“"realistically wouldn't it be possible that the ideas supporting this non-use of AI are rooted in established organizations that stand to suffer when they are completely obliterated by a tool that can not only do what they do but do it instantly and always be readily available, and do it for free?"”

“The paper establishes a complete classification for fermionic symmetry protected topological phases (FSPT) with purely discrete internal symmetries, which determines the crystalline case via the crystalline equivalence principle.”

“Both uniform attention and trainable attention architectures implement the same algorithm via topologically and geometrically equivalent representations.”

“The paper proves an orbifold type decomposition theorem and shows that the total Hochschild homology is isomorphic to a symmetric algebra.”

“The trilinear equivalence only requires an averaging over grids, which converts a difficult exponential sum into an oscillatory integral with periodic amplitude.”

“Deformed systems involve, as invariant subsets, two different off-shell versions of the irreducible multiplet ${\bf (8,8,0)}$.”

“The paper establishes general criteria that guarantee equivalences between the categories of polynomial functors of different degrees or with different base categories.”

“The paper introduces a quasi-maximum likelihood estimation (QMLE) framework, yielding consistent Wald and likelihood ratio test statistics.”

“The paper provides the first provable poly-time unbiased estimators for counting traces, a problem of considerable importance when allocating model checking resources.”

“The paper checks equivalence with instanton partition function of a 5d circular quiver gauge theory...and with partition function of a defect in the same theory, also known as the Shiraishi function.”

“The consistent orderings are in one-to-one correspondence with the Jacobians associated with all field redefinitions of a set of canonical degrees of freedom. For each admissible operator ordering--or equivalently, each path-integral measure--we identify a definite, positive Hilbert-space inner product. All such prescriptions define the same quantum theory, in the sense that they lead to identical physical observables.”

“The paper proposes I-PERI, a novel federated algorithm that first recovers the CPDAG of the union of client graphs and then orients additional edges by exploiting structural differences induced by interventions across clients.”

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“The paper proposes a higher-order argumentation framework with supports ($HAFS$), which explicitly allows attacks and supports to act as both targets and sources of interactions.”

“Semantic invariance requires a non homeomorphic, discriminative target for example, supervision via labels, cross-instance identification, or multimodal alignment that supplies explicit semantic equivalence.”

“Thermodynamics becomes the study of how these shells deform with energy: the entropy is the logarithm of a geometric area, and its derivatives satisfy a deterministic hierarchy of entropy flow equations driven by microcanonical averages of curvature invariants.”

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“The paper validates the new 3-crossed module structure by proving that the induced simplicial set forms a quasi-category and that the Moore complex of length 3 associated with a simplicial group naturally admits the structure of the proposed 3-crossed module.”

“The paper establishes an effective l=1 angular momentum algebra for the t2g case, formalizing the equivalence between p and t2g orbitals.”

“The paper establishes bounds, presents realizability results, determines exact values for some graph families, and demonstrates an equivalence between the weighted Roman domination number and the differential of a weighted graph.”

“The paper finds that a 2-dimensional subgroup of SL(2,R) acts as a higher-form symmetry group and computes Smarr formulas for black holes, showing their equivalence under specific field constraints.”

“The results of the speed measurement are compared with those of the pressure sensors and the empirical formula, revealing a maximum error of 5.20% and a minimum error of 0.06%.”

“The paper shows how to construct statistical mechanical models for stabilizer circuits subject to independent Pauli errors, by mapping logical equivalence class probabilities of errors to partition functions using the spacetime subsystem code formalism.”

“Continuous qubit measurements admit a dynamical delayed choice effect where a future experimental choice can appear to retroactively determine the type of past measurement backaction.”

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“The methodology's main ingredient is the penalization of any statistical dependence between $W$ and $Z$ conditioned on $Y$, replaced by the more readily implementable plain independence between $W$ and the random variable $Z_Y = T(Z,Y)$ that solves the [Monge] Optimal Transport Barycenter Problem for $Z\mid Y$.”

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“The article aims to explain data from ACT.”

“The paper investigates the equivalence of the null energy condition to variable lower bounds on the timelike Ricci curvature for $C^2$-Lorentzian metrics.”

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“We provide a simple derivation — based on Bayes’ rule and conditional expectations — that unifies Gaussian diffusion and flow matching without relying on ODE/SDE…”

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“The article doesn't contain a direct quote.”

“The article is about a 1996 paper discussing the relationship between Turing Machines and Recurrent Neural Networks.”