{"id":"1d3491ce-e0b3-4dec-b17e-1aed3c4cf83c","arxiv_id":"2608.05271","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Linear-cluster states yield four- and five-qubit witnesses with quantum values 4+2√2 and 6+4√2 against hidden-influence bounds 6 and 10.","lead":"Bell experiments cannot rule out hidden influences that travel faster than light but at a finite speed. This paper builds four- and five-qubit cluster-state tests whose violations of the hidden-influence bounds are far larger than earlier proposals, bringing such tests closer to experiment.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central bounds and facet claims rest on unreleased Farkas certificates; independent exact verification is required before the headline result can be accepted.","rationale":"The paper's mathematical scaffolding is otherwise careful: the block-coordinate derivations, stabilizer identities, primal attainer points, and dimension formulas are consistent, and I found no internal contradiction. The single least secure point is that the Farkas certificates, which are the only evidence for validity of the bounds over the full HIC set and for the facet dimensions, are not shown. The Supplement gives the structure of the LP but not the certificate data; the data availability statement says release will occur only upon publication. This is not a claim of error, but a verifiability gap: the central theorem is currently an assertion about an unshown computation. The reader's CONDITIONAL verdict is appropriate; the concrete test would settle whether the concern lands. I do not treat the model-class caveat as the primary concern because the paper explicitly frames the result as conditional on no-signaling and measurement independence, and the Bancal et al. argument is cited for the signaling case.","tokens_in":27598,"tokens_out":25115,"duration_ms":227682,"concrete_test":"Independently implement the LP in Supplement Secs. III–IV: build the variables t_{s_E,o_E,β,γ}, the equality system Nt = r for normalization and all single-party no-signaling setting changes, and the objectives α = M^T ω for S4 and S5; solve exactly with rational arithmetic (e.g., via an exact LP solver or Fourier–Motzkin elimination) and verify the optimal values are 6 and 10. Then reconstruct the zero-slack sets J from the dual certificates and check rank([N_J; M_J]) − rank(N_J) = 43 for LC4 and 133 for LC5, with the relative-interior feasibility epsilons 1/176 and 1/416. If both checks pass, the central claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the claimed exact certification of S4 ≤ 6, S5 ≤ 10, and the facet dimensions 43 and 133 via integer Farkas certificates (Supplement Secs. IV–V, Table S1). The certificate vectors η, the zero-slack sets J, and the verifier are not included in the manuscript; the data and code availability statement defers release until publication. The block projections and primal points only prove tightness at specific distributions, not validity over the whole HIC set, so the bounds are assertions backed by unshown computation. An error in the LP encoding (e.g., a missing no-signaling row or an incorrect pullback of correlator coefficients into t-space) would invalidate the central claim. Because the authors used GPT-assisted code and do not provide it, this is the least secure point of the argument.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes two linear-cluster-state witnesses for finite-speed hidden-influence models. The theoretical framework is a projected-polytope separation problem: define the hidden-influence set as HICE = NS ∩ CL(BC|E), project away all correlations containing both late parties, and certify linear inequalities over this projection by LP duality. The reported results are an LC4 witness with S4 ≤ 6 and quantum value 4+2√2, and an LC5 witness with S5 ≤ 10 and quantum value 6+4√2. The authors further claim, via integer Farkas certificates and exact rational rank/relative-interior computations, that both inequalities are facet-defining for the relevant projected polytopes, with projected dimensions 44 and 134 and face dimensions 43 and 133. The paper includes explicit primal HIC points, an explicit five-site spacetime arrangement, and white-noise visibility estimates of 0.8787 and 0.8579, presented as improvements over the earlier Bancal et al. witness.","tokens_in":27748,"tokens_out":8132,"duration_ms":83746,"significance":"If the computational certificates are valid, this is a significant step for experimental tests of finite-speed hidden influences: the witnesses use compact graph states, two-setting X–Z measurements, and substantially better ideal white-noise thresholds than the previous 0.9526 benchmark. The authors also give credit-worthy exact data: explicit feasible HIC distributions, exact rational projected dimensions, positive relative-interior solutions with ε = 1/176 and ε = 1/416, and a clear discussion of the no-BC projection. The main reservation is not methodological circularity but verifiability: the central bounds and facet claims rest on Farkas certificates and rank computations that are only summarized, not shipped.","major_comments":[{"comment":"The load-bearing claims S4 ≤ 6, S5 ≤ 10, and facet dimensions 43/133 are not independently verifiable because the actual Farkas certificate vectors η, the zero-slack index sets J, and the verifier code are not included. The supplement reports statistics (||η||₁ = 70/362, 22/98 nonzero entries, zero-slack counts 176/888) and states that substitution into Eq. (S62) proves the bounds, but no certificate is displayed and the Data/Code Availability statement defers release until publication. The explicit primal points prove tightness at specific distributions and the rank/relative-interior checks prove facet tightness only once J is known. Since an error in the LP encoding or in the certificate would invalidate the central claim, the revision must include the full machine-readable certificates and an independent verifier, or the headline claims should be explicitly downgraded to unverified computational assertions.","section":"Supplemental Material, Secs. IV–V; main text Eq. (4); Table S1"},{"comment":"The paper's scope statement is stronger than its model class. The main text says the criteria falsify 'all models with finite v', but Eq. (1) defines HICE as NS ∩ CL(BC|E), and Supplement I A explicitly states that these conditions are necessary but 'do not characterize all finite-speed theories'. A finite-v model whose correlations fall outside NS ∩ CL(BC|E), for example one permitting operational signaling that no user can exploit, or one with measurement dependence, is not constrained by the certified inequalities. The theorem should be stated with explicit quantification over P ∈ Π^{no-BC}(NS ∩ CL(BC|E)), and the abstract and introduction should be reworded so that 'finite-speed hidden-influence model' is understood as 'a model satisfying the assumptions listed in Sec. I of the supplement'.","section":"Main text Eq. (1); Supplement I A; main text p. 2"}],"minor_comments":[{"comment":"The 'tightness' column reports (44,43) and (134,133) without a label for the second entry; the caption should state that the first number is the projected affine dimension and the second is the active-face dimension.","section":"Table I and main text discussion of LC5"},{"comment":"The distributions P1–P3 are given in bit notation with a shared fair bit ξ; the claim that b becomes independent of w after summing over ξ in P1 is correct but would be easier to check if the summation step were written out explicitly.","section":"Supplemental Material, Sec. II C, Eq. (S47)"},{"comment":"The statement that the new witnesses give 'substantially larger margins than previous finite-speed hidden-influence witnesses' refers to ideal white-noise visibility; the readout-error analysis in Sec. VIII B correctly warns that LC5's four-body terms may offset its lower ν*. The main-text sentence should carry that qualification.","section":"Main text, 'substantially larger margins' and Supplement VIII B"}],"recommendation":"major_revision","confidential_remarks":"I recommend requiring the actual certificate files, the zero-slack index sets, and a standalone exact verifier as supplementary material in the revision. The present availability statement is insufficient for a computational proof, and the stated use of AI-assisted code makes independent verification more, not less, necessary. The scope mismatch between the abstract's 'falsify all models with finite v' and the supplement's explicit caveat should also be corrected before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a real step forward for finite-speed hidden-influence tests, conditional on certificates we can't yet see. The four- and five-qubit witnesses are new, the violation margins are substantially better than Bancal et al., and the supplement is careful about what is being proved. The soft spot is exactly where the stress test says: the bounds S4 ≤ 6, S5 ≤ 10, and the facet claims rest on integer Farkas certificates that are described but not included.\n\nWhat's new: the construction combines a distributed CHSH block on B with stabilizer 'lock' terms on C, with weights optimized over the projected HIC polytope. That's a sensible and, as far as I know, new use of cluster-state stabilizers. The LC5 dichotomic completion is also a genuine technical fix. The facet certifications are strong claims: they require exact rank and relative-interior checks in 44 and 134 dimensions, and the paper reports exact rational numbers for those (dimensions 43/44 and 133/134, epsilon values 1/176 and 1/416), which is credible scaffolding.\n\nWhat it does well: the paper is honest about the model class, stating measurement independence and no postselection up front. It also gives explicit primal points achieving the bounds, so tightness isn't just asserted. The discussion of visibility thresholds versus readout sensitivity is appropriately modest.\n\nSoft spot: the Farkas vectors and the zero-slack sets J are not shown. The reader can't check the LP encoding. The data/code statement says release upon publication, and the code was developed with GPT assistance. For a result whose entire force is an exact LP certificate, that's not acceptable for review; referees need the certificate or a machine-checkable verifier. An error in pulling the correlator coefficients back into t-space would invalidate the headline. I don't see such an error, but I can't rule it out without the files. This is a verification gap, not an identified flaw. The citation practice is appropriate, with the earlier HIC constructions properly credited.\n\nThis deserves peer review. The methods are sound enough, and the potential impact on experimental tests is real. Send it to referees, and require the certificates and verifier as supplementary material or an ancillary file before the final version. For anyone working on nonlocality, causal models, or graph-state Bell inequalities, it's worth a close look.","headline":"New cluster-state witnesses for finite-speed hidden-influence models with much larger violation margins, but the load-bearing Farkas certificates are not in the paper.","tokens_in":28289,"tokens_out":2514,"would_cite":true,"duration_ms":24797,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Ud","03.67.-a"],"model":"deepseek-v4-flash","headline":"Linear cluster states yield two facet-defining witnesses, $S_4 \\le 6$ and $S_5 \\le 10$, against all finite-speed hidden-influence theories that respect no-signaling and measurement independence.","keywords":["finite-speed hidden influences","cluster states","Bell nonlocality","no-signaling","conditional locality","projected polytopes","Farkas certificates","quantum witnesses"],"falsifier":"Maximize $S_4$ over the feasible set $\\{t \\ge 0 : Nt = r\\}$ using an independent linear-programming solver; if any feasible weight vector yields $S_4 > 6$ (or, in the five-qubit case, $S_5 > 10$), the paper's Farkas certificate is wrong. The claim stands only if every such optimization returns exactly 6 (or 10), and an experimental implementation that observes $S_4 = 4+2\\sqrt{2} > 6$ from a linear-cluster state in the prescribed $B \\sim C$ timing would confirm the claimed violation.","tokens_in":27417,"feed_emoji":"⚛️","tokens_out":11052,"duration_ms":95498,"temperature":0.7,"pith_summary":"Bell experiments rule out local hidden causes but leave room for hidden influences that travel faster than light at a finite speed in a preferred frame. This paper turns that loophole into a testable constraint: when two late parties lie outside each other's hidden-influence cone, their correlations must be Bell-local once the early-side events are fixed. The authors construct a four-qubit witness $S_4\\le 6$ with quantum value $4+2\\sqrt{2}$, and a five-qubit witness $S_5\\le 10$ with quantum value $6+4\\sqrt{2}$, both built from linear-cluster states and evaluated from marginal data containing at most one late party. They certify that both inequalities are facet-defining faces of the projected hidden-influence polytopes, giving substantially better noise tolerance than earlier finite-speed hidden-influence witnesses. If correct, any finite-speed hidden-influence model satisfying operational no-signaling, conditional late-pair locality, and measurement independence is falsified by these cluster correlations.","feed_headline":"Cluster states tighten finite-speed hidden-influence limits","feed_subtitle":"Four- and five-qubit linear clusters violate the new S4 ≤ 6 and S5 ≤ 10 bounds, giving an easy test target.","key_machinery":"The load-bearing object is the hidden-influence causality set $\\mathcal{HIC}_E = \\mathrm{NS} \\cap \\mathrm{CL}(BC|E)$: the intersection of the full no-signaling polytope with the set of distributions for which the $BC$ marginal is Bell-local after conditioning on every non-null early-side input--output event. Its image under the no-BC projection, which deletes every correlator containing both $B$ and $C$, is the polytope $\\mathcal{P}^{\\mathrm{no-BC}}_E$ over which the witnesses are optimized. The proof machinery is linear-programming duality: each witness functional is written as $\\alpha^T t$ over nonnegative hidden-influence weights $t$ constrained by $Nt=r$ (normalization plus no-signaling), and an integer dual vector $\\eta$ with $N^T\\eta \\ge \\alpha$ and $r^T\\eta = B$ certifies the bound $S \\le B$. Facet-definingness is then verified by exact rational rank computations and relative-interior feasibility on the zero-slack face. The explicit witnesses combine a distributed CHSH block on the $B$ side with stabilizer-lock blocks on the $C$ side, with relative weights fixed by the supporting facet of a two- or three-dimensional block projection.","core_discovery":"The paper establishes that the projected no-BC hidden-influence polytopes for linear-cluster states admit compact, facet-defining witnesses. For the four-qubit cluster state $|\\mathrm{LC}_4\\rangle$, it proves $S_4 \\le 6$ over $\\mathcal{P}^{\\mathrm{no-BC}}_{AD}$, with quantum value $S_4^Q = 4+2\\sqrt{2} \\approx 6.8284$. For the five-qubit cluster state $|\\mathrm{LC}_5\\rangle$, it proves $S_5 \\le 10$ over $\\mathcal{P}^{\\mathrm{no-BC}}_{ADE}$, with quantum value $S_5^Q = 6+4\\sqrt{2} \\approx 11.6569$. Both witnesses contain no term with both late parties $B$ and $C$, both bounds are attained by explicit hidden-influence distributions, and exact rational arithmetic shows that the exposed faces have codimension one in the projected polytopes: dimension 43 of 44 for LC4 and 133 of 134 for LC5. The ideal white-noise visibilities are $\\nu_4^* = 6/(4+2\\sqrt{2}) \\approx 0.8787$ and $\\nu_5^* = 10/(6+4\\sqrt{2}) \\approx 0.8579$, compared with 0.9526 for the optimized earlier witness, so linear-cluster states are presented as certifiable and experimentally friendly resources for finite-speed hidden-influence tests.","pith_inferences":["The same stabilizer-block plus projected-polytope recipe could in principle be iterated to larger linear cluster states, but the paper gives no scaling law; computing the next witness and its visibility would test whether the advantage grows or saturates.","Under realistic readout errors the comparison may flip: LC4 uses only two- and three-body correlators, while LC5 contains four-body terms that attenuate faster with per-qubit readout flips, so LC4 may be the more robust experimental target despite its higher ideal white-noise threshold.","A successful loophole-conscious implementation would not only rule out finite-speed influences; it would operationalize the known result that, within this model class, preserving the observed correlations forces faster-than-light signaling between users, because the polytope constraint is exactly what enforces no-signaling.","The four completion terms in $S_5$ vanish on the cluster state yet determine whether the inequality is a facet, so similar degenerate terms may be systematically necessary in stabilizer-based no-BC witnesses; their role in other graph states is a natural follow-up question."],"forward_implications":["If the paper is right, any finite-speed hidden-influence model that keeps operational no-signaling and conditional $BC$ locality is experimentally falsified whenever a linear-cluster state produces $S_4 > 6$ or $S_5 > 10$ in the specified spacetime geometry.","Because the certified bounds coincide with the fully local bounds, these witnesses isolate the specific nonlocality that finite-speed influences cannot generate: nonlocal correlations that survive conditioning on all early events.","The improved ideal white-noise thresholds, 0.8787 and 0.8579 versus the earlier 0.9526, bring a finite-speed hidden-influence test substantially closer to what current quantum devices can reach.","Since both inequalities are facet-defining, no strictly weaker linear inequality in the same no-BC coordinate space can expose the same face; the bounds are tight for their projected polytopes.","The five-qubit witness can be run in the same four-site spacetime layout as the earlier proposal by treating $D$ and $E$ as a single four-outcome measurement device."],"supporting_citations":[{"why":"Defines the finite-speed hidden-influence framework and supplies the earlier four-party witness whose noise threshold the new witnesses improve.","marker":"[30]"},{"why":"Introduces the projected-polytope approach to hidden-influence constraints that the paper's no-BC formulation extends.","marker":"[31]"},{"why":"Provides the stabilizer-CHSH cluster-state construction that inspires the block decomposition of LC4 and LC5.","marker":"[36]"},{"why":"Supplies the Farkas duality used to certify the exact hidden-influence support bounds.","marker":"[46]"},{"why":"Gives the polyhedral dimension theory used to verify that the exposed faces are facets.","marker":"[47]"},{"why":"Provides the facet treatment of Bell-correlation polytopes used in the tightness diagnostics.","marker":"[48]"},{"why":"Establishes Bell inequalities for graph states, the background for deriving correlator identities from stabilizers.","marker":"[39]"}],"fun_headline_variants":["Cluster-state witnesses tighten hidden-influence speed limits","Linear clusters expose faster-than-light influence bounds","New cluster-state witnesses squeeze finite-speed hidden influences","Four- and five-qubit clusters beat hidden-influence limits","Cluster states offer certifiable test of finite-speed influences"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire certification rests on the assumption that every finite-speed hidden-influence model is exactly characterized by the intersection of operational no-signaling with conditional Bell locality of the two late parties after conditioning on every non-null early input-output event, together with measurement independence and no postselection; if any of these fails, the bounds $S_4 \\le 6$ and $S_5 \\le 10$ do not apply to the broader model class.","fun_headline_variants_meta":{"raw":{"variants":["Cluster-state witnesses tighten hidden-influence speed limits","Linear clusters expose faster-than-light influence bounds","New cluster-state witnesses squeeze finite-speed hidden influences","Four- and five-qubit clusters beat hidden-influence limits","Cluster states offer certifiable test of finite-speed influences"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000679,"raw_usage":{"total_tokens":3129,"prompt_tokens":1034,"completion_tokens":2095,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":650,"completion_tokens_details":{"reasoning_tokens":2021}},"tokens_in":650,"tokens_out":2095,"duration_ms":13582,"temperature":1.0,"reasoning_tokens":2021,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T16:42:38.016484+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Maximize $S_4$ over the feasible set $\\{t \\ge 0 : Nt = r\\}$ using an independent linear-programming solver; if any feasible weight vector yields $S_4 > 6$ (or, in the five-qubit case, $S_5 > 10$), the paper's Farkas certificate is wrong. The claim stands only if every such optimization returns exactly 6 (or 10), and an experimental implementation that observes $S_4 = 4+2\\sqrt{2} > 6$ from a linear-cluster state in the prescribed $B \\sim C$ timing would confirm the claimed violation.","supporting_citations":[{"cited_title":"Schrijver,Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics and Opti- mization (John Wiley & Sons, Chichester, 1986)","cited_arxiv_id":null,"evidence_quote":"Supplies the Farkas duality used to certify the exact hidden-influence support bounds."},{"cited_title":"Coiteux-Roy, O","cited_arxiv_id":null,"evidence_quote":"Provides the stabilizer-CHSH cluster-state construction that inspires the block decomposition of LC4 and LC5."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the polyhedral dimension theory used to verify that the exposed faces are facets."},{"cited_title":"Pironio, Lifting Bell inequalities, J","cited_arxiv_id":null,"evidence_quote":"Provides the facet treatment of Bell-correlation polytopes used in the tightness diagnostics."},{"cited_title":"G ¨uhne, G","cited_arxiv_id":null,"evidence_quote":"Establishes Bell inequalities for graph states, the background for deriving correlator identities from stabilizers."}],"review_version":1}