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REVIEW 4 major objections 5 minor 23 references

This paper claims that full network sharing, where operators jointly pick which base stations stay active, can cut cellular energy use by up to about 35 percent while keeping average per-bit delay at target.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Using stochastic geometry and Paris operator traffic, the paper estimates that full network sharing between two mobile operators can save up to about 35 percent of base station energy while meeting QoS targets.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Useful analytical framework for multi-operator sharing with a plausible 35% savings figure, but the printed mean-interference expression in Lemma 1 looks dimensionally off and needs fixing before the numbers can be trusted. the 4 major comments →

arxiv 2508.19130 v1 pith:KBOVNIXR submitted 2025-08-26 cs.NI

Sharing is Caring: Analysis of Hybrid Network Sharing Strategies for Energy Efficient Multi-Operator Cellular Systems

classification cs.NI MSC 60D0560G55
keywords network sharingstochastic geometryenergy efficiencybase station sleep modesQoS-aware optimizationmulti-operator cellular networksper-bit delayload proportionality
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper builds a stochastic-geometry model that lets several mobile operators evaluate, on shared terms, the energy cost and user-perceived delay of different network-sharing strategies. Its central result is that full network sharing—operators jointly deciding which base stations stay active to serve everyone's users—can save up to about 35 percent of energy compared with each operator putting its own base stations into QoS-aware sleep mode independently. The saving holds while the average per-bit delay meets target values, and it is largest in urban areas with high peak traffic and in base stations whose energy use scales with load. The framework is applied to measured traffic and base-station data for two French operators in the Paris region across 24 hours, giving area- and time-of-day-specific estimates.

Core claim

The paper's load-bearing claim is that full network sharing outperforms both no-sharing and single-operator switchoff strategies because it solves a genuinely different optimization problem: instead of each operator minimizing its own energy under its own QoS constraint, all operators jointly choose the active fractions of their base stations to minimize total energy subject to the target mean per-bit delay of every user class. The analytical core is a fixed-point expression for the Palm expectation of the ideal per-bit delay, a function of active base-station densities, user densities, co-location probability, and channel parameters. Using measured Paris-region traffic and base-station loca

What carries the argument

The mechanism is a stochastic-geometry model of base stations as Poisson point processes, with QoS captured by the Palm expectation of per-bit delay (the inverse of short-term throughput). Theorem 1 expresses this delay for the typical user as the unique solution of a fixed-point equation in the active base-station densities; Problem 1 then minimizes total energy over those densities subject to delay targets. The per-bit delay, the weighted processor-sharing allocation, the co-location probability, and a measurement-based power model (fixed plus load-proportional terms) are the pieces that let the paper turn a sharing strategy into a number.

Load-bearing premise

The results assume that meeting the target mean delay per user class—not any per-user or worst-case delay—is an acceptable quality-of-service guarantee.

What would settle it

Re-solve the paper's Problem 1 replacing the mean-delay constraint with a percentile constraint (say, 95th percentile per-bit delay per class) and compare the resulting optimal active fractions and energy savings; if the savings drop materially or no solution exists, the 35 percent claim is tied to the average-delay metric.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If full network sharing is adopted, energy savings of roughly 33–36 percent relative to independent QoS-aware sleep modes are achievable in dense urban settings under the high-load-proportionality energy model.
  • Savings are greatest where peak traffic is high and the base-station energy model is load-proportional; combining network sharing with load-proportional architectures has a synergetic effect.
  • Full network sharing nearly doubles the savings of operator switchoff in urban areas, while switchoff remains competitive on weekends when traffic is low.
  • The analytical framework lets operators map savings as a function of area type, time of day, and traffic variability, which can inform where sharing is worth deploying.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The 35 percent figure depends on the average-delay QoS metric; if operators must guarantee per-user or tail delays, the optimal active fractions and the savings would likely shrink—this is an extension, not in the paper.
  • The same framework could extend to more than two operators and mixed cell types, but the numerical claims here are only for two operators and macrocell base stations.
  • Full network sharing concentrates traffic onto fewer active sites, which shortens average distances but may load some shared sites unevenly; the paper's average metric can hide that per-site imbalance.
  • A testable extension would compare the predicted optimal active fractions with a live two-operator trial and check whether tail delays stay acceptable in practice.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an analytical framework, based on stochastic geometry, for evaluating energy-efficient network-sharing strategies in multi-operator cellular networks. It models base station locations as Poisson point processes, user classes with different rate requirements, and a weighted processor-sharing service discipline. The main contributions are a fixed-point expression for the Palm expectation of per-bit delay (Theorem 1) and an optimization problem (Problem 1) to choose the fraction of active base stations per operator under full network sharing, minimizing total energy while meeting average per-bit delay constraints. The framework is applied to a realistic Paris dataset with two French operators, reporting energy savings up to 35% relative to independent QoS-aware sleep modes. The paper also compares full sharing with operator switch-off strategies and discusses the impact of traffic profiles and BS energy-model characteristics.

Significance. If the analytical derivations are correct, the framework would be a valuable addition to the literature, providing a tractable first-order tool for planning and assessing network-sharing strategies. The use of real operator data, the explicit modeling of user classes and energy models, and the systematic comparison of several sharing strategies are notable strengths. The paper is clearly structured and addresses a practically relevant problem. However, the quantitative results rest on a mean-interference expression that appears to be dimensionally inconsistent, and the claimed optimality of the numerical solutions is not established. These issues directly affect the central energy-savings claims, so the current version should be treated with caution until the analytical model is corrected and validated.

major comments (4)
  1. The stated mean interference expression, \bar I_i(r) = 2Pπ r^(2−α) τ0_J k(α−2) \barτ_i_J β_i λ_i, is dimensionally inconsistent. Here P is power (W), β_iλ_i is a density (m^-2), and τ0_J and \barτ_i_J are delays (s/bit), so the right-hand side has units W·m^-α·(s/bit)^2, not W. The standard Campbell–Mecke result for a PPP of active BSs with intensity β_iλ_i is 2πPβ_iλ_i r^(2-α)/(α−2), with no dependence on delay targets. Since Theorem 1 uses this expression inside C_i(r) to compute the fixed-point delays that appear in the QoS constraint (5), the error propagates directly into the optimal β_i and hence into the reported savings in Figure 5 and Table I. Please provide a derivation or correct the expression and re-evaluate the numerical results. No simulation validation is provided for this lemma.
  2. The paper states that Problem 1 'has been solved optimally using the interior point method with nonlinear constraints,' but no convexity or global-optimality argument is given. The objective is linear in β_i only if the per-BS energy E(τbar_i, P) is independent of the optimization variables; however, the energy model in Eq. (1) depends on utilization U, and the relationship between U, the decision variables β_i, the user densities, and the QoS constraints is not specified. The constraints involve the fixed-point delays of Theorem 1 and are non-linear. A local optimum from an interior-point solver does not establish global optimality. Please provide a formal statement of the optimization problem, including a definition of U and E as functions of the decision variables, and prove convexity or use a certified global optimization method.
  3. The QoS constraint is enforced on the Palm expectation of per-bit delay, as stated before Theorem 1 ('each BS tunes its utilization in such a way as to have, for each user class, the Palm expectation of the per-bit delay ... coincide with the target value'). This is an average over the user population, not a per-user or tail guarantee. The abstract's claim of 'maintaining quality of service' should be qualified accordingly. If real networks require per-user or tail delay guarantees, the feasible β_i solutions and the 35% savings figure would need re-evaluation. Please state this limitation explicitly and, if possible, provide a sensitivity analysis or bounds on tail performance.
  4. The uniqueness of the fixed-point solution is asserted by invoking the Banach fixed-point theorem with 'well-known inequalities,' but no proof is given. The numerical evaluation and the optimization constraint rely on the fixed point being well-defined and unique. Please provide the contraction argument or a reference where it is proven, and show that the conditions of the theorem are satisfied in the parameter regimes used in the numerical evaluation.
minor comments (5)
  1. The constraint is written '∀t, j' but the index t is never defined in the problem. Presumably it denotes time slots, but it should be introduced explicitly.
  2. The notation for the ideal per-bit delay is inconsistent: Eq. (2) uses \barτ_i^j, while Lemma 1 uses \barτ_i_J. Please unify the notation.
  3. There is a grammatical error: 'allow us to characterizing' should be 'allow us to characterize'.
  4. The derivation of h(r) and the probability p_i is sketched briefly; in particular, the integral defining h(r) and the thinning argument for co-located BSs are not fully justified. Expanding these steps would improve readability and verifiability.
  5. The paper uses 'Voronoi' but the text has 'V oronoi' with a space. Also check 'pd fR(r)' formatting in the proof.

Circularity Check

0 steps flagged

No significant circularity: the energy-savings result is the output of an optimization over free β_i variables with exogenous data inputs, not a restatement of the model's inputs.

full rationale

The paper's central claim (up to ~35% savings from full network sharing) is produced by solving Problem 1, which minimizes energy over the active-fraction variables β_i subject to the QoS constraints (5). The β_i are optimization variables, not fitted parameters; the BS and user densities are taken from external datasets (ANFR, NetMob23). The savings figure emerges from comparing the optimized full-sharing cost with an optimized no-sharing baseline, so it is not imposed by the choice of input. Theorem 1 is a fixed-point characterization of the Palm expectation of delay, and the uniqueness argument is a contraction argument rather than a result imported as a postulate. The only circularity-adjacent element is that Lemma 1 is attributed to ref. [18], which shares an author with the present paper; however, that lemma is an external analytical expression for mean interference, not a fit to the paper's target result, and the present paper does not define any quantity in terms of the savings it claims to predict. Accordingly, no self-definitional or fitted-input-called-prediction step is present. (A separate dimensional-consistency concern about Lemma 1 is a correctness/validity issue, not a circularity issue under the specified rubric.)

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The central result depends on standard stochastic geometry modeling choices (PPP base stations and users, path-loss-only channel, nearest-base-station association), a processor-sharing queue abstraction with Palm-average delay, a linear energy model from prior work, and an unproven but plausible optimization formulation. None of these introduce new physical entities; several are acknowledged simplifications. Numerical savings therefore inherit the accuracy of these inputs.

free parameters (4)
  • path-loss exponent alpha = not stated explicitly (assumed >=3)
    Section II invokes alpha>=3 for the nearest-BS approximation; the exact value used in the numerical evaluation is not given.
  • reuse factor k = not stated
    Appears in the capacity formula and in Lemma 1; no numerical value is supplied for the Paris evaluation.
  • energy model coefficients q1, q2, q3 = not specified; only fixed-energy fractions (36% HLP, 75% LLP) reported
    Section V-A says values follow ref [17] but exact coefficients are absent, so the energy numbers are not independently reproducible from the paper alone.
  • business traffic threshold Pth = 0.6
    Hand-chosen in Section V-A to classify a base station as business-profile based on weekday/weekend traffic ratio.
axioms (8)
  • domain assumption Base station locations of each MNO form a homogeneous Poisson point process with intensity lambda_i.
    Section II, System model; enables stochastic geometry analysis but idealizes real deployments.
  • domain assumption User locations form a homogeneous PPP per MNO with intensity lambda_i^u.
    Section II; used to compute the Palm expectation of delay and average cell load.
  • domain assumption Channel model considers only distance-dependent path loss, with no fading or shadowing.
    Section II; the paper states the model can be extended, but all numerical results use this simplified channel.
  • domain assumption The serving base station is the one with largest SINR, approximated as the nearest base station when alpha>=3.
    Section II; needed to derive the distance distribution PDF used in Theorem 1.
  • domain assumption At every co-location point there is a base station from each MNO.
    Section II; simplifies the co-location model and the derivation of p_i.
  • domain assumption Each base station tunes its utilization so the Palm expectation of per-bit delay for each user class equals the target tau0_j.
    Section III, before Theorem 1; this is the central QoS simplification and is load-bearing for the 'while maintaining QoS' claim.
  • domain assumption Energy consumption is linear in utilization: E_i(U,P)=q1+U(q2+q3P).
    Section II, Eq. (1); taken from prior measurement-based work [17] and used as the objective in Problem 1.
  • standard math The fixed-point system for mean per-bit delays is a contraction and has a unique solution.
    Invoked in the proof of Theorem 1 via the Banach fixed-point theorem; the contraction inequalities are not shown in detail.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Sharing is Caring: Analysis of Hybrid Network Sharing Strategies for Energy Efficient Multi-Operator Cellular Systems." pith.science (2026). https://pith.science/paper/KBOVNIXR

@misc{pith2026250819130,
  author       = {Pith},
  title        = {Pith review of: Sharing is Caring: Analysis of Hybrid Network Sharing Strategies for Energy Efficient Multi-Operator Cellular Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KBOVNIXR}},
  note         = {Machine review of arXiv:2508.19130}
}
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read the original abstract

This paper introduces a novel analytical framework for evaluating energy-efficient, QoS-aware network-sharing strategies in cellular networks. Leveraging stochastic geometry, our framework enables the systematic assessment of network performance across a range of sharing paradigms, including both conventional single-operator scenarios and advanced hybrid strategies that enable full integration and cooperation among multiple mobile network operators. Our framework incorporates diverse user densities, rate requirements, and energy consumption models to ensure comprehensive analysis. Applying our results to real-world datasets from French mobile network operators, we demonstrate that hybrid network sharing can yield substantial energy savings, up to $35\%$, while maintaining quality of service. Furthermore, our results allow us to characterizing how the benefits of network sharing vary as a function of the geographical and functional characteristics of the deployment area. These findings highlight the potential of collaborative sharing strategies to enhance operational efficiency and sustainability in next-generation cellular networks.

Figures

Figures reproduced from arXiv: 2508.19130 by Falko Dressler, Gianluca Rizzo, Laura Finarelli, Maoquan Ni, Michela Meo.

Figure 1
Figure 1. Figure 1: Scheme illustrating the idea underlying network sharing: when both [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The considered region of Paris, partitioned into urban, suburban, and [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mean traffic profile over 24 h per traffic class, for the Paris scenario, for the three area types. 0 5 10 15 20 25 Time [h] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 User Density [km-2 ] (a) weekday 0 5 10 15 20 25 Time [h] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 User Density [km-2 ] (b) weekend [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Mean business traffic profile over 24 h per traffic class, for the Paris scenario, per (a) weekday and (b) weekend. Despite the fact that network sharing schemes are often considered as a way to save energy in periods of low loads, the plot shows that for all strategies, the most significant savings are achieved when traffic peaks, with the full NS scheme achieving more than 30% reduction over energy￾optim… view at source ↗
Figure 5
Figure 5. Figure 5: Energy savings over the 24 h of the considered network sharing strategies with respect to the energy consumed when each MNO independently applies sleep modes to optimize its energy consumption without network sharing, for the Paris scenario. 0 5 10 15 20 Time [h] 0 10 20 30 40 50 60 70 [Wm-2 ] Full NS Switchoff MNO 1 Switchoff MNO 2 No sharing (a) 0 5 10 15 20 Time [h] 0 10 20 30 40 50 60 70 80 % active BS… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Energy consumed by the different NS strategies, as a function of the time slot over the 24 h, for the HLP BS energy model (b) Percentage of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

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Reference graph

Works this paper leans on

23 extracted references · 22 canonical work pages · 3 internal anchors

  1. [1]

    A Survey on Resource Allocation for 5G Heterogeneous Networks: Current Research, Future Trends, and Challenges,

    Y . Xu, G. Gui, H. Gacanin, and F. Adachi, “A Survey on Resource Allocation for 5G Heterogeneous Networks: Current Research, Future Trends, and Challenges,” IEEE Communications Surveys & Tutorials , vol. 23, no. 2, pp. 668–695, 2021

  2. [2]

    Toward dynamic energy- efficient operation of cellular network infrastructure,

    E. Oh, B. Krishnamachari, X. Liu, and Z. Niu, “Toward dynamic energy- efficient operation of cellular network infrastructure,” IEEE Communi- cations Magazine, vol. 49, no. 6, pp. 56–61, Jun. 2011

  3. [3]

    Infrastructure sharing for mobile network operators: Analysis of trade-offs and mar- ket,

    H. Elshaer, H. ElSawy, E. Hossain, and M.-S. Alouini, “Infrastructure sharing for mobile network operators: Analysis of trade-offs and mar- ket,” IEEE Transactions on Mobile Computing , vol. 17, no. 12, pp. 2900–2913, 2018

  4. [4]

    On optimal infrastructure sharing strategies in mobile radio networks,

    T. Mahmoodi, H. Tataria, M. Z. Shakir, and M. A. Imran, “On optimal infrastructure sharing strategies in mobile radio networks,” IEEE Trans- actions on Wireless Communications , vol. 16, no. 5, pp. 3003–3016, 2017. 7

  5. [5]

    Network sharing for fault resilience,

    M. Ni, D. Renga, M. Meo, and M. Ajmone Marsan, “Network sharing for fault resilience,” in 2024 14th International Workshop on Resilient Networks Design and Modeling (RNDM) , 2024, pp. 1–7

  6. [6]

    Infrastruc- ture sharing strategies for wireless broadband,

    T. Mahmoodi, H. Tataria, M. Z. Shakir, and M. A. Imran, “Infrastruc- ture sharing strategies for wireless broadband,” IEEE Communications Magazine, vol. 60, no. 4, pp. 32–38, 2022

  7. [7]

    Network sharing to enable sustainable communications in the era of 5g and beyond,

    D. Renga, M. Ni, M. A. Marsan, and M. Meo, “Network sharing to enable sustainable communications in the era of 5g and beyond,” in IEEE International Conference on Communications , 2024, pp. 2840– 2846

  8. [8]

    Sharing rans for energy efficiency,

    ——, “Sharing rans for energy efficiency,” in 2024 IEEE 25th Interna- tional Workshop on Signal Processing Advances in Wireless Communi- cations (SPAWC), 2024, pp. 706–710

  9. [9]

    Capacity and power consumption of multi-layer 6g networks using the upper mid-band,

    D. L ´opez-P´erez, N. Piovesan, and G. Geraci, “Capacity and power consumption of multi-layer 6g networks using the upper mid-band,”

  10. [10]

    Spectrum Sharing Between Low Earth Orbit Satellite and Terrestrial Networks: A Stochastic Geometry Perspective Analysis

    D. Kim, J. Park, J. Choi, and N. Lee, “Spectrum sharing between low earth orbit satellite and terrestrial networks: A stochastic geometry perspective analysis,” 2024. [Online]. Available: https://arxiv.org/abs/2408.12145

  11. [11]

    Quantifying the Benefits of Infrastructure Sharing

    M. Andrews, M. Bradonjic, and I. Saniee, “Quantifying the benefits of infrastructure sharing,” 2017. [Online]. Available: https: //arxiv.org/abs/1706.05735

  12. [12]

    Radio access network sharing in 5g: Strategies and benefits,

    S. Farhat, A. E. Samhat, S. Lahoud, and B. Cousin, “Radio access network sharing in 5g: Strategies and benefits,” Wireless Personal Communications, vol. 96, no. 2, pp. 2715–2740, Sep. 2017

  13. [13]

    5G 3GPP-Like Channel Models for Outdoor Urban Microcellular and Macrocellular Environments,

    K. Haneda, J. Zhang, L. Tan, G. Liu, Y . Zheng, H. Asplund, J. Li, Y . Wang, D. Steer, C. Li, T. Balercia, S. Lee, Y . Kim, A. Ghosh, T. Thomas, T. Nakamura, Y . Kakishima, T. Imai, H. Papadopoulos, T. S. Rappaport, G. R. MacCartney, M. K. Samimi, S. Sun, O. Koymen, S. Hur, J. Park, C. Zhang, E. Mellios, A. F. Molisch, S. S. Ghas- samzadeh, and A. Ghosh, ...

  14. [14]

    Stochastic geometry and wireless networks: V olume ii applications,

    F. Baccelli and B. Błlaszczyszyn, “Stochastic geometry and wireless networks: V olume ii applications,” Found. Trends Netw. , vol. 4, no. 1–2, p. 1–312, Jan. 2009. [Online]. Available: https://doi.org/10.1561/ 1300000026

  15. [15]

    Delay-based shaper with dynamic token bucket algorithm for deterministic networks,

    T. Fukui, Y . Sakaue, K. Minami, and T. Taniguchi, “Delay-based shaper with dynamic token bucket algorithm for deterministic networks,” IEEE Access, vol. 10, pp. 114 424–114 433, 2022

  16. [16]

    Energy-optimal base station density in cellular access networks with sleep modes,

    B. Rengarajan, G. A. Rizzo, and M. Ajmone Marsan, “Energy-optimal base station density in cellular access networks with sleep modes,” Elsevier Computer Networks , vol. 78, pp. 152–163, Feb. 2015

  17. [17]

    Green operations of swipt networks: The role of end-user devices,

    G. Rizzo, M. A. Marsan, C. Esposito, and B. Boi, “Green operations of swipt networks: The role of end-user devices,” IEEE Transactions on Green Communications and Networking , pp. 1–1, 2025

  18. [18]

    The energy saving potential of static and adaptive resource provisioning in dense cellular networks,

    G. A. Rizzo and M. Ajmone Marsan, “The energy saving potential of static and adaptive resource provisioning in dense cellular networks,” in 10th IEEE International Conference on Communication Systems and Networks (COMSNETS 2018) . Bengaluru, India: IEEE, Jan. 2018

  19. [19]

    Orange France 5G - NR, 4G - LTE frequency spectrum bands, 3G - WCDMA, 2G - GSM, FDD, TDD, FR1, FR2 mmWave — spectrum-tracker.com,

    spectrum tracker.com, “Orange France 5G - NR, 4G - LTE frequency spectrum bands, 3G - WCDMA, 2G - GSM, FDD, TDD, FR1, FR2 mmWave — spectrum-tracker.com,” https://www.spectrum-tracker.com/ France/Orange, [Accessed 23-04-2025]

  20. [20]

    The netmob23 dataset: A high-resolution multi-region service-level mobile data traffic cartography,

    O. E. Mart ´ınez-Durive, S. Mishra, C. Ziemlicki, S. Rubrichi, Z. Smoreda, and M. Fiore, “The netmob23 dataset: A high-resolution multi-region service-level mobile data traffic cartography,” 2023

  21. [21]

    Agence Nationale des Fr ´equences (ANFR)

    “Agence Nationale des Fr ´equences (ANFR).” [Online]. Available: https://data.anfr.fr,https://cartoradio.fr[Accessedon28June2023]

  22. [22]

    Population par sexe, ˆage et commune de r ´esidence (statistique n° 7704076),

    Institut national de la statistique et des ´etudes ´economiques (INSEE), “Population par sexe, ˆage et commune de r ´esidence (statistique n° 7704076),” https://www.insee.fr/fr/statistiques/7704076. 8

  23. [2024]

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.