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Lean 4 Machine-Verified Proof of P = NP via the Pedigree Polytope Membership Problem
arXiv:2606.03194v1 Announce Type: new Abstract: The Membership Problem for Pedigree Polytope (M3P) asks, given $X\in\mathbb{Q}^{\binom{n}{3}}$, whether $X\in\mathrm{conv}(P_n)$, where $P_n$ is the set of all pedigrees. A pedigree is a structured encoding of a Hamiltonian cycle construction in $K_n$. We establish that M3P is solvable in strongly polynomial time via a recursively constructed layered network $(N_k, R_k, \mu)$ and a multicommodity flow problem MCF$(k)$. The necessary and...
Almost covering all the layers of hypercube with multiplicities
Announce Type: replace-cross Abstract: Given a hypercube $\mathcal{Q}^{n} := \{0,1\}^{n}$ in $\mathbb{R}^{n}$ and $k \in \{0, \dots, n\}$, the $k$-th layer $\mathcal{Q}^{n}_{k}$ of $\mathcal{Q}^{n}$ denotes the set of all points in $\mathcal{Q}^{n}$ whose coordinates contain exactly $k$ many ones. For a fixed $t \in \mathbb{N}$ and $k \in \{0, \dots, n\}$, let $P \in \mathbb{R}\left[x_{1}, \dots, x_{n}\right]$ be a polynomial that has zeroes of multiplicity at least $t$ at all points of...
Distributed Instrument Simulation with Quantum Side Information in the One-Shot Regime
arXiv:2109.12586v5 Announce Type: replace-cross Abstract: Three distributed parties, two transmitters (Txs) and a receiver (Rx), hold one component each of a tripartite quantum state \(\rho^{A_1A_2C}\). The goal is to simulate the action of a separable instrument acting on the \(A_1\) and \(A_2\) components, with the Rx recovering the classical outcome. To enable this, each Tx \(k\) can transfer bits on a noiseless bit pipe and share randomness at rates \(R_k\) and \(C_k\), respectively,...
Dual-Route Top-K Retrieval with 1v1 VLM Reranking for the CoVR-R
Announce Type: new Abstract: We describe \emph{Dual-Route Top-K Retrieval with 1v1 VLM Reranking} for the CoVR-R challenge. The method treats composed video retrieval as two coupled problems: finding a sufficiently complete top-k candidate set, and then safely deciding whether any candidate should replace a strong current top-1. We first improve the reasoning/text seed with a VLM slot selector over existing candidates, without introducing DFN visual retrieval.
A Kronecker algorithm for locally closed sets over a perfect field
arXiv:2512.14888v2 Announce Type: replace-cross Abstract: We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the set of common zeros $\{F_1=0,\ldots,F_r=0,G\not=0\}$ of multivariate polynomials $F_1,\ldots,F_r\in k[X_1,\ldots,X_n]$ outside a prescribed hypersurface $\{G=0\}$. We assume that $F_1,\ldots,F_r$...
Kars4Kids jingle can continue in California after appeals court ruling
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Formal Foundations and Proof-Carrying Certificates for q-ary Covering Codes in Lean 4
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Light-induced quantum friction of carbon nanotubes in water
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Worst-Case Update Complexity of the Preisach Extremum Stack
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Building user-driven climate adaptation products
Abstract Climate adaptation products have traditionally been developed using a supply-driven model reliant on available climate information, leading to usability gaps1,2,3,4. To better meet user needs, the climate services field has recognized a need to shift towards a demand-driven model emphasizing co-production, that is, user-driven, scientifically informed products created through shared knowledge practices1,2,3,4,5. However, co-production can be challenging, especially for researchers...