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opa.phys.statistical-mechanics.3d-ising-model-exact-solution | 3D Ising Model Exact Solution | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Find an exact solution for the 3D Ising model partition function. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.3d-ising-model-exact-solution
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_3d_ising_model_exact_solution
url: https://en.wikiped... | ||
opa.phys.statistical-mechanics.3d-ising-model-phase-transition | Rigorous Analysis of the 3D Ising Model Phase Transition | mathematical-physics | ["statistical-mechanics"] | open | tier_1 | conjecture | The three-dimensional Ising model on the cubic lattice Z^3 with nearest-neighbor ferromagnetic coupling J > 0 and Hamiltonian H = -J sum_{<i,j>} sigma_i sigma_j (where sigma_i in {-1, +1}) is known to exhibit a phase transition at some critical inverse temperature beta_c in (0, infinity). While the existence of a phase... | The Ising model describes magnetic spins on a lattice that prefer to align with their neighbors. In two dimensions, Onsager found an exact solution in 1944. In three dimensions, we know a phase transition occurs (the material becomes magnetic below a critical temperature), but we cannot prove the precise mathematical n... | high | computational | high | 0.95 | 0.35 | 0.6 | 0.7 | 0.45 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- 3D Ising Model Critical Behavior
- Three-Dimensional Ising Model Exact Solution
answer_type: boolean
dates:
first_stated: 1925
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.s... |
opa.phys.statistical-mechanics.abelian-sandpile-model-theory | Abelian Sandpile Model Theory | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Develop a complete theory of the abelian sandpile model on general graphs. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.abelian-sandpile-model-theory
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_abelian_sandpile_model_theory
url: https://en.wikiped... | ||
opa.phys.quantum-information.absolutely-maximally-entangled-states | Absolutely Maximally Entangled States | mathematical-physics | ["quantum-information"] | open | tier_3 | Determine the existence of absolutely maximally entangled states for all numbers of parties. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-information.absolutely-maximally-entangled-states
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_absolutely_maximally_entangled_states
url: http... | ||
opa.phys.condensed-matter.active-matter-universal-properties | Active Matter Universal Properties | mathematical-physics | ["condensed-matter"] | open | tier_3 | Determine universal properties and phase transitions in active matter systems. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.active-matter-universal-properties
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_active_matter_universal_properties
url: https://en.wi... | ||
opa.phys.statistical-mechanics.active-matter-universality-classes | Active Matter Universality Classes | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | What are the universality classes of phase transitions in active matter systems, and how do they differ from equilibrium universality? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.active-matter-universality-classes
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_marchetti_2013
url: https://arxiv.org/abs/1207.2929
... | ||
opa.phys.quantum-information.additivity-conjecture-quantum-channel-capacity | Additivity Conjecture for Quantum Channel Capacity | mathematical-physics | ["quantum-information"] | disproved | tier_1 | conjecture | The additivity conjecture for quantum channel capacity, in its strongest form, asserted that the minimum output entropy S_min(Phi) = min_{rho} S(Phi(rho)) of a quantum channel Phi is additive under tensor products: S_min(Phi_1 tensor Phi_2) = S_min(Phi_1) + S_min(Phi_2) for all channels Phi_1, Phi_2. Hastings (2009) di... | When we send classical information through a quantum channel, can we always compute the maximum transmission rate (classical capacity) from a single use of the channel, or do we need to consider entangled inputs across many channel uses? While the general additivity conjecture was disproved, determining the classical c... | high | computational | high | 0.9 | 0.45 | 0.55 | 0.8 | 0.5 | ai:
recommended_tools:
- python
- matlab
solver_ready: false
aliases:
- Additivity of Minimum Output Entropy Conjecture
- Additivity of Holevo Capacity
answer_type: boolean
dates:
first_stated: 2002
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.quantu... |
opa.phys.quantum-information.additivity-of-minimum-output-entropy | Additivity of Minimum Output Entropy | mathematical-physics | ["quantum-information"] | open | tier_3 | Is the minimum output entropy of a quantum channel additive under tensor products? The Hastings counterexample disproved additivity in general, but the structure of violations remains poorly understood. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-information.additivity-of-minimum-output-entropy
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_hastings_2009
url: https://arxiv.org/abs/0809.3972
... | ||
opa.phys.quantum-information.additivity-of-quantum-channel-capacity | Additivity of Quantum Channel Capacity | mathematical-physics | ["quantum-information"] | open | tier_3 | Determine when the capacity of quantum channels is additive. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-information.additivity-of-quantum-channel-capacity
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_additivity_of_quantum_channel_capacity
url: ht... | ||
opa.phys.string-theory.ads-cft-correspondence-proof | AdS/CFT Correspondence Proof | mathematical-physics | ["string-theory"] | open | tier_3 | Provide a rigorous proof of the AdS/CFT correspondence. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.ads-cft-correspondence-proof
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_ads_cft_correspondence_proof
url: https://en.wikipedia.org/wik... | ||
opa.phys.condensed-matter.affleck-kennedy-lieb-tasaki-state-properties | Affleck-Kennedy-Lieb-Tasaki State Properties | mathematical-physics | ["condensed-matter"] | open | tier_3 | Determine the exact entanglement properties of AKLT states in all dimensions. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.affleck-kennedy-lieb-tasaki-state-properties
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_affleck_kennedy_lieb_tasaki_state_properties
... | ||
opa.phys.string-theory.agt-correspondence-full-proof | AGT Correspondence Full Proof | mathematical-physics | ["string-theory"] | open | tier_3 | Prove the Alday-Gaiotto-Tachikawa correspondence relating 4D N=2 gauge theories to 2D CFTs. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.agt-correspondence-full-proof
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_agt_correspondence_full_proof
url: https://en.wikipedia.org/w... | ||
opa.phys.mathematical-physics.agt-correspondence-proof | AGT Correspondence Proof | mathematical-physics | ["mathematical-physics"] | open | tier_2 | conjecture | Prove the AGT (Alday-Gaiotto-Tachikawa) correspondence: the Nekrasov instanton partition function of a 4D N=2 superconformal gauge theory of class S (obtained by compactifying the 6D (2,0) theory on a punctured Riemann surface C) equals the conformal block of 2D Toda conformal field theory on C. Specifically, prove tha... | The AGT correspondence is a surprising duality between 4D gauge theory partition functions and 2D conformal field theory correlation functions. Despite overwhelming evidence, a mathematical proof is missing.
| medium | mixed | medium | 0.88 | 0.4 | 0.3 | 0.6 | 0.2 | ai:
recommended_tools:
- mathematica
solver_ready: false
aliases:
- Alday-Gaiotto-Tachikawa Correspondence
- AGT Conjecture
answer_type: boolean
dates:
first_stated: 2009
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.mathematical-physics.agt-corresponde... |
opa.phys.statistical-mechanics.airy-process-universality | Airy Process Universality | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Prove the universality of the Airy process in models of random growth. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.airy-process-universality
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_airy_process_universality
url: https://en.wikipedia.org/w... | ||
opa.phys.condensed-matter.aklt-model-extensions | AKLT Model Extensions | mathematical-physics | ["condensed-matter"] | open | tier_3 | Extend the AKLT model solution to higher dimensions and determine the spectral gap. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.aklt-model-extensions
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_aklt_model_extensions
url: https://en.wikipedia.org/wiki/AKLT_mode... | ||
opa.phys.scattering-amplitudes.amplituhedron-and-positive-geometry | Amplituhedron and Positive Geometry | mathematical-physics | ["scattering-amplitudes"] | open | tier_3 | Can the amplituhedron framework be extended to compute full non-planar scattering amplitudes in N=4 SYM, and does it generalize to realistic gauge theories? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.scattering-amplitudes.amplituhedron-and-positive-geometry
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_arkani_hamed_2021
url: https://arxiv.org/abs/1312.2... | ||
opa.phys.quantum-field-theory.amplituhedron-and-scattering-amplitudes | Amplituhedron and Scattering Amplitudes | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Does the amplituhedron construction generalize beyond planar N=4 SYM to provide a geometric formulation of scattering amplitudes in realistic theories? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.amplituhedron-and-scattering-amplitudes
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_arkani-hamed_2014
url: https://arxiv.org/abs/131... | ||
opa.phys.quantum-field-theory.amplituhedron-geometry | Amplituhedron Geometry | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Prove that the amplituhedron computes all scattering amplitudes in N=4 super Yang-Mills. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.amplituhedron-geometry
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_amplituhedron_geometry
url: https://en.wikipedia.org/wiki/Amp... | ||
opa.phys.condensed-matter-theory.anderson-localization-in-interacting-systems | Anderson Localization in Interacting Systems | mathematical-physics | ["condensed-matter-theory"] | open | tier_3 | Does Anderson localization persist in the presence of interactions at finite temperature in dimensions d >= 2, or does it always eventually thermalize? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter-theory.anderson-localization-in-interacting-systems
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_basko_2006
url: https://arxiv.org/abs/co... | ||
opa.phys.condensed-matter.anderson-metal-insulator-transition-full-theory | Anderson Metal-Insulator Transition (Full Theory) | mathematical-physics | ["condensed-matter"] | open | tier_3 | Develop a complete theory of the Anderson metal-insulator transition in three dimensions. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.anderson-metal-insulator-transition-full-theory
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_anderson_metal_insulator_transition_full_the... | ||
opa.phys.condensed-matter-theory.anderson-metal-insulator-transition | Anderson Metal-Insulator Transition | mathematical-physics | ["condensed-matter-theory"] | open | tier_2 | conjecture | Prove the existence of the Anderson metal-insulator transition for the Anderson model (tight-binding Hamiltonian with random on-site potential) on Z^d for d >= 3. Specifically, prove that there exists a critical disorder strength W_c such that for W < W_c the spectrum contains absolutely continuous component (extended ... | In a crystal with random impurities, electrons can either spread freely (metal) or get trapped (insulator). Proving that this metal-insulator transition exists in 3D is one of the most important open problems in mathematical physics.
| high | mixed | medium | 0.9 | 0.4 | 0.3 | 0.7 | 0.2 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- Anderson Localization Transition
- Anderson Transition in 3D
answer_type: boolean
dates:
first_stated: 1958
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.condensed-matter-the... |
opa.phys.topological-phases.anomalies-and-symmetry-protected-topological-phases | Anomalies and Symmetry-Protected Topological Phases | mathematical-physics | ["topological-phases"] | open | tier_3 | Can one completely classify anomalies in quantum field theories using cobordism, establishing a bijection between anomalies and SPT phases in one dimension higher? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.topological-phases.anomalies-and-symmetry-protected-topological-phases
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_freed_2022
url: https://arxiv.org/abs/... | ||
opa.phys.quantum-field-theory.anomalous-dimensions-at-strong-coupling | Anomalous Dimensions at Strong Coupling | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Can anomalous dimensions of operators in strongly coupled gauge theories be computed exactly beyond the integrable (planar N=4 SYM) limit? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.anomalous-dimensions-at-strong-coupling
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_beisert_2012
url: https://arxiv.org/abs/1012.398... | ||
opa.phys.quantum-field-theory.anomalous-magnetic-moment-theory | Muon Anomalous Magnetic Moment Theory Prediction | mathematical-physics | ["quantum-field-theory"] | open | tier_2 | conjecture | Determine the precise Standard Model prediction for the muon anomalous magnetic moment a_mu = (g-2)/2 to sufficient accuracy to compare with the experimental measurement. The dominant theoretical uncertainty comes from the hadronic vacuum polarization (HVP) contribution. Resolve the tension between the data-driven disp... | The muon's magnetic moment has been measured to exquisite precision and may disagree with the Standard Model prediction, hinting at new physics. But the theory prediction itself is uncertain because of difficulties computing the strong-force contributions. Resolving this is one of the most pressing problems in particle... | medium | computational | high | 0.9 | 0.35 | 0.55 | 0.6 | 0.35 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- Muon g-2 Theory
- Hadronic Vacuum Polarization
answer_type: numeric
dates:
first_stated: 2001
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.quantum-field-theory.anomalous-mag... |
opa.phys.statistical-mechanics.anomalous-transport-in-low-dimensional-systems | Anomalous Transport in Low-Dimensional Systems | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | What determines whether heat transport in one-dimensional systems is anomalous (divergent thermal conductivity) or normal, and what is the universal exponent? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.anomalous-transport-in-low-dimensional-systems
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_lepri_2003
url: https://arxiv.org/abs/co... | ||
opa.phys.condensed-matter.anomalous-transport-in-low-dimensions | Anomalous Transport in Low Dimensions | mathematical-physics | ["condensed-matter"] | open | tier_3 | Develop a rigorous theory of anomalous heat and charge transport in low-dimensional systems. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.anomalous-transport-in-low-dimensions
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_anomalous_transport_in_low_dimensions
url: https:/... | ||
opa.phys.quantum-field-theory.anomaly-matching-constraints | Anomaly Matching Constraints | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Prove anomaly matching conditions for general quantum field theories. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.anomaly-matching-constraints
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_anomaly_matching_constraints
url: https://en.wikipedia.... | ||
opa.phys.quantum-field-theory.anomaly-matching-in-chiral-gauge-theories | Anomaly Matching in Chiral Gauge Theories | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Can all chiral gauge theories be consistently defined non-perturbatively on the lattice while preserving gauge invariance and anomaly matching? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.anomaly-matching-in-chiral-gauge-theories
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_luscher_2000
url: https://arxiv.org/abs/hep-th... | ||
opa.phys.quantum-field-theory.asymptotic-freedom-and-non-perturbative-qcd | Asymptotic Freedom and Non-Perturbative QCD | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Develop rigorous non-perturbative methods for QCD building on asymptotic freedom. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.asymptotic-freedom-and-non-perturbative-qcd
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_asymptotic_freedom_and_non_perturbative_qcd
... | ||
opa.phys.quantum-field-theory.asymptotic-safety-of-gravity | Asymptotic Safety of Gravity | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Does quantum gravity possess a non-trivial UV fixed point making it asymptotically safe and nonperturbatively renormalizable? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.asymptotic-safety-of-gravity
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_reuter_1998
url: https://arxiv.org/abs/hep-th/9605030
sta... | ||
opa.phys.mathematical-physics.berry-phase-and-topological-invariants | Berry Phase and Topological Invariants | mathematical-physics | ["mathematical-physics"] | open | tier_3 | Can all topological invariants arising from Berry phases in quantum systems be systematically classified using the framework of differential cohomology? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.mathematical-physics.berry-phase-and-topological-invariants
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_freed_2013
url: https://arxiv.org/abs/1404.7224
... | ||
opa.phys.condensed-matter.bethe-ansatz-completeness | Bethe Ansatz Completeness | mathematical-physics | ["condensed-matter"] | open | tier_3 | Prove the completeness of the Bethe ansatz for integrable spin chains. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.bethe-ansatz-completeness
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_bethe_ansatz_completeness
url: https://en.wikipedia.org/wiki/B... | ||
opa.phys.general-relativity.binary-black-hole-analytical-solution | Binary Black Hole Analytical Solution | mathematical-physics | ["general-relativity"] | open | tier_3 | Find an analytical solution for the two-body problem in general relativity. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.binary-black-hole-analytical-solution
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_binary_black_hole_analytical_solution
url: https... | ||
opa.phys.general-relativity.binary-black-hole-merger-analytical-models | Binary Black Hole Merger Analytical Models | mathematical-physics | ["general-relativity"] | open | tier_3 | Can analytical models accurately describe the merger phase of binary black hole coalescence, bridging the gap between post-Newtonian and perturbation theory? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.binary-black-hole-merger-analytical-models
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_buonanno_1999
url: https://arxiv.org/abs/gr-qc/... | ||
opa.phys.general-relativity.bkl-conjecture-proof | BKL Conjecture Proof | mathematical-physics | ["general-relativity"] | open | tier_3 | Prove the Belinski-Khalatnikov-Lifshitz conjecture on the structure of cosmological singularities. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.bkl-conjecture-proof
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_bkl_conjecture_proof
url: https://en.wikipedia.org/wiki/BKL_singu... | ||
opa.phys.general-relativity.bkl-conjecture-singularity-structure | BKL Conjecture on Singularity Structure | mathematical-physics | ["general-relativity"] | open | tier_3 | conjecture | Prove the BKL conjecture: generic spacelike singularities in solutions of the Einstein equations are oscillatory (Mixmaster-like), locally spatially homogeneous, and the dynamics at each spatial point near the singularity is well-approximated by a sequence of Kasner epochs connected by BKL maps (Bianchi type IX or type... | What happens at the singularity inside a black hole or at the Big Bang? The BKL conjecture predicts a wild, chaotic oscillation of the geometry where each point in space evolves independently. Proving this is one of the hardest problems in GR.
| medium | expert_review | low | 0.85 | 0.5 | 0.25 | 0.55 | 0.15 | ai:
recommended_tools:
- mathematica
solver_ready: false
aliases:
- BKL Conjecture
- Belinski-Khalatnikov-Lifshitz Conjecture
answer_type: boolean
dates:
first_stated: 1970
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.general-relativity.bkl-conjecture-... |
opa.phys.general-relativity.bkl-cosmological-singularity | BKL Cosmological Singularity | mathematical-physics | ["general-relativity"] | open | tier_3 | Is the Belinsky-Khalatnikov-Lifshitz oscillatory approach to cosmological singularities generic for solutions of the Einstein equations? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.bkl-cosmological-singularity
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_berger_2002
url: https://doi.org/10.12942/lrr-2002-1
status... | ||
opa.phys.general-relativity.black-hole-area-theorem-quantum-corrections | Black Hole Area Theorem Quantum Corrections | mathematical-physics | ["general-relativity"] | open | tier_3 | Determine quantum corrections to the classical area theorem for black holes. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.black-hole-area-theorem-quantum-corrections
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_black_hole_area_theorem_quantum_corrections
... | ||
opa.phys.quantum-gravity.black-hole-information-paradox-and-page-curve | Black Hole Information Paradox and Page Curve | mathematical-physics | ["quantum-gravity"] | open | tier_3 | Can the island formula and replica wormholes provide a fully rigorous derivation of the Page curve for black hole evaporation in a UV-complete theory? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-gravity.black-hole-information-paradox-and-page-curve
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_penington_2020
url: https://arxiv.org/abs/1911.... | ||
opa.phys.string-theory.black-hole-information-paradox-resolution | Black Hole Information Paradox Resolution | mathematical-physics | ["string-theory"] | open | tier_3 | Resolve the black hole information paradox by demonstrating unitarity of black hole evaporation. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.black-hole-information-paradox-resolution
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_black_hole_information_paradox_resolution
url: ht... | ||
opa.phys.general-relativity.black-hole-information-paradox | Black Hole Information Paradox | mathematical-physics | ["general-relativity"] | open | tier_3 | How is unitarity preserved during black hole evaporation? The island formula provides partial progress, but a complete resolution remains open. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.black-hole-information-paradox
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_hawking_1976
url: https://doi.org/10.1103/PhysRevD.14.2460
... | ||
opa.phys.general-relativity.black-hole-thermodynamics-foundations | Black Hole Thermodynamics Foundations | mathematical-physics | ["general-relativity"] | open | tier_3 | Provide a rigorous foundation for the four laws of black hole thermodynamics. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.black-hole-thermodynamics-foundations
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_black_hole_thermodynamics_foundations
url: https... | ||
opa.phys.general-relativity.black-hole-thermodynamics-from-microscopic-degrees-of-freedo | Black Hole Thermodynamics from Microscopic Degrees of Freedom | mathematical-physics | ["general-relativity"] | open | tier_3 | Can the Bekenstein-Hawking entropy be derived from a counting of microscopic degrees of freedom for generic (non-supersymmetric, non-extremal) black holes? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.black-hole-thermodynamics-from-microscopic-degrees-of-freedo
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_strominger_1996
url: https://... | ||
opa.phys.general-relativity.black-hole-uniqueness-in-higher-dimensions | Black Hole Uniqueness in Higher Dimensions | mathematical-physics | ["general-relativity"] | open | tier_3 | Classify all stationary black hole solutions in higher-dimensional general relativity. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.black-hole-uniqueness-in-higher-dimensions
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_black_hole_uniqueness_in_higher_dimensions
... | ||
opa.phys.string-theory.black-holes-in-string-theory | Black Holes in String Theory | mathematical-physics | ["string-theory"] | open | tier_3 | Can the fuzzball proposal resolve the black hole information paradox by replacing the classical interior geometry with a stringy microstate geometry for all black holes? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.black-holes-in-string-theory
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_mathur_2005
url: https://arxiv.org/abs/hep-th/0502050
status_evi... | ||
opa.phys.statistical-mechanics.boltzmann-equation-derivation | Boltzmann Equation Derivation | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Can the Boltzmann equation be rigorously derived from Newtonian mechanics for long times beyond the Lanford result which is valid only for short times? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.boltzmann-equation-derivation
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_gallagher_2014
url: https://arxiv.org/abs/1208.5753
sta... | ||
opa.phys.statistical-mechanics.boltzmann-equation-rigorous-derivation | Boltzmann Equation Rigorous Derivation | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Derive the Boltzmann equation rigorously from Newtonian mechanics for long times. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.boltzmann-equation-rigorous-derivation
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_boltzmann_equation_rigorous_derivation
url: ... | ||
opa.phys.quantum-field-theory.bootstrap-bound-on-cft-data | Bootstrap Bound on CFT Data | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Determine optimal bootstrap bounds on operator dimensions and OPE coefficients in 3D CFTs. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.bootstrap-bound-on-cft-data
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_bootstrap_bound_on_cft_data
url: https://en.wikipedia.or... | ||
opa.phys.eft.bootstrap-bounds-on-eft-coefficients | Bootstrap Bounds on EFT Coefficients | mathematical-physics | ["eft"] | open | tier_3 | Can dispersive sum rules and positivity bounds from the S-matrix bootstrap determine exact constraints on Wilson coefficients in effective field theories? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.eft.bootstrap-bounds-on-eft-coefficients
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_caron_huot_2023
url: https://arxiv.org/abs/2307.04739
status_evide... | ||
opa.phys.quantum-information.bound-entanglement-distillation | Bound Entanglement Distillation | mathematical-physics | ["quantum-information"] | open | tier_3 | Determine whether PPT bound entangled states can be activated for quantum key distribution. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-information.bound-entanglement-distillation
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_bound_entanglement_distillation
url: https://en.wikip... | ||
opa.phys.string-theory.bps-state-counting | BPS State Counting | mathematical-physics | ["string-theory"] | open | tier_3 | Count BPS states in string theory and verify agreement with black hole entropy. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.bps-state-counting
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_bps_state_counting
url: https://en.wikipedia.org/wiki/BPS_state
status... | ||
opa.phys.supersymmetry.bps-states-and-wall-crossing-formulas | BPS States and Wall-Crossing Formulas | mathematical-physics | ["supersymmetry"] | open | tier_3 | Can the Kontsevich-Soibelman wall-crossing formula for BPS states be rigorously derived from first principles in all N=2 supersymmetric field theories? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.supersymmetry.bps-states-and-wall-crossing-formulas
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_kontsevich_2022
url: https://arxiv.org/abs/2206.15462
s... | ||
opa.phys.random-geometry.brownian-motion-and-liouville-quantum-gravity | Brownian Motion and Liouville Quantum Gravity | mathematical-physics | ["random-geometry"] | open | tier_3 | Can one rigorously construct Brownian motion on Liouville quantum gravity surfaces and prove the KPZ relation for random planar maps? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.random-geometry.brownian-motion-and-liouville-quantum-gravity
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_gwynne_2021
url: https://arxiv.org/abs/1908.055... | ||
opa.phys.condensed-matter.bulk-boundary-correspondence-in-topological-insulators | Bulk-Boundary Correspondence in Topological Insulators | mathematical-physics | ["condensed-matter"] | open | tier_3 | Prove the bulk-boundary correspondence for topological insulators rigorously. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.condensed-matter.bulk-boundary-correspondence-in-topological-insulators
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_bulk_boundary_correspondence_in_topol... | ||
opa.phys.string-theory.calabi-yau-moduli-stabilization | Calabi-Yau Moduli Stabilization | mathematical-physics | ["string-theory"] | open | tier_3 | Can all moduli of Calabi-Yau compactifications be stabilized in a controlled regime of string theory, yielding a cosmologically viable vacuum? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.calabi-yau-moduli-stabilization
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_kachru_2003
url: https://arxiv.org/abs/hep-th/0301240
status_... | ||
opa.phys.conformal-field-theory.cardy-formula-for-higher-dimensional-cfts | Cardy Formula for Higher-Dimensional CFTs | mathematical-physics | ["conformal-field-theory"] | open | tier_3 | Does a universal Cardy-like formula for the density of states exist for conformal field theories in dimensions d > 2? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.conformal-field-theory.cardy-formula-for-higher-dimensional-cfts
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_pal_2023
url: https://arxiv.org/abs/2306.148... | ||
opa.phys.quantum-field-theory.casimir-effect-beyond-parallel-plates | Casimir Effect Beyond Parallel Plates | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Compute the Casimir effect for general geometries. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.casimir-effect-beyond-parallel-plates
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_casimir_effect_beyond_parallel_plates
url: htt... | ||
opa.phys.string-theory.causal-set-theory-dynamics | Causal Set Theory Dynamics | mathematical-physics | ["string-theory"] | open | tier_3 | Develop the dynamics of causal set theory and connect it to known physics. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.causal-set-theory-dynamics
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_causal_set_theory_dynamics
url: https://en.wikipedia.org/wiki/Ca... | ||
opa.phys.holography.celestial-holography-and-flat-space | Celestial Holography and Flat Space | mathematical-physics | ["holography"] | open | tier_3 | Can celestial holography provide a complete holographic dual for quantum gravity in asymptotically flat spacetimes? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.holography.celestial-holography-and-flat-space
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_pasterski_2023
url: https://arxiv.org/abs/2301.01810
status_... | ||
opa.phys.string-theory.celestial-holography-program | Celestial Holography Program | mathematical-physics | ["string-theory"] | open | tier_3 | Develop celestial holography into a complete framework for flat space holography. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.celestial-holography-program
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_celestial_holography_program
url: https://en.wikipedia.org/wik... | ||
opa.phys.string-theory.celestial-holography | Celestial Holography | mathematical-physics | ["string-theory"] | open | tier_3 | Does celestial holography provide a complete holographic dual for gravitational scattering in asymptotically flat spacetimes? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.celestial-holography
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_pasterski_2017
url: https://arxiv.org/abs/1705.01027
status_evidence:
... | ||
opa.phys.quantum-topology.chern-simons-theory-and-volume-conjecture | Chern-Simons Theory and Volume Conjecture | mathematical-physics | ["quantum-topology"] | open | tier_3 | Can the Volume Conjecture be proved: that the colored Jones polynomial of a hyperbolic knot determines the hyperbolic volume of its complement? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-topology.chern-simons-theory-and-volume-conjecture
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_murakami_2021
url: https://arxiv.org/abs/2103.0666... | ||
opa.phys.quantum-field-theory.chiral-gauge-theory-lattice-construction | Chiral Gauge Theory Lattice Construction | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Construct a lattice regularization of chiral gauge theories preserving gauge invariance. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.chiral-gauge-theory-lattice-construction
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_chiral_gauge_theory_lattice_construction
ur... | ||
opa.phys.quantum-field-theory.chiral-symmetry-breaking-mechanism | Chiral Symmetry Breaking Mechanism | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Can spontaneous chiral symmetry breaking in QCD be proven rigorously from the QCD Lagrangian without lattice or model assumptions? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.chiral-symmetry-breaking-mechanism
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_nambu_1961
url: https://doi.org/10.1103/PhysRev.122.3... | ||
opa.phys.condensed-matter-theory.classification-topological-phases-3d | Classification of Topological Phases of Matter in 3D | mathematical-physics | ["condensed-matter-theory"] | open | tier_2 | conjecture | Provide a complete mathematical classification of gapped quantum phases of matter in three spatial dimensions. Specifically: (1) For symmetry-protected topological (SPT) phases in 3D with a given symmetry group G, prove that the classification is given by the generalized cohomology theory (e.g., group cohomology H^{d+1... | Matter can exist in exotic "topological phases" where the properties are determined not by symmetry breaking (like ordinary phases) but by global quantum entanglement patterns. In two dimensions, we have a fairly complete mathematical classification of these phases. The challenge is to achieve the same in three dimensi... | medium | mixed | medium | 0.92 | 0.3 | 0.45 | 0.6 | 0.35 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- 3D Topological Phase Classification
- Three-Dimensional Topological Order
- Classification of 3D Gapped Phases
answer_type: boolean
dates:
first_stated: 2005
domain: mathematical-physics
formalization:
available: false
systems: [... |
opa.phys.quantum-gravity.cobordism-conjecture-in-quantum-gravity | Cobordism Conjecture in Quantum Gravity | mathematical-physics | ["quantum-gravity"] | open | tier_3 | Does every consistent quantum gravity theory satisfy the Cobordism Conjecture: that the bordism group of quantum gravity is trivial, requiring dynamical objects to end all topological cobordisms? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-gravity.cobordism-conjecture-in-quantum-gravity
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_mcnamara_2021
url: https://arxiv.org/abs/1909.10355
... | ||
opa.phys.quantum-field-theory.color-superconductivity-in-dense-qcd | Color Superconductivity in Dense QCD | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | What is the ground state of QCD at asymptotically high baryon density? Can color-flavor locking be demonstrated from first principles? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.color-superconductivity-in-dense-qcd
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_alford_2008
url: https://arxiv.org/abs/0709.4635
... | ||
opa.phys.quantum-field-theory.color-superconductivity-theory | Color Superconductivity Theory | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Develop a rigorous theory of color superconductivity in dense quark matter. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.color-superconductivity-theory
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_color_superconductivity_theory
url: https://en.wikipe... | ||
opa.phys.string-theory.complexity-action-conjecture | Complexity = Action Conjecture | mathematical-physics | ["string-theory"] | open | tier_3 | Prove the complexity = action conjecture relating computational complexity to gravitational action. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.complexity-action-conjecture
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_complexity_action_conjecture
url: https://en.wikipedia.org/wik... | ||
opa.phys.string-theory.complexity-volume-conjecture | Complexity = Volume Conjecture | mathematical-physics | ["string-theory"] | open | tier_3 | Prove the complexity = volume conjecture relating computational complexity to spacetime volume. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.string-theory.complexity-volume-conjecture
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_complexity_volume_conjecture
url: https://en.wikipedia.org/wik... | ||
opa.phys.quantum-field-theory.confinement-in-qcd | Confinement in Quantum Chromodynamics | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | conjecture | Prove that quantum chromodynamics (QCD), the SU(3) Yang-Mills gauge theory coupled to quarks, exhibits confinement: isolated quarks and gluons cannot exist as asymptotic particle states, and all physical states are color singlets (hadrons). Rigorously, prove that the Wilson loop expectation value satisfies an area law ... | Why can't we ever see a single quark? QCD predicts that the force between quarks grows with distance, permanently confining them inside protons and neutrons. But no one has proven this mathematically from the fundamental theory.
| medium | expert_review | low | 0.95 | 0.35 | 0.25 | 0.5 | 0.15 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- Quark Confinement
- Color Confinement Problem
answer_type: boolean
dates:
first_stated: 1973
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.quantum-field-theory.confinement-in... |
opa.phys.quantum-field-theory.conformal-bootstrap-in-3d | Conformal Bootstrap in 3D | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Determine all consistent 3D conformal field theories using the conformal bootstrap. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.conformal-bootstrap-in-3d
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_conformal_bootstrap_in_3d
url: https://en.wikipedia.org/wi... | ||
opa.phys.quantum-field-theory.conformal-bootstrap-in-d-2 | Conformal Bootstrap in d > 2 | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Can the conformal bootstrap determine all critical exponents of the 3D Ising model to arbitrary precision? More generally, can it classify all CFTs in d > 2? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.conformal-bootstrap-in-d-2
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_poland_2019
url: https://arxiv.org/abs/1805.04405
status_ev... | ||
opa.phys.statistical-mechanics.conformal-bootstrap-rigorous-bounds-in-3d-ising | Conformal Bootstrap Rigorous Bounds in 3D Ising | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Can the conformal bootstrap program produce rigorous mathematical proofs of the critical exponents of the 3D Ising model matching numerical results? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.conformal-bootstrap-rigorous-bounds-in-3d-ising
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_elshowk_2021
url: https://arxiv.org/abs... | ||
opa.phys.conformal-field-theory.conformal-field-theory-and-modular-geometry | Conformal Field Theory and Modular Geometry | mathematical-physics | ["conformal-field-theory"] | open | tier_3 | Can conformal field theory partition functions be fully classified using the theory of modular forms and vertex operator algebras for all central charges? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.conformal-field-theory.conformal-field-theory-and-modular-geometry
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_schellekens_2023
url: https://arxiv.org/ab... | ||
opa.phys.statistical-mechanics.conformal-invariance-criticality-general | Conformal Invariance at Criticality (General) | mathematical-physics | ["statistical-mechanics"] | open | tier_2 | conjecture | Prove that critical lattice models in d=2 are conformally invariant in the scaling limit, for a general class of models beyond the Ising model. Specifically, prove conformal invariance for the critical q-state Potts model for q <= 4 (the regime where the phase transition is continuous; for q > 4 the transition is first... | At a phase transition, lattice systems become scale-invariant. A stronger property, conformal invariance, is widely assumed but proven only for the 2D Ising model and a few other cases. Proving it in general is a major challenge.
| medium | mixed | medium | 0.92 | 0.4 | 0.3 | 0.6 | 0.2 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- Conformal Invariance Conjecture
- Conformal Symmetry at Critical Points
answer_type: boolean
dates:
first_stated: 1970
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.statistic... |
opa.phys.quantum-field-theory.consistent-theory-of-quantum-gravity | Existence of a Consistent Theory of Quantum Gravity | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | conjecture | Does there exist a mathematically consistent, background-independent quantum theory that reduces to general relativity in the classical limit and to quantum field theory in the weak-gravity limit? More precisely, construct a quantum theory satisfying the following: (1) the theory possesses a well-defined Hilbert space ... | General relativity describes gravity as the curvature of spacetime, and quantum mechanics describes the behavior of particles at the smallest scales. Both theories are extraordinarily successful, but they are fundamentally incompatible: attempts to combine them using standard techniques produce nonsensical infinities. ... | low | expert_review | low | 0.99 | 0.2 | 0.2 | 0.4 | 0.15 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- Quantum Gravity Problem
- Unification of General Relativity and Quantum Mechanics
- Theory of Everything (Gravity Sector)
answer_type: boolean
dates:
first_stated: 1935
domain: mathematical-physics
formalization:
available: false
... |
opa.phys.quantum-field-theory.constructive-qft-4d | Constructive Quantum Field Theory in 4D | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | conjecture | Construct a non-trivial (interacting) quantum field theory in four spacetime dimensions that satisfies the Wightman axioms or the Osterwalder-Schrader axioms. The theory should have a well-defined Hilbert space, field operators as operator-valued distributions, a unitary representation of the Poincare group, and satisf... | Despite the enormous success of quantum field theory in physics, no one has ever rigorously constructed a single interacting quantum field theory in the physical four-dimensional spacetime. Can this be done for any model?
| high | expert_review | low | 0.95 | 0.4 | 0.2 | 0.65 | 0.15 | ai:
recommended_tools:
- mathematica
solver_ready: false
aliases:
- Rigorous QFT in Four Dimensions
- Non-perturbative QFT Construction
answer_type: boolean
dates:
first_stated: 1964
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.quantum-field-theory.con... |
opa.phys.quantum-field-theory.constructive-qft-in-4d-full-program | Constructive QFT in 4D (Full Program) | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Construct a nontrivial interacting quantum field theory in four spacetime dimensions rigorously. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.constructive-qft-in-4d-full-program
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_constructive_qft_in_4d_full_program
url: https:/... | ||
opa.phys.quantum-field-theory.constructive-qft-in-4d | Constructive QFT in 4D | mathematical-physics | ["quantum-field-theory"] | open | tier_3 | Can any interacting quantum field theory be rigorously constructed in four spacetime dimensions satisfying the Wightman or Osterwalder-Schrader axioms? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-field-theory.constructive-qft-in-4d
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_glimm_1987
url: https://doi.org/10.1007/978-1-4612-4728-9
statu... | ||
opa.phys.statistical-mechanics.contact-process-critical-behavior | Contact Process Critical Behavior | mathematical-physics | ["statistical-mechanics"] | open | tier_3 | Determine the exact critical behavior of the contact process in all dimensions. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.statistical-mechanics.contact-process-critical-behavior
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_contact_process_critical_behavior
url: https://en... | ||
opa.phys.general-relativity.cosmic-censorship-conjecture-strong-form | Cosmic Censorship Conjecture (Strong Form) | mathematical-physics | ["general-relativity"] | open | tier_3 | Prove that generic gravitational collapse leads to singularities hidden behind event horizons. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.cosmic-censorship-conjecture-strong-form
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_cosmic_censorship_conjecture_strong_form
url:... | ||
opa.phys.general-relativity.cosmic-censorship-conjecture | Cosmic Censorship Conjecture | mathematical-physics | ["general-relativity"] | open | tier_2 | conjecture | The cosmic censorship conjecture, proposed by Roger Penrose in 1969, comes in two forms. The Weak Cosmic Censorship Conjecture (WCCC) states that for generic asymptotically flat initial data for the Einstein equations satisfying appropriate energy conditions, the maximal Cauchy development possesses a complete future n... | When a massive star collapses under its own gravity, general relativity predicts that a singularity (a point of infinite density) forms. The cosmic censorship conjecture says that such singularities are always hidden inside black holes and can never be "naked" (visible to distant observers). The strong version addition... | high | mixed | medium | 0.95 | 0.4 | 0.35 | 0.65 | 0.25 | ai:
recommended_tools:
- python
- mathematica
solver_ready: false
aliases:
- Penrose Cosmic Censorship
- Strong Cosmic Censorship Conjecture
- Weak Cosmic Censorship Conjecture
answer_type: boolean
dates:
first_stated: 1969
domain: mathematical-physics
formalization:
available: false
systems: []
wanted:... |
opa.phys.general-relativity.cosmic-no-hair-conjecture-proof | Cosmic No-Hair Conjecture Proof | mathematical-physics | ["general-relativity"] | open | tier_3 | Prove that all expanding universes with a positive cosmological constant approach de Sitter space. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.cosmic-no-hair-conjecture-proof
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_cosmic_no_hair_conjecture_proof
url: https://en.wikipe... | ||
opa.phys.general-relativity.cosmic-no-hair-conjecture | Cosmic No-Hair Conjecture | mathematical-physics | ["general-relativity"] | open | tier_2 | conjecture | Prove the cosmic no-hair conjecture: all initially expanding cosmological solutions of the Einstein equations with a positive cosmological constant Lambda > 0 and satisfying the strong and dominant energy conditions asymptotically approach the de Sitter solution as t -> infinity. More precisely, prove that for generic ... | Does every expanding universe with a positive cosmological constant eventually look like de Sitter space (exponentially expanding, empty space)? This conjecture suggests that the cosmological constant dominates all other forms of matter and energy at late times.
| high | mixed | low | 0.82 | 0.45 | 0.3 | 0.65 | 0.15 | ai:
recommended_tools:
- mathematica
solver_ready: false
aliases:
- de Sitter Cosmic No-Hair
- Asymptotic de Sitter Conjecture
answer_type: boolean
dates:
first_stated: 1983
domain: mathematical-physics
formalization:
available: false
systems: []
wanted: true
id: opa.phys.general-relativity.cosmic-no-hair... |
opa.phys.general-relativity.cosmic-strings-gravitational-effects | Cosmic Strings Gravitational Effects | mathematical-physics | ["general-relativity"] | open | tier_3 | Determine the exact gravitational effects of cosmic strings. | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.general-relativity.cosmic-strings-gravitational-effects
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: curated_cosmic_strings_gravitational_effects
url: https:/... | ||
opa.phys.quantum-gravity.cosmological-constant-and-vacuum-energy | Cosmological Constant and Vacuum Energy | mathematical-physics | ["quantum-gravity"] | open | tier_3 | Can the enormous discrepancy between the observed cosmological constant and quantum field theory predictions be resolved through a rigorous mathematical framework? | medium | expert_review | low | 0 | 0 | 0 | 0 | 0 | domain: mathematical-physics
id: opa.phys.quantum-gravity.cosmological-constant-and-vacuum-energy
kind: problem
provenance:
created_from: radar_promotion
parser_version: 0.3.1
schema_version: 1.0.0
sources:
canonical:
- kind: website
source_id: src_polchinski_2021
url: https://arxiv.org/abs/hep-th/060... |
End of preview. Expand in Data Studio
OpenProblemAtlas: Open Problems Dataset
A structured, machine-readable dataset of unsolved problems in mathematics, theoretical computer science, and mathematical physics.
Why This Dataset?
Existing math benchmarks (MATH, GSM8K, MiniF2F) contain solved problems. This dataset contains unsolved problems -- the frontier of human knowledge.
Use it to:
- Benchmark AI theorem proving systems on problems with unknown answers
- Train models to understand the structure of open problems
- Build tools for mathematical research navigation
Dataset Structure
Each problem includes:
id: Unique identifier (e.g.,opa.mathematics.number-theory.collatz-conjecture)title: Canonical titledomain: mathematics / theoretical-cs / mathematical-physicsstatement_canonical: Formal problem statementstatement_informal: Accessible descriptionstatus: open / partially_solved / solved / disprovedtier: tier_1 (machine-ready) / tier_2 / tier_3verification_profile: statement precision, solution checkability, machine actionabilityscores: impact, underexplored, toolability, formality, ai_fit (0-1)full_yaml: Complete problem metadata in YAML format
Quick Start
from datasets import load_dataset
ds = load_dataset("OpenProblemAtlas/open-problems")
# Filter for machine-actionable problems
tier1 = ds.filter(lambda x: x["tier"] == "tier_1")
# Find high-impact underexplored problems
gems = ds.filter(lambda x: x["impact"] > 0.7 and x["underexplored"] > 0.5)
Also Available
- PyPI:
pip install openproblem-atlas - GitHub: https://github.com/OpenProblemAtlas/open-problem-atlas
- Website: https://openproblem-atlas.org
Citation
@misc{openproblem-atlas,
title = {OpenProblemAtlas: A Living Atlas of Open Problems},
year = {2026},
url = {https://github.com/OpenProblemAtlas/open-problem-atlas}
}
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