Sample Reuse Does Not Beat Second-Order Query Limits
A curvature-first algorithm and reuse-aware lower bounds match total derivative complexity at near ε⁻³ + γ⁻³ scaling.
Oct 14, 20263 min2610.16832
Mathematics
Pure and applied mathematics including algebra, analysis, geometry, and combinatorics.
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Lower Bound Extends Beyond Tensor Algorithms
Exactly flat gates turn a scalar convex–concave chain into a hard instance, matching the known $2/(3p-1)$ higher-order exponent up to logarithmic factors.
Oct 12, 20264 min2609.28246
Common-Loss Oracles Match Second-Order Tolerance Bounds
Random-line Hessian estimates and a dyadic gradient tracker attain the minimax $\widetilde{\Theta}(\epsilon^{-3}+\gamma^{-5})$ oracle rate without the earlier mixed tolerance cost.
Oct 9, 20264 min2609.28238
Higher-Order Finite-Sum Bounds Close the Square-Root-n Gap
Verified recursive estimation and dense weak hiding yield matching higher-order oracle bounds with an $n^{1-1/(2p)}$ finite-sum term.
Oct 5, 20263 min2609.28202
Twisted Chowla Method Proves Strong Van der Waerden for Degrees 40 and Above
A new twisted function-field version of Chowla's conjecture yields the required density-zero bound for irreducible non-$S_n$ polynomials in every degree $n \geq 40$.
Oct 3, 20262 min2608.22297
Matrix-Vector Query Bounds Match for Low-Rank Approximation
Adaptive access to $A$ and $A^\top$ yields matching polynomial query bounds for rank-$k$ projectors with $(1+\varepsilon)$-optimal Schatten-$p$ residuals.
Sep 30, 20264 min2609.35840
Diffeomorphic Traces Fail To Detect High-Dimensional Knots
Generalized RBG links and a Plotnick-based construction give counterexamples in every dimension $n \geq 4$, while preserving trace detection for the unknot.
Sep 28, 20264 min2511.07251
Proof Establishes Iwaniec’s Exact Beurling–Ahlfors Norm Conjecture
A quasiconvexity proof for a piecewise matrix integrand yields the exact $L^p$ operator norm: $p-1$ above $p=2$ and its reciprocal below.
Sep 25, 20264 min2609.28311
Forbidden Bicliques Bound Tree-Independence in P5-Free Graphs
A decomposition-repair proof establishes a $4\ell-4$ bag-independence bound when induced $P_5$ paths and $K_{\ell,\ell}$ bicliques are excluded.
Sep 23, 20264 min2605.03965
Exact Values Still Require Square-Root Query Complexity
Coordinate finite differences plus accelerated projection attain the deterministic rate, while a transcript-consistent hard instance proves it cannot generally be improved.
Sep 20, 20264 min2609.18230