Aix-en-Provence - Wikipedia
At Aix, the line from Paris branches to Marseille and Nice; it takes about 3 hours to get from Paris to Aix by TGV. Aix also has a railway station near the centre, Gare d'Aix-en-Provence, with connections to …
On a conjecture of Krukenberg and a problem of Dalton and Trifonov
We prove that if the smallest modulus of a covering system with distinct moduli is $5$, then the largest modulus is at least 108. We also prove that if the smallest modulus of a covering system with distinct moduli is $5$, then the least common multi...
Prove that the manifold $SO (n)$ is connected
The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected. it is very easy to see that the elements of $SO (n ...
Using Edge-induced and Vertex-induced Subhypergraph Polynomials
For a hypergraph $\mathcal H$, we consider the edge-induced and vertex-induced subhypergraph polynomials and study their relation. We use this relation to prove that both polynomials are reconstructible, and to prove a theorem relating the Hilbert se...
The prescribed point area estimate for minimal submanifolds in constant curvature
We prove a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in hyperbolic space, in any dimension and codimension. In certain cases, we also prove the corresponding estimate in the sphere. Our estim...
Coalition for Content Provenance and Authenticity Insights
The Coalition for Content Provenance and Authenticity (C2PA) is a Linux Foundation project that develops open technical standards to certify the origin and history of digital media, aiming to combat …
Content Provenance & Authenticity Standard | C2PA
C2PA (Coalition for Content Provenance and Authenticity) is an open standard that adds cryptographically signed metadata to media files, enabling verification of content origin and editing …
Linear independence of time-frequency translates for ultimately positive functions
We prove that the HRT conjecture holds when the Gabor system consists of a 4-point set in the time-frequency plane and a square-integrable function that is ultimately positive. We also prove the conjecture for Gabor systems generated by an ultimately...
Proof of Northshield's conjecture concerning an analogue of Stern's sequence for $\mathbb{…
We prove a conjecture of Northshield by determining the maximal order of his analogue of Stern's sequence for $\mathbb{Z}[\sqrt{2}]$. In particular, if $b$ is Northshield's analogue, we prove that $$\limsup_{n\to\infty}\frac{2b(n)}{(2n)^{\log_3 (\sqr...
Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE
This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalence (FLE) at the critical level; (2) Study the interaction between...
Coalition for Content Provenance and Authenticity Insights
The Coalition for Content Provenance and Authenticity (C2PA) is a Linux Foundation project that develops open technical standards to certify the origin and history of digital media, aiming to combat …
Content Provenance & Authenticity Standard | C2PA
C2PA (Coalition for Content Provenance and Authenticity) is an open standard that adds cryptographically signed metadata to media files, enabling verification of content origin and editing …
Prove that the manifold $SO (n)$ is connected
The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected. it is very easy to see that the elements of $SO (n ...
Paths, cycles and sprinkling in random hypergraphs
We prove a lower bound on the length of the longest $j$-tight cycle in a $k$-uniform binomial random hypergraph for any $2 \le j \le k-1$. We first prove the existence of a $j$-tight path of the required length. The standard "sprinkling" argument is...
Based on the stats, Mahomes has been the 15th-20th best QB in the league over the past 3 y…
His TD vs INT ratio ranks 22nd over the last 3 years Passer rating 2023: 14th 2024: 16th 2025: 23rd Completion% 2023: 9th 2024: 10th 2025: 28th Yards per attempt 2023: 19th 2024: 26th 2025...
MerkleSpeech: Public-Key Verifiable, Chunk-Localised Speech Provenance via Perceptual Fing…
Speech provenance goes beyond detecting whether a watermark is present. Real workflows involve splicing, quoting, trimming, and platform-level transforms that may preserve some regions while altering others. Neural watermarking systems have made stri...
Coalition for Content Provenance and Authenticity Insights
The Coalition for Content Provenance and Authenticity (C2PA) is a Linux Foundation project that develops open technical standards to certify the origin and history of digital media, aiming to combat …
Interoperable Provenance Authentication of Broadcast Media using Open Standards-based Meta…
The spread of false and misleading information is receiving significant attention from legislative and regulatory bodies. Consumers place trust in specific sources of information, so a scalable, interoperable method for determining the provenance and...
Content Provenance & Authenticity Standard | C2PA
C2PA (Coalition for Content Provenance and Authenticity) is an open standard that adds cryptographically signed metadata to media files, enabling verification of content origin and editing …
Authenticated Contradictions from Desynchronized Provenance and Watermarking
Cryptographic provenance standards such as C2PA and invisible watermarking are positioned as complementary defenses for content authentication, yet the two verification layers are technically independent: neither conditions on the output of the other...