Pith. sign in

REVIEW 3 minor 42 references

A Hamilton-Jacobi reachability method grades safety in emergency landing envelopes through continuous violation costs rather than pointwise binary checks.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Introduces a graded safety framework for emergency landing flight envelopes using state- and time-dependent violation cost functions in Hamilton-Jacobi reachability, with monotonicity properties and a convergent synthesis algorithm for least conservative parameters.

T0 review reviewed 2026-06-28 challenge →

load-bearing objection This paper extends Hamilton-Jacobi reachability to graded safety for emergency landing envelopes by introducing a class of continuous violation cost functions, their monotonicity properties, and a convergent synthesis algorithm for least-conservative parameters.

arxiv 2606.05350 v1 pith:CPTPRJ3N submitted 2026-06-03 eess.SY cs.SY

Characterization and Analysis of Emergency Landing Flight Envelopes with Graded Safety Specifications

Chams Eddine Mballo , Bryce L. Ferguson , Inkyu Jang , Donggun Lee , Claire J. Tomlin This is my paper
classification eess.SY cs.SY
keywords emergency landingflight envelopegraded safetysoft constraintsHamilton-Jacobi reachabilityviolation cost functionfixed-wing aircraft
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

The paper replaces the traditional binary definition of safety in flight envelope analysis with a graded notion that tolerates limited time in degraded states. It encodes this grading via designer-specified continuous violation cost functions that assign zero cost in nominal flight and increasing cost for more critical off-nominal states. The authors establish monotonicity and continuity properties showing how the reachable flight envelope changes with the cost function, then give a synthesis algorithm that tunes parameters in this class to meet a prescribed off-nominal safety requirement while remaining as permissive as possible. Numerical results on a fixed-wing aircraft with propulsion failure illustrate the sensitivity of the envelope to the cost parameters and confirm that the algorithm converges to the least conservative feasible value.

Core claim

Safety in emergency landing trajectories is assessed by a trajectory-dependent criterion using a continuous violation cost function that is zero inside the nominal regime and rises with the severity and duration of off-nominal states; Hamilton-Jacobi reachability applied to this soft-constraint formulation yields monotonic and continuous dependence of the safe set on the cost parameters, and a parameter-tuning algorithm converges to the least conservative value satisfying a given off-nominal safety threshold.

What carries the argument

Hamilton-Jacobi reachability applied to a soft constraint defined by a state- and time-dependent continuous violation cost function that replaces pointwise binary safety checks.

Load-bearing premise

A designer must supply a continuous violation cost function that correctly encodes the intended continuum from nominal to critical states.

What would settle it

Run the synthesis algorithm on a concrete aircraft model and violation-cost family; if the returned parameter set fails to keep the integrated violation cost below the prescribed threshold for all trajectories in the computed envelope, the convergence claim is false.

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

If this is right

  • The reachable set of safe states expands monotonically as the violation cost function is made less penalizing.
  • Small changes in the cost parameters produce continuous changes in the size of the emergency landing envelope.
  • The algorithm returns the minimal parameter value that still satisfies any chosen off-nominal safety bound.
  • The same framework applies to any dynamical system whose safety requirement can be expressed by an integrable continuous cost.

Where Pith is reading between the lines

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

  • The method could be used to compare different aircraft recovery strategies by measuring how much each strategy relaxes the required violation cost.
  • If the cost function is chosen to reflect regulatory or insurance limits on exposure time, the resulting envelope directly gives the largest allowable operating region under those limits.
  • Extending the cost function to include actuator limits or sensor uncertainty would produce envelopes that already incorporate those practical constraints.
Share X Bluesky LinkedIn Reddit HN

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

0 major / 3 minor

Summary. The paper develops a Hamilton-Jacobi reachability framework for emergency landing flight envelopes that replaces binary pointwise safety constraints with a graded notion of safety. Safety is encoded via a designer-specified class of state- and time-dependent continuous violation cost functions that assign zero cost inside the nominal regime and increasing cost for more critical off-nominal states. The authors establish monotonicity and continuity properties of the resulting flight envelope with respect to the cost-function parameters, then propose a synthesis algorithm that is proven to converge to the least-conservative parameter satisfying a prescribed off-nominal safety requirement. Numerical results on a fixed-wing aircraft under propulsion failure illustrate the sensitivity properties and algorithm behavior.

Significance. If the claimed monotonicity, continuity, and convergence results hold, the work supplies a principled sensitivity analysis that directly links safety conservativeness to operational capability, moving beyond binary envelopes to a continuum model that better matches operational practice. The explicit convergence guarantee for the parameter-selection algorithm is a concrete strength that supports reproducible design tuning.

minor comments (3)
  1. [Abstract / §2] The abstract and introduction refer to 'a general class of state- and time-dependent violation cost functions' without an explicit functional form or parameter count; a compact definition (e.g., in §2 or §3) would clarify the scope of the monotonicity theorems.
  2. [Numerical results] Numerical results section would benefit from an explicit statement of the discretization parameters (grid size, time step) used for the Hamilton-Jacobi PDE solve, to allow direct reproduction of the reported envelopes.
  3. [Figures] Figure captions should indicate which curves correspond to the nominal, degraded, and critical regimes so that the graded-safety interpretation is immediately visible without reference to the text.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. The referee's description accurately captures the paper's framework, properties, and algorithm. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper extends standard Hamilton-Jacobi reachability by introducing a parameterized class of continuous violation cost functions for graded safety, then derives monotonicity/continuity properties of the resulting flight envelopes and a convergent synthesis algorithm for the least-conservative parameter satisfying a safety requirement. These steps rely on explicit designer-specified inputs and standard reachability theory rather than reducing any claimed prediction or uniqueness result to a fitted parameter or self-citation chain. The dependence on the cost-function class is stated as an assumption, not derived from the outputs, and no equations or results are shown to be equivalent to their inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The paper introduces a new class of state- and time-dependent violation cost functions as the core modeling tool for graded safety, relying on standard reachability assumptions plus domain-specific properties of the cost functions.

free parameters (1)
  • violation cost function parameters
    The synthesis algorithm searches over these parameters to satisfy the off-nominal safety requirement at minimal conservativeness.
axioms (2)
  • domain assumption The violation cost function assigns zero cost in the nominal regime and larger cost to more safety-critical off-nominal states
    Used to encode the graded safety notion via soft constraints.
  • domain assumption Monotonicity and continuity properties characterize how the flight envelope varies with the cost of off-nominal operation
    Established for the general class of cost functions to enable sensitivity analysis.

reviewed 2026-06-28 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Characterization and Analysis of Emergency Landing Flight Envelopes with Graded Safety Specifications." pith.science (2026). https://pith.science/paper/CPTPRJ3N

@misc{pith2026260605350,
  author       = {Pith},
  title        = {Pith review of: Characterization and Analysis of Emergency Landing Flight Envelopes with Graded Safety Specifications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CPTPRJ3N}},
  note         = {Machine review of arXiv:2606.05350}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Emergency landing flight envelope analysis traditionally adopts a binary notion of safety, whereby a trajectory is safe only if state constraints are satisfied pointwise in time. In practice, ensuring a successful landing requires recognizing that aircraft operation spans a continuum in the state space from the nominal to the critical regime. Between these regimes lies a degraded regime of states outside nominal operation that may be visited only for limited durations. Safety is therefore inherently graded, in the sense that limited exposure to degraded states may be tolerated, and must be assessed using a trajectory-dependent criterion rather than a purely pointwise-in-time one. This paper develops a Hamilton-Jacobi reachability framework for analyzing emergency landing flight envelopes under this graded notion of safety. Safety is encoded through a soft constraint defined by a designer-specified continuous violation cost function that assigns zero cost in the nominal regime and larger cost to more safety-critical off-nominal states. We introduce a general class of state- and time-dependent violation cost functions and establish monotonicity and continuity properties that characterize how the flight envelope varies with the cost of off-nominal operation. These results provide a principled sensitivity analysis linking safety conservativeness to operational capability. Building on this analysis, we propose a synthesis algorithm for parameterized violation cost functions in this class. The algorithm provably converges to the least conservative parameter under which a prescribed off-nominal safety requirement is satisfied. Numerical results for a fixed-wing emergency landing scenario under propulsion failure demonstrate the sensitivity properties and validate the algorithm.

Figures

Figures reproduced from arXiv: 2606.05350 by Bryce L. Ferguson, Chams Eddine Mballo, Claire J. Tomlin, Donggun Lee, Inkyu Jang.

Figure 1
Figure 1. Figure 1: Computed emergency landing flight envelope [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Asymptotic behavior of the soft-constrained reach-avoid set [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Parameter tuning via Algorithm 1. The figure depicts the iterative [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 2 canonical work pages

  1. [1]

    Data-driven safety filters: Hamilton– jacobi reachability, control barrier functions, and predictive methods for uncertain systems,

    K. P. Wabersich, A. J. Taylor, J. J. Choi, K. Sreenath, C. J. Tomlin, A. D. Ames, and M. N. Zeilinger, “Data-driven safety filters: Hamilton– jacobi reachability, control barrier functions, and predictive methods for uncertain systems,”IEEE Control Systems Magazine, vol. 43, no. 5, pp. 137–177, Oct. 2023

    2023

  2. [2]

    Control barrier function based quadratic programs for safety critical systems,

    A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,”IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, Aug. 2017

    2017

  3. [3]

    Design of a flight envelope protection system for NASA’s transport class model,

    N. Tekles, J. Chongvisal, E. Xargay, R. Choe, D. A. Talleur, N. Hov- akimyan, and C. M. Belcastro, “Design of a flight envelope protection system for NASA’s transport class model,”Journal of Guidance, Con- trol, and Dynamics, vol. 40, no. 4, pp. 863–877, 2017

    2017

  4. [4]

    Methodologies for adaptive flight envelope estimation and protection,

    L. Tang, M. Roemer, J. Ge, A. Crassidis, J. V . R. Prasad, and C. Belcastro, “Methodologies for adaptive flight envelope estimation and protection,” inProceedings of the AIAA Guidance, Navigation, and Control Conference, Chicago, IL, USA, Aug. 2009

    2009

  5. [5]

    Envelope protec- tion for autonomous unmanned aerial vehicles,

    I. Yavrucuk, J. V . R. Prasad, and S. Unnikrishnan, “Envelope protec- tion for autonomous unmanned aerial vehicles,”Journal of Guidance, Control, and Dynamics, vol. 32, no. 1, pp. 248–261, 2009

    2009

  6. [6]

    Reachability-based forced landing system,

    A. K. Akametalu, C. J. Tomlin, and M. Chen, “Reachability-based forced landing system,”Journal of Guidance, Control, and Dynamics, vol. 41, no. 12, pp. 2529–2542, 2018. 14

    2018

  7. [7]

    Flight envelope,

    H. Walgemoed, “Flight envelope,” inIntroduction to Flight Test Engi- neering, ser. RTO AGARDograph 300, Flight Test Techniques Series, F. N. Stoliker, Ed. North Atlantic Treaty Organisation, Research and Technology Organisation, 2005, vol. 14, ch. 12

    2005

  8. [8]

    Flight evaluation of a reactionary envelope protection system for uavs,

    S. Unnikrishnan, J. V . R. Prasad, and I. Yavrucuk, “Flight evaluation of a reactionary envelope protection system for uavs,”Journal of the American Helicopter Society, vol. 56, no. 1, 2011

    2011

  9. [9]

    Investigation of practical flight envelope protection systems for small aircraft,

    W. Falkena, C. Borst, Q. P. Chu, and J. A. Mulder, “Investigation of practical flight envelope protection systems for small aircraft,”Journal of Guidance, Control, and Dynamics, vol. 34, no. 4, pp. 976–988, Aug. 2011

    2011

  10. [10]

    Adaptive limit margin prediction and control cueing for carefree maneuvering of vtol aircraft,

    I. Yavrucuk and J. V . R. Prasad, “Adaptive limit margin prediction and control cueing for carefree maneuvering of vtol aircraft,” inProceed- ings of the AHS Flight Controls and Crew System Design Technical Specialists’ Meeting, Philadelphia, PA, Oct. 2002

    2002

  11. [11]

    A piloted simulation investigation of helicopter limit cueing,

    M. S. Whalley, “A piloted simulation investigation of helicopter limit cueing,” U.S. Army Aviation and Troop Command, Aeroflightdynamics Directorate, Moffett Field, CA, Tech. Rep. USAATCOM Technical Report 94-A-020, Oct. 1994

    1994

  12. [12]

    Comparison of active sidestick and conventional inceptors for helicopter flight envelope tactile cueing,

    M. S. Whalley, B. Hindson, and G. Thiers, “Comparison of active sidestick and conventional inceptors for helicopter flight envelope tactile cueing,” NASA Ames Research Center, Moffett Field, CA, Tech. Rep., Jan. 2000

    2000

  13. [13]

    Develop a method of compliance to support certification of advanced flight controls in general aviation and hybrid vehicles,

    M. Lotterio, “Develop a method of compliance to support certification of advanced flight controls in general aviation and hybrid vehicles,” National Test Pilot School, Atlantic City International Airport, NJ, Tech. Rep. DOT/FAA/TC-21/6, Feb. 2022

    2022

  14. [14]

    Mission task element development process: An approach to FAA handling qualities certification,

    D. H. Klyde, P. C. Schulze, D. G. Mitchell, D. Sizoo, R. Schaller, and R. McGuire, “Mission task element development process: An approach to FAA handling qualities certification,” inAIAA Aviation Forum, 2020

    2020

  15. [15]

    A time-dependent Hamilton–Jacobi formulation of reachable sets for continuous dynamic games,

    I. M. Mitchell, A. M. Bayen, and C. J. Tomlin, “A time-dependent Hamilton–Jacobi formulation of reachable sets for continuous dynamic games,”IEEE Transactions on Automatic Control, vol. 50, no. 7, pp. 947–957, Jul. 2005

    2005

  16. [16]

    Hamilton–Jacobi formulation for reach– avoid differential games,

    K. Margellos and J. Lygeros, “Hamilton–Jacobi formulation for reach– avoid differential games,”IEEE Transactions on Automatic Control, vol. 56, no. 8, pp. 1849–1861, Aug. 2011

    2011

  17. [17]

    A Hamilton–Jacobi reacha- bility framework with soft constraints for safety-critical systems,

    C. E. Mballo, D. Lee, and C. J. Tomlin, “A Hamilton–Jacobi reacha- bility framework with soft constraints for safety-critical systems,”arXiv preprint arXiv:2510.24933, 2025, under review for IEEE Transactions on Automatic Control

    work page arXiv 2025

  18. [18]

    Robust maneuvering envelope estimation based on reachability analysis in an optimal control formulation,

    T. Lombaerts, S. Schuet, K. R. Wheeler, D. Acosta, and J. Kaneshige, “Robust maneuvering envelope estimation based on reachability analysis in an optimal control formulation,” inProceedings of the 3rd Interna- tional Conference on Control and Fault-Tolerant Systems (SysTol), Nice, France, Oct. 2013, pp. 1–8

    2013

  19. [19]

    Effects of structural failure on the safe flight envelope of aircraft,

    H. N. Nabi, T. Lombaerts, Y . Zhang, E. van Kampen, Q. P. Chu, and C. C. de Visser, “Effects of structural failure on the safe flight envelope of aircraft,”Journal of Guidance, Control, and Dynamics, vol. 41, no. 6, pp. 1257–1275, Jun. 2018

    2018

  20. [20]

    Autonomous flight envelope estimation for loss-of-control prevention,

    S. Schuet, T. Lombaerts, D. Acosta, J. Kaneshige, K. Wheeler, and K. Shish, “Autonomous flight envelope estimation for loss-of-control prevention,”Journal of Guidance, Control, and Dynamics, vol. 40, no. 4, pp. 847–862, 2017

    2017

  21. [21]

    Towards flight envelope protection for the NASA tilt- wing eVTOL flight-mode transition using Hamilton–Jacobi reachability,

    T. Hsu, J. J. Choi, D. Amin, C. J. Tomlin, S. C. MacWherter, and M. Piedmonte, “Towards flight envelope protection for the NASA tilt- wing eVTOL flight-mode transition using Hamilton–Jacobi reachability,” Journal of the American Helicopter Society, vol. 69, no. 2, pp. 1–18, Apr. 2024

    2024

  22. [22]

    Aircraft autolander safety analysis through optimal-control-based reach- set computation,

    A. M. Bayen, I. M. Mitchell, M. M. K. Oishi, and C. J. Tomlin, “Aircraft autolander safety analysis through optimal-control-based reach- set computation,”Journal of Guidance, Control, and Dynamics, vol. 30, no. 1, pp. 68–77, Jan. 2007

    2007

  23. [23]

    A general safety framework for learning-based control in uncertain robotic systems,

    J. F. Fisac, A. K. Akametalu, M. N. Zeilinger, S. Kaynama, J. Gillula, and C. J. Tomlin, “A general safety framework for learning-based control in uncertain robotic systems,”IEEE Transactions on Automatic Control, vol. 64, no. 7, pp. 2737–2752, Jul. 2019

    2019

  24. [24]

    Altman,Constrained Markov Decision Processes

    E. Altman,Constrained Markov Decision Processes. Boca Raton, FL: CRC Press, 1999

    1999

  25. [25]

    Robust constrained MDPs: Soft-constrained robust policy optimization under model uncer- tainty,

    R. H. Russel, M. Benosman, and J. van Baar, “Robust constrained MDPs: Soft-constrained robust policy optimization under model uncer- tainty,”arXiv preprint arXiv:2010.04870, 2020

    work page arXiv 2010

  26. [26]

    Soft constrained model predictive control with robust stability guarantees,

    M. N. Zeilinger, M. Morari, and C. N. Jones, “Soft constrained model predictive control with robust stability guarantees,”IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1190–1202, May 2014

    2014

  27. [27]

    A soft constrained mpc formulation enabling learning from trajectories with constraint violations,

    K. P. Wabersich, R. Krishnadas, and M. N. Zeilinger, “A soft constrained mpc formulation enabling learning from trajectories with constraint violations,”IEEE Control Systems Letters, vol. 6, pp. 980–985, 2022

    2022

  28. [28]

    Hierarchical relaxation of safety- critical controllers: Mitigating contradictory safety conditions with ap- plication to quadruped robots,

    J. Lee, J. Kim, and A. D. Ames, “Hierarchical relaxation of safety- critical controllers: Mitigating contradictory safety conditions with ap- plication to quadruped robots,” inProceedings of the IEEE/RSJ Inter- national Conference on Intelligent Robots and Systems (IROS), Detroit, MI, USA, Oct. 2023, pp. 2384–2391

    2023

  29. [29]

    Rule-based optimal control for autonomous driv- ing,

    W. Xiao, N. Mehdipour, A. Collin, A. Y . Bin-Nun, E. Frazzoli, R. D. Tebbens, and C. Belta, “Rule-based optimal control for autonomous driv- ing,” inProceedings of the ACM/IEEE 12th International Conference on Cyber-Physical Systems (ICCPS), Nashville, TN, USA, May 2021, pp. 143–154

    2021

  30. [30]

    Risk- constrained reinforcement learning with percentile risk criteria,

    Y . Chow, M. Ghavamzadeh, L. Janson, and M. Pavone, “Risk- constrained reinforcement learning with percentile risk criteria,” inPro- ceedings of the 34th International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, vol. 70, Sydney, Australia, 2017, pp. 607–616

    2017

  31. [31]

    Reward constrained policy optimization,

    C. Tessler, D. J. Mankowitz, and S. Mannor, “Reward constrained policy optimization,” inProceedings of the AAAI Conference on Artificial Intelligence, Honolulu, HI, USA, 2019, pp. 5020–5027

    2019

  32. [32]

    Soft constraints and exact penalty functions in model predictive control,

    E. C. Kerrigan and J. M. Maciejowski, “Soft constraints and exact penalty functions in model predictive control,” inProceedings of the UKACC International Conference on Control, Cambridge, U.K., Sep. 2000, pp. 2319–2327

    2000

  33. [33]

    Soft constraints in the robust mpc design via lmis,

    J. Oravec and M. Bako ˇsov´a, “Soft constraints in the robust mpc design via lmis,” inProceedings of the American Control Conference, Boston, MA, USA, Jul. 2016, pp. 3588–3593

    2016

  34. [34]

    Fast model predictive control with soft constraints,

    A. Richards, “Fast model predictive control with soft constraints,” European Journal of Control, vol. 25, pp. 51–59, Apr. 2015

    2015

  35. [35]

    E. A. Coddington and N. Levinson,Theory of Ordinary Differential Equations. Malabar, FL, USA: Krieger, 1984

    1984

  36. [36]

    Differential games and representation formulas for solutions of Hamilton–Jacobi–Isaacs equations,

    L. C. Evans and P. E. Souganidis, “Differential games and representation formulas for solutions of Hamilton–Jacobi–Isaacs equations,”Indiana University Mathematics Journal, vol. 33, no. 5, pp. 773–797, 1984

    1984

  37. [37]

    Optimal control helper toolbox,

    M. Chen, S. Herbert, S. Bansal, and C. J. Tomlin, “Optimal control helper toolbox,” https://github.com/HJReachability/helperOC, 2023

    2023

  38. [38]

    The flexible, extensible and efficient toolbox of level set methods,

    I. M. Mitchell, “The flexible, extensible and efficient toolbox of level set methods,”Journal of Scientific Computing, vol. 35, pp. 300–329, 2008

    2008

  39. [39]

    Viscosity solutions of Hamilton–Jacobi equations,

    M. G. Crandall and P.-L. Lions, “Viscosity solutions of Hamilton–Jacobi equations,”Transactions of the American Mathematical Society, vol. 277, no. 1, pp. 1–42, May 1983

    1983

  40. [40]

    A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives,

    T. R. Chandrupatla, “A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives,” Advances in Engineering Software, vol. 28, no. 3, pp. 145–149, 1997

    1997

  41. [41]

    14 CFR §25.125: Landing,

    Federal Aviation Administration, “14 CFR §25.125: Landing,” Code of Federal Regulations, Title 14, Part 25, 2026, airworthiness Standards: Transport Category Airplanes. Chams Eddine Mballoreceived the Ph.D. degree in aerospace engineering (2022) and the M.S. degree in mathematics (2021) from the Georgia Institute of Technology, Atlanta. He is currently a ...

    2026

  42. [42]

    candidate in Aerospace Engineering at Seoul National University, Seoul, Korea

    He is currently a Ph.D. candidate in Aerospace Engineering at Seoul National University, Seoul, Korea. His research interests include safety-critical control and stochastic control and their connection with machine learning, with applications to robotics. Donggun Leereceived the Ph.D. degree in me- chanical engineering from the University of Cal- ifornia,...

    1998

This paper was first reviewed by grok-4.3 on June 28, 2026.