embed_injective

"rigorous angular momentum conservation (AMC) in elastic, inelastic, and decay channels"

"metastable core shift structures can be obtained only when the core-shift times for the ABC stacking unit above is the same as that below or 1 more than that below... total numbers... 2^(csd/3)-1"

"Theorem 1 ... all maps in it are isomorphisms. ... The Gauss-Manin connection on H^i_dR(X/S, (V,∇/S)) corresponds to the action of Π(S/k) on H^i(π_geom(X/S),V) induced from the Lyndon-Hochschild-Serre sequence."

"We term the root cause as Contextual Inertia... over 70%–90% of multi-turn errors traced to propagation of previous responses"

"diffusion models generate novel samples by interpolating between training data and iFID measures the validity of these interpolated samples."

"transfer-matrix representation of the cumulant generating function"

"an online, entity-agnostic embedding model trained via contrastive learning for robust matching"

"fixed continuation distribution Db ... QDb(h, a) ≜ EDb[R|h, a]"

"We show that our definition of polytopes captures optimization over the Hilbert cube"

"Under power-law regularity at the boundaries (Assumption 3(b)), any such SNR profile decomposes as p^{a'}(1-p)^{b'}·e^r(p) with bounded remainder (Proposition 2)."

"We measure pairwise and group-level agreement using set-, rank-, and consensus-based metrics including Average Overlap, Jaccard similarity, Rank-Biased Overlap, Kendall's tau, Kendall's W, and Cronbach's alpha."

"Dynamic Temporal Re-anchoring (DTR)... assigns fixed index n corresponding to the timestep when the image was captured... Score(q_m, k_VL_n) = q^T R(m-n) k_VL"

"Theorem 1.1. Any Dehn twist tγ … is conjugate to tc, td, or te … in terms of Dynnikov coordinates (a,b) of γ: tγ conjugate to te if b even, …"

"gauge invariance guarantees discretization-invariant learning with bounded discretization mismatch error"

"We connect partition logic with Generative Logic by translating finite partition logics into Prolog-based Simple Generative Logic Grammars... the grammar GL constructed from Eqs.(17)–(19) preserves the incidence relation between atoms and two-valued states."

"When user data are scarce, new users are represented as linear combinations of existing preference embeddings learned during training"

"C ≤ (1/b log b) ∑_{r=0}^{b-1} D(b,r) for any b≥2"

"non-centered inner product form ... LRR = 1/d(d-1) Σ i≠j ([C(Z)]ij)^2 where [C(Z)]ij = 1/(N-1) Σ zb,i zb,j"

"The encoder is trained using kernel mean embeddings, ensuring that the learned representation space reflects population-level policy dissimilarities."

"Theorem 1 (Exact joint law). Under Eq. 5, the sequence produced by FeF-DLLM satisfies Pr(ˆX0,Jt=xJt|Xt,t)=∏p⋆(Xjm0=xjm|X≥jm t,x<jm0,t)=p⋆(xJt|Xt,t)."

"Theorem 1 (Weak convergence for KDE process). Suppose 0 < hn ≤ C n^−δ ... Then P(Pn ⇀ P) = 1 ... supported on a (random) compact set V"

"The resulting Fokker–Planck model associated with (2.18) reads ∂tfJ(x,w,t)=1/τ ∑ QJ(fJ,fH)(x,w,t)"

"Functional Equivalence Hypothesis... instruction I and optimal action a* are two forms of the same underlying GUI Affordance"

"Definition 6.8. ... (•)-q-connected ... directed (•)-q-chain"

"From the inequality (7), when x_{2p-1}=0 and p=3,4,… we have |ω11 x1 + ω31 x3|² + … ≤ |x1|² + |x3|²/3"

"Superhypergraphs extend higher-order network models by allowing the vertex domain itself to be hierarchical... iterated powerset constructions"

"SVD generalized density matrix ρ_SVD=√(ρ†ρ)/Tr√(ρ†ρ) for bi-orthogonal entanglement"

"Proposition 2. A graded nilpotent Lie algebra with reduced growth vector (2,1,1,…) is either Goursat … or … (5)"

"Assumption 2 (Ranking-list refill)... instrument and policy operate on same margin"

"token-level supervision anchored at the first correct solution"