artifacts, but they do not address the decompositional artifact embedded in Eq. (3). Because the paper's stated central finding is mechanistic ('policies suppress the free-exploration tail') and because that mechanism is definitionally entangled with the recompute-every-step rule, the missing verification under an alternative steering model is the most load-bearing open question. The central quantitative claim that assignment policy can change Tc more than persistence is credible and likely survives, so rejection is not warranted. Conditional acceptance with a request for the committed-pursuit control and a total-assigned-time instrument is the correct outcome.","tokens_in":6255,"tokens_out":9319,"duration_ms":91027,"concrete_test":"Run a committed-pursuit variant of the model: once a walker is assigned to a target under the same matching policy, the walker continues to move greedily toward that target for up to D steps (e.g., D=R) or until capture, instead of reassigning every step; compare baseline, cascading, and maximum-cardinality matching at R=5, 10, and 20. If the max-matching speedup factor and the fraction of Tc attributable to directed time remain large under committed pursuit, the free-exploration-tail interpretation is robust. If the speedup collapses, or if total assigned time becomes a substantial fraction of Tc, the headline mechanism is an artifact of the one-step recomputation rule.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The raw speedup of maximum-cardinality matching (Tc 33 vs. 467 at R=5) is a strong empirical result, and the paper reports useful controls: 100 replicas, error bars, bootstrap caveats, and explicit checks against candidate-graph truncation and matching degeneracy. The load-bearing weakness is the mechanistic interpretation attached to that speedup. Under the kinematic rule of Sec. II.0.0.4, assignment is recomputed every step and an assigned walker moves only one greedy cardinal step. A walker that is assigned to target A for several steps, then to B, and only finally captures C has all of that A/B directed motion classified by Eq. (3) as part of the 'free exploration' period before t_start, because t_start is defined as the start of the final uninterrupted assignment run that ends in capture. The observation that mean tau_steer is below 1.1 steps and max(t_start)/Tc is near 1 is then largely guaranteed by the definition: assigned steps that do not lead directly to capture cannot count as steering. The conclusion that policies 'do not primarily accelerate the already-directed final approach; instead, they suppress the long intervals...' therefore conflates churned directed motion with free exploration. If one instead measured total time spent assigned to any target, or adopted a committed multi-step pursuit rule, the policy speedup might be attributable mostly to increased total directed time, reversing the stated mechanism. This does not invalidate the Tc numbers, but it weakens the paper's central conceptual claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a minimal lattice model of collective search-and-capture in which persistent random walkers capture immobile targets under a finite-range, mutually exclusive assignment rule. It reports that the collective completion time T_c depends non-monotonically on the walker reorientation probability alpha, with a minimum at intermediate persistence that flattens as the search radius R grows. It further argues that T_c is governed by an extreme late-time tail, not by typical capture events, and that this tail is controlled mainly by the free-exploration phase rather than by the final directed approach. Comparing single-round, cascading, and maximum-cardinality matching policies, the paper finds that maximum-cardinality matching strongly reduces T_c, by more than an order of magnitude at moderate R, and concludes that the assignment policy can control collective capture time more strongly than walker persistence.","tokens_in":6565,"tokens_out":3482,"duration_ms":33691,"significance":"If the empirical results hold, the paper identifies a new and practically relevant control parameter for collective search-and-capture problems: the quality of the matching policy rather than single-walker persistence. The reported speedups are large and supported by several good practices: 100 replicas per parameter set, reported standard deviations, bootstrap-based caveats for the flat parts of the alpha scan, and explicit controls for candidate-graph truncation and degeneracy of the maximum matching. The paper also makes a clean conceptual distinction between the typical capture time and the extreme completion time. The main weakness is that the mechanistic interpretation attached to the speedup—that policies act mainly by suppressing free exploration rather than by increasing directed motion—is not actually established by the reported decomposition, because the definition of t_start classifies all churned, non-final assigned motion as free exploration. The quantitative T_c values are credible, but the headline mechanism needs either revision or additional analysis.","major_comments":[{"comment":"The decomposition T_i = t_start_i + tau_steer_i is defined so that t_start resets whenever the walker is unassigned for a step or is assigned to a different target; consequently all steps spent under a non-final assignment are counted as part of the free-exploration phase. The observations that the mean tau_steer is below 1.1 steps and that max(t_start)/T_c is close to 1 are therefore to a large extent guaranteed by this definition rather than being empirical discoveries about the dynamics. In particular, a walker that is assigned to target A for several steps, then to B, and only finally captures C contributes all of its A/B directed motion to the 'free exploration' part of the decomposition. The claim that policies 'do not primarily accelerate the already-directed final approach; instead, they suppress the long intervals...' is not supported unless one measures separately the total time spent assigned to any target, or implements a committed multi-step pursuit rule in which an assignment persists until capture. Please add such an analysis, or revise the mechanistic interpretation accordingly.","section":"III.2, Eq. (3)"},{"comment":"The causal statement that maximum-cardinality matching works by suppressing the long free-exploration tail rests on the same Eq. (3) classification. The paper reports an instrumented campaign showing that maximum-cardinality matching reassigns walkers much more often per step, and notes that this is 'associated with (though not, by this correlation alone, proven to cause) the suppression of the late free-exploration tail.' Given the definitional issue in Eq. (3), the association is even weaker than stated: the suppressed quantity labeled 'free exploration' includes a substantial amount of churned directed motion. To make the mechanism claim load-bearing, the paper should quantify the total assigned time per walker (regardless of whether the assignment ultimately leads to capture) under the three policies, or otherwise separate churned directed motion from true unassigned exploration.","section":"III.3 and Discussion"}],"minor_comments":[{"comment":"The author name appears with LaTeX accent artifacts ('N´ estor') and the arXiv date line is embedded in the main text; these should be cleaned up in the final version.","section":"Header and abstract"},{"comment":"The figure caption reports mean±SEM over 100 replicas, while the text in Section III.1 reports s.d. for specific values; please make the error-bar convention consistent and clearly state which quantity is plotted.","section":"Figure 1 caption and Section III.1"},{"comment":"The fractional value T_50% = 0.4 is explained in the text, but the explanation should appear at the first mention of T_50% in the results section, not only after the table, to avoid confusion.","section":"Table I"},{"comment":"The statement that single-round assignment requires 'no communication beyond a target's immediate neighborhood' is imprecise for R>1, since each target must know the positions of all walkers within distance R; please rephrase to 'within its search radius R' or similar.","section":"Section V, Conclusion"},{"comment":"The sentence 'policies do not primarily accelerate the already-directed final approach...' appears in both the Introduction and the Conclusion; if the mechanistic claim is revised in response to the major comments, both passages must be updated consistently.","section":"Introduction and Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The paper reports a substantial and likely reproducible simulation result: maximum-cardinality matching reduces the completion time by an order of magnitude at moderate R, with sensible error bars and controls. My recommendation for major revision is driven by the mismatch between the empirical T_c numbers and the mechanistic interpretation built on Eq. (3). If the authors add a clean separation between churned directed motion and true free exploration, or explicitly reframe the claims as being about the effective 'unassigned tail' rather than 'free exploration' in the dynamical sense, the paper would be considerably stronger. The current version should not be accepted without that clarification."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The empirical core is solid. At R=5, switching from single-round to maximum-cardinality matching cuts the completion time from ~467 to ~33 steps, an order-of-magnitude speedup that dominates anything persistence tuning can do at the same radius. That makes the assignment policy a stronger control knob than persistence, and that's a transferable result.\n\nThe model is minimal and easy to understand, and the authors are honest. They explicitly disclaim novelty for the intermediate-persistence minimum, cite the cover-time and first-passage literature, and report useful controls: 100 replicas, bootstrap caveats, tie-breaking randomization, and an explicit check that the candidate graph is untruncated at R=5. The f_assigned(t) population-level diagnostic is a good addition.\n\nThe weak spot is the mechanism claim. Eq. (3) defines t_start as the start of the final uninterrupted assignment run that ends in capture. Any earlier assigned motion, even if it's directed toward a different target, is counted as part of the 'free exploration' period. Because the kinematic rule recomputes assignment every step and moves the walker one greedy cardinal step, a walker can be assigned to A for many steps, then B, then finally capture C; all that A/B motion lands before t_start. So the finding that tau_steer is below 1.1 steps and t_start tracks Tc is partly guaranteed by the definition. At small R that's not a big problem, because f_assigned falls below 0.05, meaning almost nobody is ever assigned. But at R=30, the assigned fraction stays 0.3–0.4, so a large fraction of the pre-t_start period is actually directed, churned motion, not free exploration. The paper's claim that policies 'suppress the long free-exploration tail' is therefore not established. They could be reducing assignment churn or increasing total directed time. The Tc numbers stand, but the headline interpretation doesn't.\n\nThere's also a practical issue: the Supplemental Material, code, and data are absent. For a simulation-only paper with no analytical theory, that makes independent verification impossible.\n\nI'd send this to peer review. It deserves a serious referee, and the mechanism question is exactly what the referee should push on. Ask the authors to release code/data and to test the decomposition against a multi-step pursuit rule or a total-assigned-time metric. I would not accept it as is, but it's a legitimate conditional acceptance.","headline":"A credible, policy-speedup simulation result with a mechanism interpretation that is partly definitional; worth a serious referee.","tokens_in":7062,"tokens_out":3712,"would_cite":true,"duration_ms":31433,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Assignment policy, not walker persistence, is the main lever on collective capture time","keywords":["search-and-capture","persistent random walk","assignment policy","maximum-cardinality matching","completion time","extreme-value statistics","active matter"],"falsifier":"Re-run the same model with multi-step waypoint pursuit replacing the one-step greedy steering rule and check whether the latest assignment-start time still tracks $T_c$; if $T_c$ then ceases to be dominated by the free-exploration tail, or if the assignment-policy speedups shrink, the paper's central mechanism is refuted.","tokens_in":6025,"feed_emoji":"🎯","tokens_out":9196,"duration_ms":71672,"temperature":0.7,"pith_summary":"The paper studies a minimal lattice model in which persistent random walkers capture immobile targets through a finite-range, mutually exclusive assignment rule, and asks what actually controls the time until every target is captured. It finds that the completion time $T_c$ is an extreme, late-time statistic: the last target is captured one to three orders of magnitude after half the targets are already gone, and this tail is governed by free exploration, not by the final directed approach. The central claim is that the assignment policy reshapes that tail: switching from a single-round greedy rule to maximum-cardinality matching cuts $T_c$ from about 467 to 33 steps at search radius $R=5$, a larger change than the entire persistence optimum produces at the same radius. The paper thereby argues that, in depletion-coupled collective search, how walkers are matched to targets can matter more for completion than how persistently they move.","feed_headline":"Better assignments beat persistence in search-and-capture","feed_subtitle":"Maximum-cardinality matching cuts completion time from 467 to 33 steps at search radius 5.","key_machinery":"The machinery is a discrete-time persistent random walk on a periodic square lattice with reorientation probability $\\alpha$, combined with a three-way competition over assignments. The identity that carries the argument is the decomposition $T_c=\\max_i T_i$ with $T_i=t_i^{\\mathrm{start}}+\\tau_i^{\\mathrm{steer}}$, where $t_i^{\\mathrm{start}}$ is the step at which the capturing walker begins its final uninterrupted run and $\\tau_i^{\\mathrm{steer}}$ is the length of that directed approach. The alternative assignment policies are single-round greedy selection (each target claims its nearest walker once per step), cascading reassignment (greedy acceptance of distance-sorted pairs), and maximum-cardinality matching computed by augmenting paths on the candidate graph. This decomposition lets the paper attribute changes in $T_c$ to the free-exploration tail rather than to steering, and the policy comparison isolates how matching quality affects that tail.","core_discovery":"On the paper's own terms, the discovery is that an assignment policy can control the collective completion time more strongly than the walkers' reorientation rate. Decomposing each capture time as $T_i = t_i^{\\mathrm{start}} + \\tau_i^{\\mathrm{steer}}$, the measured steering duration stays below about one lattice step, while the population's latest assignment-start time tracks $T_c$ (ratio 1.00 at $R=1$, falling to 0.81 at $R=30$). Policies therefore do not primarily accelerate an already-directed final approach; they suppress the long intervals during which the last few unmatched walkers and targets fail to form a productive assignment. The numerical comparison is direct: cascading reassignment reduces $T_c$ by factors of several at large $R$, and maximum-cardinality matching on the candidate graph reduces it by more than an order of magnitude at moderate $R$ (at $R=5$, from about 467 steps to about 33 steps), with the speedup unchanged under tie-breaking in the matching algorithm.","pith_inferences":["Editorial extension: if the free-exploration tail is the bottleneck, a local anti-churn heuristic that prevents a walker from being assigned back to a target it just failed near might capture much of the matching speedup at far lower communication cost; the paper does not test this.","Editorial extension: the decomposition applies to biological or robotic clearing tasks where the measurable quantity is the time until the last target is serviced; a quantitative prediction is that such systems will be optimized more for coordination than for persistence.","Editorial extension: a continuous-time or off-lattice version with multi-step waypoint steering would test whether the tail attribution is an artifact of the one-step greedy kinematic rule."],"forward_implications":["Wherever a completion or cover time is set by the last target, improved global matching can yield order-of-ten speedups, a far larger lever than tuning individual search behaviour.","At small search radius $R\\le 5$, single-round and cascading greedy policies agree within uncertainty, while maximum-cardinality matching separates from both already at moderate $R$.","The persistence optimum becomes shallow at large $R$, so reorientation tuning is a weak control once assignments can reach far across the lattice.","Maximum-cardinality matching sustains far more dynamic reassignment throughout the run, not merely a larger initial assignment fraction; the instrumented campaign reports about 30 times more reassignment events per step than either greedy heuristic."],"supporting_citations":[{"why":"Supplies the cover-time perspective for many independent searchers that the paper extends to depletion-coupled walkers.","marker":"[14]"},{"why":"Provides the Gumbel-type extreme-value statistics that motivate the claim that the completion time is governed by the late tail.","marker":"[15]"},{"why":"Gives the fastest-of-many-searchers result that the paper contrasts with its assignment-coupled completion time.","marker":"[16]"},{"why":"Supplies the augmenting-path algorithm used to compute the maximum-cardinality matching.","marker":"[17]"}],"fun_headline_variants":["Matching beats reorientation in collective capture","Assignment policy outdoes persistence in search","Better matching cuts capture time 14-fold","Optimal matching trumps walker persistence","Policy choice matters more than walker persistence"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing kinematic premise is that an assigned walker is steered only one greedy cardinal step before the assignment is recomputed, so the final directed run almost always begins when the walker is already adjacent to its target; if pursuit lasted many steps or failed assignments counted as directed time, the conclusion that policies act on free exploration would need revision.","fun_headline_variants_meta":{"raw":{"variants":["Matching beats reorientation in collective capture","Assignment policy outdoes persistence in search","Better matching cuts capture time 14-fold","Optimal matching trumps walker persistence","Policy choice matters more than walker persistence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000235,"raw_usage":{"total_tokens":1528,"prompt_tokens":1000,"completion_tokens":528,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":616,"completion_tokens_details":{"reasoning_tokens":463}},"tokens_in":616,"tokens_out":528,"duration_ms":5292,"temperature":1.0,"reasoning_tokens":463,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:14:42.213281+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the same model with multi-step waypoint pursuit replacing the one-step greedy steering rule and check whether the latest assignment-start time still tracks $T_c$; if $T_c$ then ceases to be dominated by the free-exploration tail, or if the assignment-policy speedups shrink, the paper's central mechanism is refuted.","supporting_citations":[{"cited_title":"Kim and S","cited_arxiv_id":null,"evidence_quote":"Supplies the cover-time perspective for many independent searchers that the paper extends to depletion-coupled walkers."},{"cited_title":"Chupeau, O","cited_arxiv_id":null,"evidence_quote":"Provides the Gumbel-type extreme-value statistics that motivate the claim that the completion time is governed by the late tail."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the augmenting-path algorithm used to compute the maximum-cardinality matching."}],"review_version":1}