{
  "journal": "Mathematical Programming",
  "corpusBasis": "online publication date",
  "publicationYear": 2025,
  "statusCheckedThrough": "2026-07-13",
  "caveat": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
  "problemCount": 32,
  "problems": [
    {
      "title": "Characterize Frank–Wolfe acceleration on the nuclear-norm ball",
      "topic": "Convex & nonlinear optimization",
      "series": "A",
      "publicationDate": "2025-01-06",
      "sourceLocation": "Section 6, Other numerical experiments",
      "sourceQuote": "This raises the open question to characterize the acceleration FW enjoys when optimizing over the nuclear norm ball.",
      "problemStatement": "Characterize when Frank–Wolfe with open-loop step sizes accelerates on nuclear-norm-ball problems, including the observed primal, dual-gap, and primal–dual rates.",
      "status": "partial_progress",
      "statusEvidence": "Garber (2025) gives accelerated Frank–Wolfe-family algorithms for nuclear-norm and spectrahedral domains under complementarity and sparsity conditions, but does not fully characterize the source algorithm’s observed acceleration.",
      "literature": [
        {
          "title": "Accelerated Frank-Wolfe Algorithms: Complementarity Conditions and Sparsity",
          "url": "https://arxiv.org/abs/2511.02821",
          "relation": "Later partial progress"
        }
      ],
      "keywords": [
        "Frank–Wolfe",
        "nuclear norm",
        "open-loop step size",
        "accelerated rate"
      ],
      "source": {
        "title": "Accelerated affine-invariant convergence rates of the Frank–Wolfe algorithm with open-loop step-sizes",
        "authors": [
          "Elias Wirth",
          "Javier Peña",
          "Sebastian Pokutta"
        ],
        "doi": "10.1007/s10107-024-02180-2",
        "url": "https://doi.org/10.1007/s10107-024-02180-2",
        "preprintUrl": "https://arxiv.org/abs/2310.04096"
      },
      "id": "mp-2025-001",
      "number": 1,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Evolution of solution-norm bounds in quantum-inspired refinement",
      "topic": "Matrix & semidefinite optimization",
      "series": "B",
      "publicationDate": "2025-01-11",
      "sourceLocation": "Conclusion",
      "sourceQuote": "An interesting question … is how ω⁽ᵏ⁾ evolves through iterations of the IR methods.",
      "problemStatement": "Analyze how the solution-norm bound ω⁽ᵏ⁾ changes across semidefinite iterative-refinement subproblems and derive a useful bound that sharpens total IR–IF–QIPM complexity.",
      "keywords": [
        "iterative refinement",
        "quantum interior point",
        "semidefinite optimization",
        "norm bound"
      ],
      "source": {
        "title": "Quantum computing inspired iterative refinement for semidefinite optimization",
        "authors": [
          "Mohammadhossein Mohammadisiahroudi",
          "Brandon Augustino",
          "Pouya Sampourmahani",
          "Tamás Terlaky"
        ],
        "doi": "10.1007/s10107-024-02183-z",
        "url": "https://doi.org/10.1007/s10107-024-02183-z",
        "preprintUrl": "https://arxiv.org/abs/2312.11253"
      },
      "id": "mp-2025-002",
      "number": 2,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Matroid Secretary Conjecture",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-01-15",
      "sourceLocation": "Introduction, Conjecture 1.1",
      "sourceQuote": "Whereas the MSP Conjecture remains open.",
      "problemStatement": "Determine whether a universal O(1)-competitive online algorithm exists for the Matroid Secretary Problem on arbitrary matroids in uniformly random arrival order.",
      "status": "partial_progress",
      "statusEvidence": "A May 2026 technical report still describes the general conjecture as open. Later work improves restricted matroid classes and related formulations, but does not settle arbitrary matroids.",
      "literature": [
        {
          "title": "Matroid Secretary via Labeling Schemes",
          "url": "https://egres.elte.hu/www/tr-25-09.html",
          "relation": "May 2026 source still describing the general conjecture as open"
        },
        {
          "title": "Beating Competitive Ratio 4 for Graphic Matroid Secretary",
          "url": "https://doi.org/10.4230/LIPIcs.ESA.2025.52",
          "relation": "Later progress for a restricted matroid class"
        }
      ],
      "keywords": [
        "matroid secretary",
        "online algorithms",
        "competitive analysis",
        "random order"
      ],
      "source": {
        "title": "Constant-competitiveness for random assignment Matroid secretary without knowing the Matroid",
        "authors": [
          "Richard Santiago",
          "Ivan Sergeev",
          "Rico Zenklusen"
        ],
        "doi": "10.1007/s10107-024-02177-x",
        "url": "https://doi.org/10.1007/s10107-024-02177-x",
        "preprintUrl": "https://arxiv.org/abs/2305.05353"
      },
      "id": "mp-2025-003",
      "number": 3,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Core-membership complexity in partitioned matching games",
      "topic": "Game theory & matching",
      "series": "A",
      "publicationDate": "2025-02-11",
      "sourceLocation": "Conclusions",
      "sourceQuote": "We do not know if P2 … is co-NP-complete.",
      "problemStatement": "Decide whether core-membership problem P2 is co-NP-complete for b-matching games with b not bounded by 2 and for partitioned matching games of width at least 3.",
      "keywords": [
        "matching games",
        "core membership",
        "co-NP-completeness",
        "kidney exchange"
      ],
      "source": {
        "title": "Partitioned matching games for international kidney exchange",
        "authors": [
          "Márton Benedek",
          "Péter Biró",
          "Walter Kern",
          "Dömötör Pálvölgyi",
          "Daniel Paulusma"
        ],
        "doi": "10.1007/s10107-025-02200-9",
        "url": "https://doi.org/10.1007/s10107-025-02200-9"
      },
      "id": "mp-2025-004",
      "number": 4,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "The four-thirds conjecture for the Subtour LP",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-02-17",
      "sourceLocation": "Abstract and Introduction",
      "sourceQuote": "A long-standing conjecture … states that the integrality gap … is at most 4/3.",
      "problemStatement": "Prove that the integrality gap of the Subtour (Held–Karp) LP relaxation for metric TSP is at most 4/3, matching the known lower bound.",
      "statusEvidence": "Two 2026 papers still call this a conjecture: one verifies additional small instances, and one improves the max-entropy analysis on half-integral cycle-cut instances without settling the general gap.",
      "literature": [
        {
          "title": "Extending Exact Integrality Gap Computations for the Metric TSP",
          "url": "https://arxiv.org/abs/2603.12995",
          "relation": "2026 computational evidence; conjecture remains"
        },
        {
          "title": "Maximum Entropy is a 10/7-Approximation Algorithm for the TSP on Half-Integral Cycle Cut Instances",
          "url": "https://arxiv.org/abs/2607.01536",
          "relation": "2026 progress on a special class"
        }
      ],
      "keywords": [
        "traveling salesman",
        "Subtour LP",
        "integrality gap",
        "four-thirds conjecture"
      ],
      "source": {
        "title": "A 4/3-approximation algorithm for half-integral cycle cut instances of the TSP",
        "authors": [
          "Billy Jin",
          "Nathan Klein",
          "David P. Williamson"
        ],
        "doi": "10.1007/s10107-025-02193-5",
        "url": "https://doi.org/10.1007/s10107-025-02193-5",
        "preprintUrl": "https://arxiv.org/abs/2211.04639"
      },
      "id": "mp-2025-005",
      "number": 5,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Lower envelope of bounded monomials in higher dimension",
      "topic": "Mixed-integer & global optimization",
      "series": "B",
      "publicationDate": "2025-03-17",
      "sourceLocation": "Section 4",
      "sourceQuote": "The lower envelope for Wᵢⱼ is an open problem for n > 2.",
      "problemStatement": "Derive the lower envelope, completing the convex-envelope description, for a bounded monomial over X ∩ Wᵢⱼ when the ambient dimension exceeds two.",
      "status": "resolved",
      "statusEvidence": "Yang and Zhang’s June 2026 paper proves that the missing higher-dimensional lower envelope is flat at the lower monomial bound and gives the resulting convexification.",
      "literature": [
        {
          "title": "Flat lower envelopes solve bounded monomial convexification on two-variable cones",
          "url": "https://doi.org/10.36922/IJOCTA026220100",
          "relation": "Resolution published online 29 June 2026"
        }
      ],
      "keywords": [
        "convex envelope",
        "bounded monomial",
        "factorable programming",
        "global optimization"
      ],
      "source": {
        "title": "Convex envelopes of bounded monomials on two-variable cones",
        "authors": [
          "Pietro Belotti"
        ],
        "doi": "10.1007/s10107-025-02212-5",
        "url": "https://doi.org/10.1007/s10107-025-02212-5",
        "preprintUrl": "https://arxiv.org/abs/2308.12650"
      },
      "id": "mp-2025-006",
      "number": 6,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Matrix-LASSO landscape at intermediate ranks",
      "topic": "Matrix & semidefinite optimization",
      "series": "A",
      "publicationDate": "2025-05-24",
      "sourceLocation": "Section 4, rank-constrained guarantees",
      "sourceQuote": "What the situation is for intermediate values of r is still an open question.",
      "problemStatement": "Characterize the rank-constrained matrix-LASSO landscape at ranks beyond the available (2r,δ)-RIP guarantees but below the trivially full-rank regime.",
      "keywords": [
        "matrix LASSO",
        "rank constraint",
        "restricted isometry",
        "overparameterization"
      ],
      "source": {
        "title": "Low solution rank of the matrix LASSO under RIP with consequences for rank-constrained algorithms",
        "authors": [
          "Andrew D. McRae"
        ],
        "doi": "10.1007/s10107-025-02236-x",
        "url": "https://doi.org/10.1007/s10107-025-02236-x"
      },
      "id": "mp-2025-007",
      "number": 7,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "The strongest practical encoding of a disjunctive program",
      "topic": "Mixed-integer & global optimization",
      "series": "B",
      "publicationDate": "2025-06-09",
      "sourceLocation": "Introduction",
      "sourceQuote": "The best encoding of a disjunctive program … as an MIP is an open question.",
      "problemStatement": "Characterize how a disjunctive constraint should be partitioned and encoded so formulation strength, size, and computational performance are balanced within the P-split hierarchy.",
      "keywords": [
        "P-split",
        "disjunctive programming",
        "mixed-integer programming",
        "extended formulation"
      ],
      "source": {
        "title": "P-split formulations: a class of intermediate formulations between big-M and convex hull for disjunctive constraints",
        "authors": [
          "Jan Kronqvist",
          "Ruth Misener",
          "Calvin Tsay"
        ],
        "doi": "10.1007/s10107-025-02232-1",
        "url": "https://doi.org/10.1007/s10107-025-02232-1",
        "preprintUrl": "https://arxiv.org/abs/2202.05198"
      },
      "id": "mp-2025-008",
      "number": 8,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Reinhardt’s maximum-perimeter problem for powers of two",
      "topic": "Mixed-integer & global optimization",
      "series": "B",
      "publicationDate": "2025-06-21",
      "sourceLocation": "Introduction",
      "sourceQuote": "The perimeter problem is still open for the case when n > 8 is a power of two.",
      "problemStatement": "Determine the maximum perimeter of a convex n-gon of diameter at most one when n > 8 is a power of two, and characterize the maximizers.",
      "keywords": [
        "small polygons",
        "maximum perimeter",
        "Reinhardt problem",
        "global optimization"
      ],
      "source": {
        "title": "A zonogon approach for computing small convex polygons of maximum perimeter",
        "authors": [
          "Bernd Mulansky",
          "Andreas Potschka"
        ],
        "doi": "10.1007/s10107-025-02244-x",
        "url": "https://doi.org/10.1007/s10107-025-02244-x"
      },
      "id": "mp-2025-009",
      "number": 9,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Sinkhorn rates under a Poincaré inequality",
      "topic": "Optimal transport",
      "series": "A",
      "publicationDate": "2025-07-01",
      "sourceLocation": "Section 3, before Remark 3.2",
      "sourceQuote": "Assuming that μ satisfies a Poincaré inequality should be a sufficient condition for our results to hold.",
      "problemStatement": "Extend the sharper exponential convergence guarantees for continuous Sinkhorn iterations to measures satisfying an appropriate Poincaré inequality.",
      "keywords": [
        "Sinkhorn algorithm",
        "entropic optimal transport",
        "Poincaré inequality",
        "exponential convergence"
      ],
      "source": {
        "title": "Sharper exponential convergence rates for Sinkhorn’s algorithm in continuous settings",
        "authors": [
          "Lénaïc Chizat",
          "Alex Delalande",
          "Tomas Vaškevičius"
        ],
        "doi": "10.1007/s10107-025-02242-z",
        "url": "https://doi.org/10.1007/s10107-025-02242-z",
        "preprintUrl": "https://arxiv.org/abs/2407.01202"
      },
      "id": "mp-2025-010",
      "number": 10,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Convergence of PDQP’s practical adaptive rules",
      "topic": "Convex & nonlinear optimization",
      "series": "A",
      "publicationDate": "2025-07-02",
      "sourceLocation": "Section 6, p. 27",
      "sourceQuote": "Currently, we do not have a proof of convergence for the adaptive step size rule.",
      "problemStatement": "Prove convergence of PDQP with the adaptive-restart and adaptive step-size rules used in its practical implementation.",
      "statusEvidence": "A 2026 analysis proves adaptive restart for a different nonlinear-conic primal–dual method under metric subregularity; it does not establish convergence of PDQP’s exact rules.",
      "literature": [
        {
          "title": "Restarted Accelerated Primal-Dual Algorithms with Adaptive Stepsizes for Nonlinear Conic Constrained Convex Optimization",
          "url": "https://arxiv.org/abs/2605.29291",
          "relation": "Related 2026 analysis for a different algorithm"
        }
      ],
      "keywords": [
        "quadratic programming",
        "PDQP",
        "adaptive restart",
        "step size"
      ],
      "source": {
        "title": "A Practical and Optimal First-Order Method for Large-Scale Convex Quadratic Programming",
        "authors": [
          "Haihao Lu",
          "Jinwen Yang"
        ],
        "doi": "10.1007/s10107-025-02241-0",
        "url": "https://doi.org/10.1007/s10107-025-02241-0",
        "preprintUrl": "https://arxiv.org/abs/2311.07710"
      },
      "id": "mp-2025-011",
      "number": 11,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Complexity of sortation on out-trees",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-07-17",
      "sourceLocation": "Section 6, p. 19",
      "sourceQuote": "It remains open whether or not out-tree instances are NP-hard.",
      "problemStatement": "Decide whether min-degree-SPP restricted to out-tree instances is NP-hard.",
      "keywords": [
        "sortation",
        "out-trees",
        "NP-hardness",
        "network design"
      ],
      "source": {
        "title": "Fast Combinatorial Algorithms for Efficient Sortation",
        "authors": [
          "Madison Van Dyk",
          "Kim Klause",
          "Jochen Koenemann",
          "Nicole Megow"
        ],
        "doi": "10.1007/s10107-025-02239-8",
        "url": "https://doi.org/10.1007/s10107-025-02239-8",
        "preprintUrl": "https://arxiv.org/abs/2311.05094"
      },
      "id": "mp-2025-012",
      "number": 12,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "A stronger pseudopolynomial state space for matroid interdiction",
      "topic": "Combinatorial optimization",
      "series": "A",
      "publicationDate": "2025-08-19",
      "sourceLocation": "Section 2.3, p. 13",
      "sourceQuote": "The existence of a pseudopolynomial sized T … with worst-case performance of o(m)OPT is an open question.",
      "problemStatement": "Construct a pseudopolynomial-size dynamic-programming state space whose upper bound is o(m)OPT in the worst case, or prove that none exists.",
      "keywords": [
        "interdiction",
        "matroid bases",
        "dynamic programming",
        "pseudopolynomial"
      ],
      "source": {
        "title": "Interdiction of minimum spanning trees and other matroid bases",
        "authors": [
          "Noah Weninger",
          "Ricardo Fukasawa"
        ],
        "doi": "10.1007/s10107-025-02273-6",
        "url": "https://doi.org/10.1007/s10107-025-02273-6",
        "preprintUrl": "https://arxiv.org/abs/2407.14906"
      },
      "id": "mp-2025-013",
      "number": 13,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Guarantees for a tractable copositive-cone replacement",
      "topic": "Mixed-integer & global optimization",
      "series": "B",
      "publicationDate": "2025-08-25",
      "sourceLocation": "Section 5, p. 36",
      "sourceQuote": "An interesting open question is to provide some theoretical guarantee on such modification.",
      "problemStatement": "Quantify the approximation or sensitivity-bound quality obtained when the copositive cone in the mixed-binary quadratic dual is replaced by S₊ + Sₚ.",
      "keywords": [
        "mixed-binary quadratic",
        "copositive optimization",
        "sensitivity",
        "tractable relaxation"
      ],
      "source": {
        "title": "Sensitivity analysis for mixed binary quadratic programming",
        "authors": [
          "Diego Cifuentes",
          "Santanu S. Dey",
          "Jingye Xu"
        ],
        "doi": "10.1007/s10107-025-02265-6",
        "url": "https://doi.org/10.1007/s10107-025-02265-6",
        "preprintUrl": "https://arxiv.org/abs/2312.06714"
      },
      "id": "mp-2025-014",
      "number": 14,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Uniform high-probability price of adaptivity",
      "topic": "Stochastic optimization",
      "series": "A",
      "publicationDate": "2025-09-03",
      "sourceLocation": "Section 6, p. 20",
      "sourceQuote": "Characterizing the uniform-high-probability PoA is an open problem.",
      "problemStatement": "Obtain tight bounds, as functions of distance uncertainty ρ, on the price of adaptivity for guarantees that hold uniformly over every confidence level.",
      "keywords": [
        "stochastic convex optimization",
        "parameter-free methods",
        "price of adaptivity",
        "oracle complexity"
      ],
      "source": {
        "title": "The Price of Adaptivity in Stochastic Convex Optimization",
        "authors": [
          "Yair Carmon",
          "Oliver Hinder"
        ],
        "doi": "10.1007/s10107-025-02268-3",
        "url": "https://doi.org/10.1007/s10107-025-02268-3",
        "preprintUrl": "https://arxiv.org/abs/2402.10898"
      },
      "id": "mp-2025-015",
      "number": 15,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Trajectory predictions with sample reuse",
      "topic": "Stochastic optimization",
      "series": "B",
      "publicationDate": "2025-09-17",
      "sourceLocation": "Concluding discussion, p. 34",
      "sourceQuote": "Understand the effect of sample re-use and develop trajectory predictions in this setting.",
      "problemStatement": "Establish deterministic trajectory predictions and convergence guarantees when stochastic prox-linear matrix-sensing iterations reuse a fixed finite sample instead of fresh minibatches.",
      "keywords": [
        "matrix sensing",
        "prox-linear",
        "sample reuse",
        "trajectory prediction"
      ],
      "source": {
        "title": "Hyperparameter tuning via trajectory predictions: stochastic prox-linear methods in matrix sensing",
        "authors": [
          "Mengqi Lou",
          "Kabir Aladin Verchand",
          "Ashwin Pananjady"
        ],
        "doi": "10.1007/s10107-025-02279-0",
        "url": "https://doi.org/10.1007/s10107-025-02279-0",
        "preprintUrl": "https://arxiv.org/abs/2402.01599"
      },
      "id": "mp-2025-016",
      "number": 16,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Diamond-type quadratic-form optimal transport",
      "topic": "Optimal transport",
      "series": "A",
      "publicationDate": "2025-09-22",
      "sourceLocation": "Appendix D(iv)(a), p. 35",
      "sourceQuote": "We conjecture that some ‘diamond-type’ coupling is the minimizer of the corresponding QOT problem.",
      "problemStatement": "Without symmetric marginals, prove or disprove that an appropriate four-piece diamond coupling minimizes the quadratic-form optimal-transport objective in the setting of Theorem 12.",
      "keywords": [
        "quadratic-form transport",
        "diamond coupling",
        "dependence optimization",
        "marginal symmetry"
      ],
      "source": {
        "title": "Quadratic-form optimal transport",
        "authors": [
          "Ruodu Wang",
          "Zhenyuan Zhang"
        ],
        "doi": "10.1007/s10107-025-02282-5",
        "url": "https://doi.org/10.1007/s10107-025-02282-5",
        "preprintUrl": "https://arxiv.org/abs/2501.04658"
      },
      "id": "mp-2025-017",
      "number": 17,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Unconditional expectation complexity for stochastic Bregman proximal gradient",
      "topic": "Stochastic optimization",
      "series": "A",
      "publicationDate": "2025-10-06",
      "sourceLocation": "Discussion after Theorem 3.8, p. 17",
      "sourceQuote": "Whether one can … obtain the standard in expectation complexity bound.",
      "problemStatement": "Replace the conditional high-probability-event bound in Theorem 3.8 with a comparable, unconditional expectation-complexity guarantee.",
      "keywords": [
        "Bregman proximal gradient",
        "variance reduction",
        "expectation complexity",
        "nonconvex optimization"
      ],
      "source": {
        "title": "Stochastic Bregman Proximal Gradient Method Revisited: Kernel Conditioning and Painless Variance Reduction",
        "authors": [
          "Junyu Zhang"
        ],
        "doi": "10.1007/s10107-025-02285-2",
        "url": "https://doi.org/10.1007/s10107-025-02285-2",
        "preprintUrl": "https://arxiv.org/abs/2401.03155"
      },
      "id": "mp-2025-018",
      "number": 18,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Heavy-ball acceleration in one dimension",
      "topic": "Convex & nonlinear optimization",
      "series": "B",
      "publicationDate": "2025-10-27",
      "sourceLocation": "Section 7, p. 23",
      "sourceQuote": "The potential acceleration of (HB) in a one-dimensional space is thus left open.",
      "problemStatement": "Determine whether fixed-parameter heavy-ball can attain an accelerated worst-case rate on one-dimensional L-smooth, μ-strongly convex functions.",
      "keywords": [
        "heavy-ball",
        "acceleration",
        "one dimension",
        "performance estimation"
      ],
      "source": {
        "title": "Provable non-accelerations of the heavy-ball method",
        "authors": [
          "Baptiste Goujaud",
          "Adrien Taylor",
          "Aymeric Dieuleveut"
        ],
        "doi": "10.1007/s10107-025-02269-2",
        "url": "https://doi.org/10.1007/s10107-025-02269-2",
        "preprintUrl": "https://arxiv.org/abs/2307.11291"
      },
      "id": "mp-2025-019",
      "number": 19,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Improve the lower bound for the max-entropy TSP algorithm",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-10-27",
      "sourceLocation": "Section 5, p. 14",
      "sourceQuote": "Whether one can obtain a lower bound … larger than 11/8.",
      "problemStatement": "Construct metric or graphic TSP instances on which the max-entropy algorithm has asymptotic approximation ratio strictly above 11/8, or prove that 11/8 is tight.",
      "keywords": [
        "TSP",
        "maximum entropy",
        "lower bound",
        "randomized rounding"
      ],
      "source": {
        "title": "A lower bound for the max entropy algorithm for TSP",
        "authors": [
          "Billy Jin",
          "Nathan Klein",
          "David P. Williamson"
        ],
        "doi": "10.1007/s10107-025-02289-y",
        "url": "https://doi.org/10.1007/s10107-025-02289-y",
        "preprintUrl": "https://arxiv.org/abs/2311.01950"
      },
      "id": "mp-2025-020",
      "number": 20,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "PTAS versus constant-additive hardness for robust Stackelberg equilibria",
      "topic": "Game theory & matching",
      "series": "A",
      "publicationDate": "2025-11-12",
      "sourceLocation": "Section 4.2, p. 16",
      "sourceQuote": "To understand whether a PTAS exists for δ-RSE.",
      "problemStatement": "Determine whether approximate δ-robust Stackelberg equilibrium admits a PTAS, or prove hardness of constant-additive approximation.",
      "keywords": [
        "Stackelberg equilibrium",
        "robust equilibrium",
        "PTAS",
        "bilevel optimization"
      ],
      "source": {
        "title": "Robust Stackelberg Equilibria",
        "authors": [
          "Jiarui Gan",
          "Minbiao Han",
          "Jibang Wu",
          "Haifeng Xu"
        ],
        "doi": "10.1007/s10107-025-02291-4",
        "url": "https://doi.org/10.1007/s10107-025-02291-4",
        "preprintUrl": "https://arxiv.org/abs/2304.14990"
      },
      "id": "mp-2025-021",
      "number": 21,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Characterization of uniformly robust norms",
      "topic": "Robust & network optimization",
      "series": "A",
      "publicationDate": "2025-11-24",
      "sourceLocation": "Section 9, Conjecture 9.1, p. 31",
      "sourceQuote": "A norm is uniformly robust if and only if it is polyhedral.",
      "problemStatement": "Prove or disprove that a finite-dimensional norm has uniformly robust Fermat–Weber estimators exactly when its unit ball is polyhedral.",
      "keywords": [
        "Fermat–Weber",
        "breakdown point",
        "polyhedral norm",
        "robust location"
      ],
      "source": {
        "title": "Breakdown points of Fermat–Weber problems under gauge distances",
        "authors": [
          "Andrei Comăneci",
          "Frank Plastria"
        ],
        "doi": "10.1007/s10107-025-02302-4",
        "url": "https://doi.org/10.1007/s10107-025-02302-4",
        "preprintUrl": "https://arxiv.org/abs/2306.13424"
      },
      "id": "mp-2025-022",
      "number": 22,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Constant-factor approximation under fixed non-uniform fault width",
      "topic": "Robust & network optimization",
      "series": "A",
      "publicationDate": "2025-12-01",
      "sourceLocation": "Section 6, p. 27",
      "sourceQuote": "Is there a constant factor approximation for fixed width/connectivity?",
      "problemStatement": "Give a constant-factor approximation for fixed-width Bulk-Robust SNDP and fixed-connectivity flexible network design, or rule one out.",
      "keywords": [
        "survivable network design",
        "non-uniform faults",
        "approximation",
        "fixed width"
      ],
      "source": {
        "title": "Approximation algorithms for network design in non-uniform fault models",
        "authors": [
          "Chandra Chekuri",
          "Rhea Jain"
        ],
        "doi": "10.1007/s10107-025-02298-x",
        "url": "https://doi.org/10.1007/s10107-025-02298-x",
        "preprintUrl": "https://arxiv.org/abs/2403.15547"
      },
      "id": "mp-2025-023",
      "number": 23,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Upper boundary of caterpillar and even-tree profiles",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-12-16",
      "sourceLocation": "Section 5.2, Conjecture 1, p. 21",
      "sourceQuote": "DCat∞ₚ,₁₋ₚ lies on the upper boundary … for all k ≥ 4 and p ∈ [0,1].",
      "problemStatement": "Prove that, for every k ≥ 4 and p ∈ [0,1], the infinite double caterpillar DCat∞ₚ,₁₋ₚ traces the upper boundary of the joint (Catₖ,E₆)-density profile.",
      "keywords": [
        "tree limits",
        "caterpillars",
        "flag algebras",
        "inducibility"
      ],
      "source": {
        "title": "Getting to the root of the problem: sums of squares for limits of trees",
        "authors": [
          "Daniel Brosch",
          "Diane Puges"
        ],
        "doi": "10.1007/s10107-025-02305-1",
        "url": "https://doi.org/10.1007/s10107-025-02305-1",
        "preprintUrl": "https://arxiv.org/abs/2404.12838"
      },
      "id": "mp-2025-024",
      "number": 24,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Efficiently enforce route-level TSP optimality",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-12-16",
      "sourceLocation": "Concluding discussion, p. 31",
      "sourceQuote": "Efficiently ensuring TSP-optimality of selected routes in the CVRP remains an interesting open problem.",
      "problemStatement": "Develop an effective exact formulation or branch-price mechanism that ensures every selected CVRP route is TSP-optimal under non-monotone fairness objectives.",
      "status": "partial_progress",
      "statusEvidence": "The same authors’ April 2026 paper adds TSP-optimality cuts to branch-price-and-cut and reports strong computational performance, but does not provide a general complexity-theoretic resolution.",
      "literature": [
        {
          "title": "Enforcing TSP-Optimality in Fair Vehicle Routing by Cutting Planes",
          "url": "https://arxiv.org/abs/2604.23748",
          "relation": "Direct 2026 partial progress"
        }
      ],
      "keywords": [
        "vehicle routing",
        "TSP-optimality",
        "branch-and-price",
        "fairness"
      ],
      "source": {
        "title": "Efficient branching rules for optimizing range and order-based objective functions",
        "authors": [
          "Bart van Rossum",
          "Rui Chen",
          "Andrea Lodi"
        ],
        "doi": "10.1007/s10107-025-02306-0",
        "url": "https://doi.org/10.1007/s10107-025-02306-0",
        "preprintUrl": "https://arxiv.org/abs/2311.03885"
      },
      "id": "mp-2025-025",
      "number": 25,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Dimension-independent guarantees for matrix fixed-point projection",
      "topic": "Matrix & semidefinite optimization",
      "series": "A",
      "publicationDate": "2025-12-16",
      "sourceLocation": "Section 9, p. 19",
      "sourceQuote": "Of particular interest is whether this approach can yield theoretical dimension-independent guarantees.",
      "problemStatement": "Establish dimension-independent convergence guarantees for the general fixed-point or Riemannian unit-step matrix-projection method beyond the special cases proved in the paper.",
      "keywords": [
        "matrix projection",
        "fixed point",
        "Bures–Wasserstein",
        "quantum information"
      ],
      "source": {
        "title": "A fixed-point algorithm for matrix projections with applications in quantum information",
        "authors": [
          "Shrigyan Brahmachari",
          "Roberto Rubboli",
          "Marco Tomamichel"
        ],
        "doi": "10.1007/s10107-025-02318-w",
        "url": "https://doi.org/10.1007/s10107-025-02318-w",
        "preprintUrl": "https://arxiv.org/abs/2312.14615"
      },
      "id": "mp-2025-026",
      "number": 26,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Deterministic complexity of Exact Perfect Matching",
      "topic": "Combinatorial optimization",
      "series": "A",
      "publicationDate": "2025-02-11",
      "sourceLocation": "Section 1.4, p. 10",
      "sourceQuote": "The complexity status of Exact Perfect Matching is a longstanding open problem.",
      "problemStatement": "Determine whether a deterministic polynomial-time algorithm can decide if a red–blue graph has a perfect matching containing exactly k red edges.",
      "status": "partial_progress",
      "statusEvidence": "A 2025 paper gives parameterized and subexponential results for structured instances. A June 2026 primary source still describes even the bipartite deterministic case as open.",
      "literature": [
        {
          "title": "Exact Matching and Top-k Perfect Matching Parameterized by Neighborhood Diversity or Bandwidth",
          "url": "https://arxiv.org/abs/2510.12552",
          "relation": "Parameterized partial progress"
        },
        {
          "title": "Matroids are Equitable",
          "url": "https://doi.org/10.1007/s00493-026-00217-y",
          "relation": "June 2026 source still describing the deterministic question as open"
        }
      ],
      "keywords": [
        "exact matching",
        "derandomization",
        "perfect matching",
        "complexity"
      ],
      "source": {
        "title": "Partitioned matching games for international kidney exchange",
        "authors": [
          "Márton Benedek",
          "Péter Biró",
          "Walter Kern",
          "Dömötör Pálvölgyi",
          "Daniel Paulusma"
        ],
        "doi": "10.1007/s10107-025-02200-9",
        "url": "https://doi.org/10.1007/s10107-025-02200-9"
      },
      "id": "mp-2025-027",
      "number": 27,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Nucleolus complexity for matching-game variants",
      "topic": "Game theory & matching",
      "series": "A",
      "publicationDate": "2025-02-11",
      "sourceLocation": "Conclusions, p. 34",
      "sourceQuote": "Determining the complexity of computing the nucleolus is still open for the following games.",
      "problemStatement": "Classify the complexity of nucleolus computation for b-matching games with b ≤ 2 and for the listed bounded-width partitioned matching games.",
      "status": "partial_progress",
      "statusEvidence": "Ebert and Ellerbrock (2026) reduce the b ≤ 2 case to Shortest Non-Zero Cycle and solve certain subclasses, but do not settle all families listed by the source.",
      "literature": [
        {
          "title": "Nucleolus Computation by Non-Zero-Constrained Optimization",
          "url": "https://arxiv.org/abs/2605.29571",
          "relation": "Direct 2026 partial progress"
        }
      ],
      "keywords": [
        "nucleolus",
        "cooperative games",
        "b-matching",
        "computational complexity"
      ],
      "source": {
        "title": "Partitioned matching games for international kidney exchange",
        "authors": [
          "Márton Benedek",
          "Péter Biró",
          "Walter Kern",
          "Dömötör Pálvölgyi",
          "Daniel Paulusma"
        ],
        "doi": "10.1007/s10107-025-02200-9",
        "url": "https://doi.org/10.1007/s10107-025-02200-9"
      },
      "id": "mp-2025-028",
      "number": 28,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "A 3/2-approximation for Prize-Collecting TSP",
      "topic": "Combinatorial optimization",
      "series": "B",
      "publicationDate": "2025-05-12",
      "sourceLocation": "Introduction, p. 4",
      "sourceQuote": "It remains open whether there is an efficient algorithm for PCTSP that matches … the 3/2-approximation for TSP.",
      "problemStatement": "Find a polynomial-time 3/2-approximation for metric Prize-Collecting TSP, or an approximation-preserving reduction from metric TSP.",
      "statusEvidence": "No 3/2-approximation was located. An August 2025 paper still identifies the source paper’s ratio, slightly below 1.6, as the best known guarantee.",
      "literature": [
        {
          "title": "Prize-Collecting TSP and Related Problems",
          "url": "https://doi.org/10.4230/LIPIcs.MFCS.2025.7",
          "relation": "Later 2025 status context"
        }
      ],
      "keywords": [
        "prize-collecting TSP",
        "approximation",
        "LP rounding",
        "metric routing"
      ],
      "source": {
        "title": "A better-than-1.6-approximation for prize-collecting TSP",
        "authors": [
          "Jannis Blauth",
          "Nathan Klein",
          "Martin Nägele"
        ],
        "doi": "10.1007/s10107-025-02221-4",
        "url": "https://doi.org/10.1007/s10107-025-02221-4"
      },
      "id": "mp-2025-029",
      "number": 29,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists."
    },
    {
      "title": "Improve feasibility rates for primal constrained VI methods",
      "topic": "Convex & nonlinear optimization",
      "series": "B",
      "publicationDate": "2025-03-20",
      "sourceLocation": "Section 7, p. 23",
      "sourceQuote": "It remains unknown whether such guarantees can be improved.",
      "problemStatement": "Improve the strongly-monotone constraint-violation rate of the paper’s constrained gradient method to O(1/T) or better without requiring multiplier information.",
      "keywords": [
        "variational inequality",
        "functional constraints",
        "feasibility rate",
        "first-order method"
      ],
      "source": {
        "title": "Primal methods for variational inequality problems with functional constraints",
        "authors": [
          "Liang Zhang",
          "Niao He",
          "Michael Muehlebach"
        ],
        "doi": "10.1007/s10107-025-02206-3",
        "url": "https://doi.org/10.1007/s10107-025-02206-3"
      },
      "id": "mp-2025-030",
      "number": 30,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Acceleration using only currently violated nonlinear constraints",
      "topic": "Convex & nonlinear optimization",
      "series": "A",
      "publicationDate": "2025-04-21",
      "sourceLocation": "Introduction, p. 2",
      "sourceQuote": "We conjecture that the same rates can be achieved asymptotically for I = Iₓ.",
      "problemStatement": "Prove asymptotic accelerated linear rates for the discrete velocity-projection method when it enforces only currently violated constraints rather than every constraint.",
      "keywords": [
        "nonlinear constraints",
        "acceleration",
        "active set",
        "velocity projection"
      ],
      "source": {
        "title": "Accelerated first-order optimization under nonlinear constraints",
        "authors": [
          "Michael Muehlebach",
          "Michael I. Jordan"
        ],
        "doi": "10.1007/s10107-025-02224-1",
        "url": "https://doi.org/10.1007/s10107-025-02224-1"
      },
      "id": "mp-2025-031",
      "number": 31,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    },
    {
      "title": "Strong regularity for general C²-cone-reducible constraints",
      "topic": "Convex & nonlinear optimization",
      "series": "A",
      "publicationDate": "2025-06-02",
      "sourceLocation": "Remark 4.4, p. 30",
      "sourceQuote": "It is still unknown if the strong regularity of the KKT system … is equivalent to the constraint nondegeneracy.",
      "problemStatement": "For an arbitrary C²-cone-reducible set, characterize whether KKT strong regularity is equivalent to constraint nondegeneracy plus an appropriate second-order sufficient condition.",
      "keywords": [
        "strong regularity",
        "KKT system",
        "cone reducibility",
        "Aubin property"
      ],
      "source": {
        "title": "Characterizations of the Aubin property of the solution mapping for nonlinear semidefinite programming",
        "authors": [
          "Liang Chen",
          "Ruoning Chen",
          "Defeng Sun",
          "Liping Zhang"
        ],
        "doi": "10.1007/s10107-025-02231-2",
        "url": "https://doi.org/10.1007/s10107-025-02231-2",
        "preprintUrl": "https://arxiv.org/abs/2408.08232"
      },
      "id": "mp-2025-032",
      "number": 32,
      "recordType": "reviewed",
      "sourceClaim": "explicit_open_problem",
      "status": "no_resolution_found",
      "statusCheckedThrough": "2026-07-13",
      "statusEvidence": "Targeted title, exact-statement, and forward-literature searches located no later paper claiming a complete resolution.",
      "verificationNote": "No resolution found is an evidence-bounded search result, not proof that no resolution exists.",
      "literature": []
    }
  ]
}