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Does Complexity Equal Anything?
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We present a new infinite class of gravitational observables in asymptotically Anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switch-back effect in shock wave geometries. We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.
Forward citations
Cited by 13 Pith papers
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Comments on holographic spread complexity
The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.
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Holographic timelike complexity for de Sitter
Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.
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Page transition for the complexity of an evaporating black hole
The complexity of radiation from an evaporating black hole is argued to undergo a sharp Page-like transition, dominated after the Page time by the volume of an island in the entanglement wedge.
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Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity
Full-spectrum Krylov complexity provably saturates at ~e^{S(E)} log(1/λ) in every low-energy state — near the energy-dependent Heisenberg time, not the maximal e^{S_max} — because discrete-spectrum orthogonal polynomi...
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Probing holographic conformal field theories
In a holographic CFT on a cylinder, a qutrit Unruh-DeWitt detector harvests more mana when the dual bulk scalar uses standard (Δ+) quantization than alternate (Δ−) quantization.
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Holography of K-complexity: Switchbacks and Shockwaves
Operator Krylov complexity in triple-scaled DSSYK matches JT-gravity geodesic lengths with shockwaves and exhibits the switchback effect when the Lanczos algorithm is perturbed by two-sided operator insertions.
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De Sitter Complexity Grows Linearly in the Static Patch
Timelike extremal volume in the de Sitter static patch gives a holographic complexity that grows linearly with time and is proportional to horizon entropy times temperature.
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Volume as an index of a subalgebra
Proposes that the exponential of the maximal volume slice in AdS equals the index of inclusion of boundary subalgebras, but the supplied text is an unrelated astrochemistry paper.
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CFT Complexity and Penalty Factors
A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.
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$T\bar{T}$ deformation and multiple-flavor Lorentzian threads
TTbar-induced corrections to complexity=anything expand into generalized Willmore functionals that admit a local multi-flavor Lorentzian-thread decomposition by curvature sector.
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Delay-Independent Stability of Nonlinear Delay Differential Equations via Isospectral Reduction
Claims a delay-independent global exponential stability criterion for a broad class of nonlinear nonautonomous delay differential equations using isospectral reduction of an associated sequence of matrices.
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Learning shadows to predict quantum ground state correlations
The manuscript body does not match the claimed paper: the abstract promises a shadow-tomography ground-state scheme, while the text is the Leutheusser-Liu preprint on bulk volume and subalgebra indices.
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$R^2$ corrections to Complexity Growth with a Probe String
In Gauss-Bonnet AdS5, the probe-string complexity growth is maximized at zero velocity, independent of the GB coupling when stationary, and linear in temperature.
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