Anthropic may ask Claude users to verify their age and identity
by uploading their government-issued documents,
according to a new version of the company’s privacy policy.
The AI giant says the move was to allow users to appeal having their account flagged for potentially fraudulent activity
rather than outright banning them,
-- but comes at a time when Anthropic seeks to placate the Trump administration
amid an ongoing standoff over who gets access to th…
A strict second-eigenvalue estimate for the scalar stability operator on surfaces in $\mathbb{RP}^{3}$
M\'arcio Batista, Abra\~ao Mendes
https://arxiv.org/abs/2608.05458 https://arxiv.org/pdf/2608.05458 https://arxiv.org/html/2608.05458
arXiv:2608.05458v1 Announce Type: new
Abstract: Let $\varphi:\Sigma^2\looparrowright\mathbb{RP}^3$ be a closed immersed surface, with no orientability or, equivalently, two-sidedness assumptions. We establish the sharp quantitative estimate $$ \lambda_2(\Delta |\sigma|^2 2)\leq2-\frac{2}{\operatorname{Area}(\Sigma)}\int_\Sigma H^2d\Sigma \frac{4\pi\chi(\Sigma)}{\operatorname{Area}(\Sigma)}. $$ Our main contribution is the analysis of the borderline case, which rules out equality when $\chi(\Sigma)\leq0$. More precisely, $$ \lambda_2(\Delta |\sigma|^2 2)<2\quad\text{whenever}\quad\chi(\Sigma)\leq0. $$ The proof combines the canonical Veronese embedding of $\mathbb{RP}^3$ into $\mathbb{S}^8$, the conformal test function method, an Obata-type rigidity argument, and the classification of closed flat minimal surfaces in $\mathbb{RP}^3$.
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"Bern landet in den Rankings zur Velofreundlichkeit schweizweit immer wieder auf den vorderen Plätzen. Flächenmässig verfügen Velospuren aber nicht über mehr Raum als in anderen Städten."
"Im Richtplan für den Veloverkehr hat ein gut zusammenhängendes Velonetz in der Stadt hohe Priorität. Wichtig sind aber auch Faktoren wie gute Veloabstellplätze oder eine sichere Verkehrsführung bei der Kreuzung von Tramschienen."
Classical Acceptance Is Not Hybrid Authentication: Measuring X.509 Verifier Semantics in Post-Quantum Migration
Taesung Kim, Boheung Chung, Keonwoo Kim, Yousung Kang
https://arxiv.org/abs/2607.20800 https://arxiv.org/pdf/2607.20800 https://arxiv.org/html/2607.20800
arXiv:2607.20800v1 Announce Type: new
Abstract: A relying party validating a hybrid X.509 certificate --- carrying both a classical and a post-quantum credential --- must distinguish whether its accepting judgment rests on the post-quantum evidence or only on the classical path. To preserve compatibility, the separable designs place that evidence where classical path validation may ignore it. A verifier can then validate the classical path and accept while the post-quantum evidence never bears on the decision --- a valid classical result silently promoted to a hybrid conclusion it did not establish. We measure this across eight path-validation stacks (seven independent codebases), in nine validation modes, over six certificate schemes. Under a hybrid-required policy, nearly every stack parsing a separable hybrid certificate accepts on the classical path without making the post-quantum evidence outcome-bearing; one enforcing mode instead fractures interoperability over a signature-input encoding not yet interoperably profiled; and stacks that verify post-quantum signatures still do not enforce the binding by default: the gap is structural, not explained by missing primitive capability alone. Under lifecycle desynchronization the downgrade is realized: when a bound post-quantum credential is revoked while the classical certificate stays valid, the default path still accepts, because the bound credential lies outside the decision's scope. Binding success is not authentication success. We contribute a specification-derived verifier model and an executable, policy-parametric reference contract --- what a verifier must recognize, verify, make outcome-bearing, and check before reporting a validation as hybrid --- with a diagnosis of why standards do not require it.
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Compact balanced threefolds and LCK manifolds with constant holomorphic sectional curvature
Shuwen Chen, Junpeng Li
https://arxiv.org/abs/2608.05598 https://arxiv.org/pdf/2608.05598 https://arxiv.org/html/2608.05598
arXiv:2608.05598v1 Announce Type: new
Abstract: A long-standing conjecture in Hermitian geometry says that a compact Hermitian manifold with constant Chern holomorphic sectional curvature $c$ is K\"ahler for $c\neq 0$ and Chern flat for $c=0$. Although the conjecture has been established in complex dimension two, it remains open in general in higher dimensions. We verify the conjecture for compact balanced threefolds when $c\leq 0$. For compact locally conformally K\"ahler manifolds, Chen, Chen, and Nie established the case $c\leq 0$, while Huang and Wan recently settled the remaining case. Inspired by the approach of Huang and Wan, we investigate a generalization of the conjecture for canonical metric connections and establish it for connected compact locally conformally K\"ahler manifolds.
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Die Bundesregierung möchte, daß Klagen von Umweltverbänden keine aufschiebende Wirkung mehr haben. Nun gut, wenn das Gericht dann im Nachhinein feststellt, daß das Wegbaggern des Bannwaldes eine dumme Idee und rechtswidrig war, ist dieser Wald trotzdem weg.
Um dafür einen Ausgleich herzustellen, müßte der Staat also gezwungen werden, kurzfristig einen gleichwertigen Ersatz zu schaffen. Und damit die Entscheidungsträgys sich auch der Tragweise ihrer Beschlüsse bewußt sind, sollten sie…
Weighted Nuclear Elastic Net Estimation of (Near-) Low-Rank Drift Matrices in Ornstein-Uhlenbeck Processes
Dmytro Marushkevych, Francisco Pina, Mark Podolskij
https://arxiv.org/abs/2608.12838 https://arxiv.org/pdf/2608.12838 https://arxiv.org/html/2608.12838
arXiv:2608.12838v1 Announce Type: new
Abstract: We study estimation of the drift matrix in a continuously observed high-dimensional Ornstein-Uhlenbeck process when the drift is exactly or approximately low rank. In this setting, exact low rank induces non-stable directions and hence a non-ergodic regime, resulting in a poorly conditioned empirical covariance matrix. To address this difficulty, we introduce a Weighted Nuclear Elastic Net Estimator that combines ridge regularization with a nuclear-norm penalty expressed in the empirical likelihood geometry.
Under a general diagonalizable spectral framework, we establish oracle inequalities relative to arbitrary low-rank comparison matrices. For near low-rank drifts, the approximation error is naturally measured through the singular-value decay of the drift after weighting by the regularized empirical covariance. The stochastic term is controlled by self-normalized martingale arguments under appropriate choice of the tuning parameter.
For a symmetric positive-semidefinite exact low-rank model, we verify the empirical-curvature condition required to translate the weighted bound into a Frobenius-norm bound. With an appropriate choice of tuning parameters, the resulting estimator satisfies, up to a logarithmic factor, the standard rank-$r$ matrix-estimation scaling $r d/T$: specifically, its squared Frobenius error is of order $r d\log(T)/T$ with high probability, under an explicit dimension-horizon condition.
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Themis Consensus Extension v1: MEV Mitigation by Randomized Delayed Execution and Intent-Hiding Transactions in Application-Specific Blockchains
Shoeb Siddiqui, Mateusz Nowakowski, Stanislav Vozarik, Gleb Urvanov, Peter Kris
https://arxiv.org/abs/2607.21406 https://arxiv.org/pdf/2607.21406 https://arxiv.org/html/2607.21406
arXiv:2607.21406v1 Announce Type: new
Abstract: Maximal extractable value (MEV) arises when privileged participants select, exclude, insert, or reorder pending transactions for private gain. We specify and analyze the Themis Consensus Extension v1, first published by Mangata in 2021. The design separates value extraction by reordering (VER) from value extraction by denial (VED). For VER, block construction and execution occur across consecutive producers: one producer commits a transaction set, and the next derives a publicly verifiable, deterministic, previously un- predictable seed and executes a seed-determined, dependency-preserving permutation. For selective VED, a user may encrypt a transaction for a designated builder and executor. The builder removes an outer layer and commits the opaque inner ciphertext; the executor reveals and executes the plaintext only after commitment. Under selfish but non-colluding validators, an adversary below the underlying consensus fault threshold, secure cryptography, and accountable role performance, the construction limits unilateral post-commit ordering control and hides transaction intent from relays and the builder. It does not provide send-order or receive-order fairness, complete censorship resistance, resistance to builder-executor collusion, or per-transaction price guarantees. We analyze probabilistic extraction, spam, dependent transactions, decryption liveness, session boundaries, total denial, and threshold coalitions. We also document the initial Aura-based Substrate implementation and its subsequent transition to a BABE-based sr25519/VRF seed path, together with delayed execution, Fisher-Yates shuffling, and Xoshiro256 . The result preserves the original proposal while narrowing its claims to explicit assumptions.
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