Frontier Questions

Frontier questions are easiest to navigate when the claim, evidence standard, and unresolved step are visible together. Each dossier below states a normative question, separates established results from assumptions and interpretation, compares live positions claim by claim, and names the observation or theorem that would change its assessment.

Evidence cutoff. This directory reflects dossier assessments and public sources available through 11 August 2026. Each dossier gives its own finite source-selection protocol and the conditions that should trigger an update.

Frontier questions by the claim they test

Scattering, amplitudes, and precision EFT

• Infrared-complete scattering observables asks which inclusive, dressed, memory-sector, or detector-level quantities remain finite and operational in theories with massless gauge fields.
• The domain of color–kinematics duality and double copy separates demonstrated tree-level relations from loop, classical, curved-background, and nonperturbative conjectures.
• SMEFT validity and truncation in global fits asks when power counting, event scales, correlations, and a remainder model make a truncated inference trustworthy.
• Electroweak vacuum stability distinguishes the conditional Standard Model metastability calculation from claims about cosmology or ultraviolet completion.

Gauge theory and finite-density matter

• Confinement with dynamical matter asks what replaces a Wilson-loop area law when fundamental matter screens center charge.
• Controlled regimes of finite-density QCD maps the low-density, small-chemical-potential, and asymptotic regimes against the uncontrolled intermediate-density gap.
• The four-dimensional Yang–Mills mass gap separates continuum-extrapolated numerical evidence from the open theorem-level existence-and-gap problem.
• The QCD critical point assesses whether lattice singularity searches and heavy-ion fluctuation measurements establish or exclude an endpoint.

Conformal theories, dualities, and reconstruction

• Reconstructing non-Lagrangian QFTs asks when geometry, anomalies, protected sectors, defects, and bootstrap data uniquely determine a full theory.
• Non-supersymmetric dualities in three dimensions distinguishes exact anomaly, phase, and topological checks from conjectural equality of interacting fixed points.
• From crossing solutions to actual CFTs asks what existence and reconstruction input must supplement crossing, unitarity, and numerical islands.
• Certification in the numerical conformal bootstrap distinguishes reproducible solver output from an end-to-end certificate that also controls conformal-block approximations.

Real-time dynamics, quantum matter, and information

• Real-time continuum dynamics from regulated computations compares the observable classes accessible to finite volume, analytic continuation, tensor networks, truncation, and quantum simulation.
• The predictive domain of hydrodynamic attractors asks when an attractor improves on ordinary hydrodynamics for a specified moment, norm, and flow.
• The order of deconfined quantum critical transitions tests continuous fixed-point, walking, and weak-first-order accounts of Néel–VBS and related transitions.
• What Planckian dissipation means separates an observable-specific scaling pattern from a universal relaxation bound or microscopic mechanism.
• Operational entanglement in continuum QFT identifies which algebraic and separated-region quantities remain finite and operational when sharp-region entropy does not.
• Complexity in continuum QFT asks whether task, reference, gate set, cost, tolerance, and regulator can yield a non-arbitrary interacting continuum quantity.

Curved spacetime, black holes, and holography

• Robustness and backreaction in Hawking radiation separates robust low-energy mode conversion from a self-consistent four-dimensional evaporation history.
• Hypotheses of the generalized second law identifies the horizon-algebra, renormalization, coupling, and gravitational assumptions under which monotonicity is proved.
• Islands and unitary black-hole evaporation asks what a Page curve establishes beyond its semiclassical replica, factorization, and microscopic-completion assumptions.
• Bulk reconstruction beyond semiclassical code subspaces asks for finite-$N$, finite-coupling error control across changing geometries and state sets.

Mathematical definition and construction

• Interacting constructive QFT in four dimensions compares scalar triviality theorems and gauge-theory partial constructions with the full cutoff-free existence standard.
• Equivalence of axiomatic QFT frameworks maps the exact hypotheses for OS/Wightman, field/net, locally covariant, perturbative, and factorization-algebra comparisons.

Read by current answer shape

These labels describe the logical shape of the answer, not a grade for a field. “Established” always means established inside the scope and assumptions named by the dossier.

Established core, broader extension open

These dossiers contain a theorem, controlled calculation, or operational diagnostic that answers a central subquestion, while a wider extrapolation remains open.

• Infrared-complete scattering observables — inclusive safety is broad; a universal asymptotic-state formulation is not.
• Confinement with dynamical matter — exact order-parameter diagnostics are classified; a unique microscopic mechanism is not.
• Electroweak vacuum stability — the flat-space Standard Model lifetime is conditionally controlled; cosmology and ultraviolet physics are not fixed.
• SMEFT validity and truncation — defensible convergence tests exist; no universal pass/fail prescription does.
• Numerical-bootstrap certification — reproducible bounds and partial certificates exist; complete analytic-plus-numerical certification is uncommon.
• Hydrodynamic attractors — controlled reductions exhibit attractors; generic multidimensional predictive gain is unresolved.
• Operational continuum entanglement — the sharp-region entropy obstruction and several algebraic alternatives are established; no universal resource measure follows.
• Hawking-radiation robustness — the leading low-energy flux is robust under stated conditions; the global backreacting history is open.
• Generalized-second-law hypotheses — important semiclassical theorem domains are known; fully quantum and general higher-curvature extensions are not.
• Bulk reconstruction — exact and approximate code-subspace theorems are precise; uniform global reconstruction is not.
• Axiomatic-framework equivalence — several restricted equivalences are theorems; a universal all-framework equivalence is false or unproved as stated.

Strong evidence or a tightly constrained conjecture

Here, independent checks sharply restrict viable formulations, but the headline claim still lacks a proof or unique mechanism in its broadest intended domain.

• Color–kinematics and double copy — demonstrated in major domains, conjectural as a universal loop or nonperturbative principle.
• Non-supersymmetric three-dimensional dualities — anomaly and phase tests are strong, while most finite-rank continuum equalities remain conjectural.
• The Yang–Mills mass gap — strongly supported numerically, open as a continuum existence-and-gap theorem.
• Deconfined quantum criticality — deconfined phenomena are well supported, while the canonical transition’s order remains disputed.
• Planckian dissipation — a recurring scaling pattern is real, but a universal bound and unique mechanism are not established.
• Islands and unitary evaporation — the Page-curve mechanism is controlled in important models, but it is not a general microscopic unitarity theorem.

Controlled in separated regimes or selected families

These dossiers have rigorous or systematically improvable answers in distinct windows, without a verified bridge or universal uniqueness criterion.

• Finite-density QCD — small density, low-density EFT, and asymptotic density are controlled separately.
• Crossing solutions and actual CFTs — selected constructive classes are resolved; a general finite existence criterion is absent.
• Non-Lagrangian reconstruction — controlled families can be identified; finite protected data do not universally fix a full QFT.
• Real-time continuum dynamics — spectra, smeared response, and bounded systems can be controlled; generic long-time continuum dynamics cannot.

Central existence or definition still open

In these cases the target object itself is unestablished in the stated physical domain, or no non-arbitrary universal definition has been demonstrated.

• The QCD critical point — neither existence nor exclusion is established over the target region.
• Complexity in continuum QFT — regulated task-dependent costs exist, but no universal interacting continuum scalar does.
• Interacting constructive QFT in four dimensions — decisive partial constructions and obstructions exist, but no standard complete interacting construction meets the full criterion used here.

Read by method

Start from a method when the main question is not “what does the field believe?” but “which inference can this tool actually support?” The method pages explain assumptions and validation; the linked dossiers show them under stress.

• Multiloop amplitudes and resummation: infrared-complete scattering, color–kinematics and double copy, and SMEFT fits.
• EFT inference, power counting, and truncation: SMEFT validity, electroweak vacuum stability, Hawking robustness, and the generalized second law.
• Functional equations and functional RG: finite-density QCD, the QCD critical point, deconfined criticality, Planckian dissipation, and four-dimensional constructive QFT.
• Euclidean lattice and continuum extrapolation: confinement, finite-density QCD, the Yang–Mills mass gap, the QCD critical point, deconfined criticality, and constructive QFT.
• Hamiltonian truncation, tensor networks, and quantum simulation: real-time continuum dynamics, three-dimensional dualities, deconfined criticality, and continuum entanglement.
• Analytic and numerical conformal bootstrap: bootstrap certification, crossing-to-CFT reconstruction, non-Lagrangian QFT data, and three-dimensional dualities.
• Semiclassics, resurgence, and transseries: confinement, three-dimensional dualities, electroweak vacuum decay, and Hawking radiation.
• Schwinger–Keldysh, kinetic, and hydrodynamic methods: real-time dynamics, the QCD critical point, hydrodynamic attractors, Planckian dissipation, and Hawking backreaction.
• Replica, modular, and operator-algebra methods: continuum entanglement, continuum complexity, the generalized second law, islands, bulk reconstruction, and axiomatic equivalence.
• Holographic reconstruction and gravitational path integrals: hydrodynamic attractors, continuum complexity, Hawking radiation, islands, and bulk reconstruction.

For source-centered navigation, continue to Research Evidence. Executable checks, reconstructions, and sensitivity studies should be distributed with their inputs, environments, and validation criteria. For a broader subject map, use Research Fields.