{"id":"b563c53f-53a9-4bb5-a03d-23eb26e5368c","arxiv_id":"2506.07771","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A theoretical formula for successful transmission probability in multi-waveguide pinching-antenna indoor systems is derived and supported by Monte Carlo simulation.","lead":"This paper develops a 3D model of a room where several pinching antennas on ceiling waveguides serve users on the floor, and derives the probability that a user's connection is good enough for immersive applications. It gives network planners a quantitative tool for choosing the number of waveguides, ceiling height, and power settings in an indoor pinching-antenna system.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1's exponent A is algebraically inconsistent with the SINR model in Eq. (6), so the central formula does not follow from Proposition 1 or Appendix B; the paper's main claim is not established as written.","rationale":"Good-faith reading: the paper aims to provide a closed-form STP for a multi-waveguide PASS, and the derivation is simple enough that correctness hinges on algebra. Independent support is limited to claimed Monte Carlo agreement; there are no machine-checked proofs, code, or data. The reader's weakest-assumption focused on the blockage-free LoS channel model, which is a modeling idealization rather than an internal contradiction. My concern is stronger and more specific: the displayed Theorem 1 is algebraically inconsistent with the SINR expression in Eq. (6) and with the Gil-Pelaez inversion in Appendix B. The A appearing in Theorem 1 is dimensionally inconsistent and cannot be obtained by substituting any of the z definitions in the paper into A=−z+Σ r_k. This means the central formula as printed is not a consequence of the stated system model. Since the paper's numerical results and guidelines rest entirely on that formula, the current version cannot be accepted; a corrected derivation and re-run figures are necessary before the claim can be verified. I would therefore move from the reader's CONDITIONAL to REJECT for the current manuscript, while acknowledging that a revised version that corrects the algebra and re-verifies the numerics may be viable.","tokens_in":8019,"tokens_out":11254,"duration_ms":135682,"concrete_test":"Re-derive Theorem 1 symbolically: substitute z = 1/(γ0 d0^2) − σ^2/(η P_t) into A = −z + Σ r_k and simplify; if the printed A differs from the result, run Fig. 3 with the corrected formula. The decisive check is whether the corrected Theo curves still match the reported Monte Carlo dots; if not, the claim that Theorem 1 is verified fails.","verdict_should_be":"REJECT","load_bearing_attack":"From Eq. (6), SINR = (1/d0^2)/(Σ_{k≠i}1/d_k^2 + σ^2/(ηP_t)), with d0^2=(id−y_i^u)^2+h^2. Thus P(γ>γ0) is P(R≤z) with z=1/(γ0 d0^2)−σ^2/(ηP_t). The Gil-Pelaez step in Appendix B requires A=−z+Σ r_k = Σ r_k − 1/(γ0 d0^2)+σ^2/(ηP_t). Theorem 1 instead prints A=σ^2/(ηP_t)+Σ_{k≠i}(r_k−1/d0^2)/(η γ0). Since r_k=1/d_k^2, the two expressions differ in the factor multiplying Σ r_k and in the coefficient of 1/d0^2; the printed A also has mixed units (the summation terms are m^-4). Hence Theorem 1 is not a consequence of Proposition 1/Appendix B. The related Proposition 1 also omits η from the σ^2/P_t term in z. Because all numerical results and design guidelines are obtained from this formula, the central claim is unverified without a corrected derivation and re-run simulations.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates downlink successful transmission probability (STP) in indoor pinching-antenna systems (PASS). It sets up a 3D deployment model with multiple ceiling-mounted waveguides, PAs positioned vertically above their served users, and a free-space LoS channel model. The main analytical contribution is Theorem 1, a Gil-Pelaez inversion formula that expresses STP as a multi-dimensional integral depending on deployment parameters and transmission configurations. The paper also reports Monte Carlo simulations and uses them to support design guidelines for system parameters such as waveguide count, room dimensions, transmit power, noise, and SINR threshold.","tokens_in":8262,"tokens_out":7149,"duration_ms":82861,"significance":"If the theoretical formula were correct, the paper would offer a useful, parameter-free STP expression for arbitrary user locations in a multi-waveguide PASS, eliminating the need for Monte Carlo simulation in this idealized LoS setting. The stated model has no fitted parameters, and the authors explicitly verify against simulations, which is a strength. However, the central formula as written does not follow from the stated SINR model, and the internal inconsistencies described below affect every numerical result and design guideline in Section IV. The paper therefore needs a corrected derivation and re-run results before its contributions can be assessed.","major_comments":[{"comment":"The SINR expression in Eq. (6) is inconsistent with the received-power expressions in Eqs. (4) and (5). From Eq. (4), the desired received power is ηP_t/||p_i-u_i||^2, and from Eq. (5) the aggregate interference is ηP_t Σ_{k≠i} ||p_k-u_i||^{-2}. Therefore the correct SINR is γ_i^u = (1/||p_i-u_i||^2) / (Σ_{k≠i} ||p_k-u_i||^{-2} + σ^2/(ηP_t)). Eq. (6) instead has η multiplying the interference sum and σ^2/P_t in the denominator, which corresponds to neither the stated power model nor the subsequent derivation. Appendix A, Eq. (7), in turn derives z = ((id-y_i^u)^2+h^2)^{-1}/(η γ0) - σ^2/(ηP_t), which is different from the z printed in Proposition 1. The authors must reconcile these three different expressions; as written, the proof of Proposition 1 is not aligned with the proposition statement.","section":"Section III-A, Eq. (6) and Appendix A, Eq. (7)"},{"comment":"The exponent A in Theorem 1 is not what follows from Appendix B. In Appendix B, A is defined as A = -z + Σ_{k∈K/{i}} r_k, with r_k = ((x_k^u - x_i^u)^2 + (kd - y_i^u)^2 + h^2)^{-1}. Using the z from Appendix A, this gives A = Σ_{k≠i} r_k - 1/(γ0 ((id-y_i^u)^2+h^2)) + σ^2/(ηP_t). The printed A in Theorem 1 is σ^2/(ηP_t) + Σ_{k≠i} ((r_k)^{-1} - (r_0)^{-1})/(η γ0), which has squared distances in place of the reciprocal distances and thus has both incorrect algebraic form and incorrect units. Consequently, Theorem 1 does not follow from Proposition 1 or Appendix B, and the claimed closed-form STP is not established as written.","section":"Theorem 1 and Appendix B"},{"comment":"The paper claims that Ps has a minimum along each waveguide centerline and increases as the user moves away from the centerline, and that Ps increases with ||x_i^u|| or ||y_i^u|| away from the center. This is presented as a key deployment insight. However, due to the error in Theorem 1, this observation is currently not supported by a correct formula. In addition, the verbal explanation based on 'longer propagation distance of the interference signal' ignores that the desired-link distance also grows as the user moves away from its serving PA; the net effect requires a correct evaluation of the CDF of R, which itself depends on y_i^u. This claim should be re-derived and re-verified after the formula is corrected.","section":"Section IV, Fig. 3 and surrounding text"}],"minor_comments":[{"comment":"The abbreviation PASS is used inconsistently: the abstract introduces 'Pinching-antenna systems (PASS)' while the title and text sometimes say 'pinching-antenna system'; please standardize.","section":"Abstract and Introduction"},{"comment":"The multiple-integral notation is malformed: the underbraces labeled '2K' and the expression 'd . . .dx_k^u' do not clearly specify the integration variables and order. Please use a standard product-of-integrals notation, e.g., ∏_{k≠i} ∫_{-L/2}^{L/2} dx_k^u.","section":"Theorem 1"},{"comment":"The proof labels steps (a) and (b), but Eq. (10) in Appendix B refers to a step (c) that never appears; please renumber.","section":"Appendix A, Eq. (7)"},{"comment":"In the first bullet under Fig. 4, the text says 'L increases' and then concludes that Ps decreases, but the following explanation says a larger L reduces aggregate interference and increases Ps; the conclusion and the explanation appear to contradict each other and should be checked.","section":"Section IV"},{"comment":"The model assumes all links, including interfering links, are free-space LoS with no blockage or fading, while the introduction motivates PAs by their ability to combat LoS blockage. This idealization should be stated more prominently as a limitation, even though the paper does list random blockage as future work.","section":"Section II-C"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has a potentially useful framework, but the central Theorem 1 is algebraically inconsistent with the stated SINR model, and Proposition 1 also contains a missing-η inconsistency with its own appendix. The numerical section cannot validate the printed formula unless the implementation matches the erroneous printed formula, so the current version is not publishable. The issues are fixable in principle, which is why I recommend major revision rather than rejection. I did not see a circularity problem: the derivation is model-based and the simulations are used for verification, not calibration. The scope is appropriate for a performance-analysis paper, but the authors should carefully re-derive Eqs. (6), (7), and Theorem 1, rerun the simulations, and revisit the spatial-pattern claims in Section IV."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a plausible-looking STP analysis for pinching-antenna indoor deployments, but as printed the central formula is not right, and one of the paper's own design trends contradicts it. I would not use the results until the derivation is corrected and the numerics re-run.\n\nWhat is new: it extends earlier PA performance analysis to a 3D multi-waveguide room model with nearest-waveguide association and PA-user x-alignment. The model setup is sensible and the Gil-Pelaez inversion is standard. The Monte Carlo verification is claimed for the printed formula, which makes the error more concerning.\n\nThree issues. (1) Theorem 1's exponent A does not follow from Appendix B. Appendix B gives A = -z + Σ r_k, with z = r0/(η γ0) - σ^2/(η Pt), so A = σ^2/(η Pt) + Σ r_k - r0/(η γ0). Theorem 1 instead prints A = σ^2/(η Pt) + Σ_{k≠i}(r_k - r0)/(η γ0). These differ by a factor 1/(η γ0) on all interference terms and by an extra r0/(η γ0). The units also don't match. This is not a typo-level discrepancy.\n\n(2) Proposition 1 in the main text omits η from the noise term; the Appendix has it. So the statement is inconsistent.\n\n(3) Section IV's Pattern 1 says Ps is minimized at the waveguide centerline and increases toward edges, but Proposition 1 has z = (1/d0^2)/γ0 - ... , which decreases as the user moves away from the centerline because d0 grows. Unless the CDF is decreasing in z, which it is not, the trend is opposite. The physical explanation in the paper doesn't fix that.\n\nAlso no code/data, but that's minor compared to the above.\n\nWho this is for: anyone working on pinching-antenna performance analysis. The scenario is relevant, but the main result needs derivation audit and re-simulation.\n\nI would not accept the paper in its current form; it needs a major revision with corrected formulas and re-run simulations. It deserves a serious referee rather than a desk reject, because the model and approach are worth engaging with, but the current version's central claim is unverified.","headline":"Central STP formula is inconsistent with its own derivation and with the paper's design trend; needs major revision before use.","tokens_in":8787,"tokens_out":3487,"would_cite":false,"duration_ms":36809,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single integral formula gives the success probability of any downlink link in a pinching-antenna indoor network, verified by simulation.","keywords":["pinching antenna systems","indoor immersive communications","successful transmission probability","3D system modeling","downlink SINR analysis","6G wireless networks"],"falsifier":"Run a Monte Carlo or measurement campaign in the same rectangular geometry but with one or more absorbing screens placed between some interfering antenna and the reference user, or with the serving antenna randomly offset from the user's horizontal position; if the empirical success fraction departs systematically from Theorem 1, the blockage-free and perfect-alignment assumptions are carrying the result.","tokens_in":7817,"feed_emoji":"📶","tokens_out":6795,"duration_ms":82017,"temperature":0.7,"pith_summary":"This paper claims that in a room with multiple ceiling-mounted waveguides, each carrying a movable pinching antenna, the probability that a chosen user's downlink transmission succeeds can be written as an integral over the possible user positions. The formula, Theorem 1, takes as input the room geometry, the number and spacing of waveguides, transmit power, noise, the line-of-sight distances, and the SINR threshold, and returns the successful transmission probability for any reference user location. The authors verify the formula against Monte Carlo simulations and use it to map how reliability varies across the room and with system parameters. If correct, the formula gives network designers a direct way to compare pinching-antenna deployment choices for indoor immersive 6G services without simulating every configuration.","feed_headline":"One formula predicts link reliability for every pinching-antenna user","feed_subtitle":"A 3D model plus one integral gives the chance any indoor user beats the SINR threshold, verified by simulation.","key_machinery":"The load-bearing mechanism is the deployment rule that each pinching antenna is moved along its ceiling waveguide until it sits directly above its served user, so the antenna's horizontal coordinate equals the user's. This makes the desired-link distance depend only on the waveguide height and the user's lateral offset, while each interfering antenna's distance to the reference user keeps a random horizontal coordinate uniformly distributed over the room length $L$. The mathematical engine is the characteristic-function inversion formula applied to the sum $R$ of inverse-squared interference distances; independence of the users turns the product of characteristic functions into the $2K$-fold integral stated in Theorem 1.","core_discovery":"The central claim is that the downlink SINR of a user served by a pinching antenna depends only on inverse-square distances to its own antenna and to all other antennas, and that the only random ingredient in those distances is the horizontal coordinate of each interferer's served user. Because those coordinates are independent and uniform along the waveguide, the interference sum $R$ has a characteristic function that factors into one-dimensional integrals, and the successful transmission probability $P_s$ can be recovered by a Fourier inversion identity. Theorem 1 packages this as a $2K$-fold integral over the interfering users' positions, with an exponent containing the room length, the SINR threshold, the power, and the noise. The paper presents this formula as a general performance model that captures the correlation between pinching-antenna positions and user locations and quantifies the effect of deployment settings and transmission configurations.","pith_inferences":["Editorial inference: because every link is assumed to be unobstructed free-space line of sight, the absolute $P_s$ values are likely optimistic for real indoor clutter; the parameter trends are the safer conclusions to export to practice.","Editorial inference: real pinching antennas cannot track users perfectly, so a natural extension is to perturb the antenna's horizontal coordinate around the user's and measure the loss in $P_s$; the present model serves as the zero-error baseline.","Editorial inference: for large numbers of waveguides the interference sum $R$ should be approximately Gaussian by the central limit theorem, which could replace the $2K$-fold integral with a two-moment approximation and yield a simpler deployment rule.","Editorial inference: a blockage-aware variant could test the paper's motivating claim directly by placing random absorbing screens between interferers and the reference user; comparing that with Theorem 1 would show when pinching antennas' flexibility actually overcomes indoor obstruction."],"forward_implications":["Scanning deployments becomes direct: given a reference user location, Theorem 1 computes $P_s$ for any combination of waveguide count, height, length, spacing, power, noise, and SINR threshold, so the model can replace Monte Carlo runs for configuration comparisons.","Spatial placement matters: the paper's numerical results show $P_s$ is lowest directly beneath each waveguide and rises symmetrically as the user moves sideways, producing a periodic reliability pattern across the room.","More waveguides can hurt under equal power splitting: increasing the number of waveguides while keeping total power and room width fixed adds interference and lowers per-antenna power, so $P_s$ decreases.","Geometry trades off: larger ceiling height lowers $P_s$ because the desired signal weakens faster than interference, whereas a longer room spreads interferers and raises $P_s$.","The same formula supports optimization: because transmit power and path-loss parameters can vary per user, the model can be extended toward dynamic power allocation and different multiple-access schemes, as the paper notes."],"supporting_citations":[{"why":"Documents the original pinching-antenna demonstration that motivates the PASS deployment under study.","marker":"[3]"},{"why":"Supplies the guided-wave phase-shift model and the pinching-antenna channel assumptions used in the link model.","marker":"[4]"},{"why":"Provides the PASS architecture and the equal power splitting convention used in the link model.","marker":"[5]"},{"why":"Justifies the identity that a unit-magnitude complex exponential has magnitude one, which collapses the desired-signal phase terms in the received power expression.","marker":"[10]"},{"why":"Provides the characteristic-function inversion identity used to turn the interference-sum distribution into the integral formula in Theorem 1.","marker":"[11]"}],"fun_headline_variants":["One integral predicts each pinching-antenna user's success","Pinching antennas: a single formula for indoor link odds","Fourier inversion yields a one-liner for pinching-antenna SINR","3D model plus one integral gives pinching-antenna reliability","Pinching antennas: one formula predicts every user's success"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that every link, including interfering links, is an unobstructed free-space line-of-sight path with no blockage, shadowing, or fading, and that each pinching antenna is placed exactly above its served user.","fun_headline_variants_meta":{"raw":{"variants":["One integral predicts each pinching-antenna user's success","Pinching antennas: a single formula for indoor link odds","Fourier inversion yields a one-liner for pinching-antenna SINR","3D model plus one integral gives pinching-antenna reliability","Pinching antennas: one formula predicts every user's success"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000958,"raw_usage":{"total_tokens":4029,"prompt_tokens":838,"completion_tokens":3191,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":454,"completion_tokens_details":{"reasoning_tokens":3101}},"tokens_in":454,"tokens_out":3191,"duration_ms":27004,"temperature":1.0,"reasoning_tokens":3101,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:26:55.244890+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a Monte Carlo or measurement campaign in the same rectangular geometry but with one or more absorbing screens placed between some interfering antenna and the reference user, or with the serving antenna randomly offset from the user's horizontal position; if the empirical success fraction departs systematically from Theorem 1, the blockage-free and perfect-alignment assumptions are carrying the result.","supporting_citations":[{"cited_title":"Pinching antenna: Using a dielectric waveguide as an antenna,","cited_arxiv_id":null,"evidence_quote":"Documents the original pinching-antenna demonstration that motivates the PASS deployment under study."},{"cited_title":"Flexible-antenna systems: A pinching-antenna perspective,","cited_arxiv_id":null,"evidence_quote":"Supplies the guided-wave phase-shift model and the pinching-antenna channel assumptions used in the link model."},{"cited_title":"Stochastic geometry framework for ultrareliable cooperative communications with random blockages,","cited_arxiv_id":null,"evidence_quote":"Provides the characteristic-function inversion identity used to turn the interference-sum distribution into the integral formula in Theorem 1."}],"review_version":1}