Tootfinder

Letter: Stripe told investors January 1 marked the "beginning of the singularity", a major inflection point in long-term trends, and H1 revenue rose 41% YoY (Axios)
https://www.axios.com/2026/08/19/stripe-payments-openrouter-singularity

Scoop: Stripe says "the singularity" has begun
Stripe today sent a letter to investors, which was shared with Axios.

#blackholes

"OpenAI's CEO says we've reached a point in the AI race that is the stuff of science fiction novels.
"We are now, like, in the singularity," Sam Altman said on Saturday's episode of the "Relentless" podcast."
"OpenAI, incidentally, has said it is preparing to IPO later this year."

OpenAI CEO Sam Altman says the singularity has arrived
OpenAI CEO Sam Altman said he believes the technological singularity, the moment when artificial intelligence surpasses humans intelligence, is here.

After the Singularity

After the Singularity

Gorgeous 🥹
SINGULARITY by Blender Studio
https://video.blender.org/w/4pSeQCu9XXz9wWMh5gTNMf

Reading "Singularity Sky" by @… .
Recently learned a bit about the Eschaton. Finally.
I'm now at the revolutionary dialectic exchange between Burya Rubenstein and Sister of Stratagems, the Seventh.
"Only sapient organism could exhibit superlative irrationally".
😬

Certain real surfaces in $\mathbb{C}^2$ with degenerated CR singularities
Sushil Gorai, Suman Karak, Golam Mostafa Mondal
https://arxiv.org/abs/2607.17016 https://arxiv.org/pdf/2607.17016 https://arxiv.org/html/2607.17016
arXiv:2607.17016v1 Announce Type: new
Abstract: In this paper, we study the local polynomial convexity of certain smooth real surfaces in \(\mathbb{C}^2\) with isolated CR singularity at the origin with higher-order of degeneracy. Under the assumption that the surface can be pulled back to a union of finitely many pairwise transverse totally real surfaces by a proper holomorphic map from $\mathbb{C}^2$ to $\mathbb{C}^2$, we obtain a normal form for such surfaces near the origin as
$\{(z,w)\in\mathbb{C}^2: w= \overline{z}^k o(|z|^{k})\}$
or
$M_t
:=
\left\{
(z,w)\in\mathbb{C}^2 :
w=(z t\overline{z})^k o(|z|^k)
\right\}$,
for some \(t>0\), where the parameter $t$ is a local biholomorphic invariant. We focus on the surfaces with order of degeneracy $k\geq 3$.
We prove that $M_t$ is locally polynomially convex at the origin if $t>cosec\left(\frac{\pi}{k}\right)$.
On the other hand, for $0<\frac{1}{k-2}$, we will also show that $M_t$ fails to be locally polynomially convex at the origin; and furthermore, a $(2k-3)$-parameter family of analytic discs attached to $M_t$ for $0<\min\left\{\sin\left(\frac{\pi}{k}\right),\frac{1}{k-2}\right\}$.
toXiv_bot_toot

Life after the Singularity

Phase transition from eigenstate thermalization: forbidden singularity and instanton proliferation via AGT correspondence
Yongjiang Xu, Weixin Sun, Chushun Tian, Huajia Wang
https://arxiv.org/abs/2608.13246 https://arxiv.org/pdf/2608.13246 https://arxiv.org/html/2608.13246
arXiv:2608.13246v1 Announce Type: new
Abstract: In theoretical physics, finding connections between problems that appear in distinct contexts is an important way to leapfrog progresses, often by illuminating deep aspects that may otherwise seem obscure. In this paper, we consider in 2d CFTs the phenomenon of forbidden singularities in auto-correlation functions -- a key signature of eigenstate thermalization. We show that they correspond to phase transitions in the context of eigenstates. The connection is made explicit by utilizing the AGT correspondence, which relates eigenstate auto-correlations to the Nekrasov partition functions describing an instanton gas of the $\mathcal{N}=2$ SUSY gauge theories. We show that by taking the counter-part of the heavy-light limit, two phases emerge for the instanton gas. They are dominated by configurations represented by string-like Young tableaux with distinct structures and thermodynamic properties, which bare resemblance to the confined and the deconfined phases. A phase transition occurs as instantons proliferate from one side, in a manner that mimics the Lee-Yang theory. We work out the critical fugacity and find it corresponding exactly to the forbidden singularity.
toXiv_bot_toot

Sorry, Sam and Elon, we have not reached the Singularity as most see it. https://garymarcus.substack.com/p/sorry-sam-and-elon-we-have-not-reached

after the singularity.

Non-symmetric vector dyson equations
Jiaoyang Huang, Zhonggen Su, Ruizhe Xu
https://arxiv.org/abs/2607.16333 https://arxiv.org/pdf/2607.16333 https://arxiv.org/html/2607.16333
arXiv:2607.16333v1 Announce Type: new
Abstract: We study the vector Dyson equation $$-\frac{1}{m(z)}=z\mathbf{1} \mathbf{a} Sm(z),$$ with parameter $z$ in the complex upper half-plane $\mathbb{C}_ $, where $\mathbf{a}\in\mathbb R^d$ and $S$ is a nonnegative matrix, not necessarily symmetric. This equation has a unique vector solution $m(z)\in\mathbb{C}_ ^d$, for which we establish a complete measure decomposition and prove regularity. We then develop a graph-theoretic approach to the singularity and stability problem for non-symmetric matrices $S$. The graph structure of $S$ identifies the possible degeneracies of the stability operator as $z$ approaches the real axis. In particular, for non-backtracking matrices, we prove square-root growth at regular edges, cubic-root growth at regular cusps, and complete stability estimates. We also obtain the corresponding estimates for symmetric matrices in the periodic setting.
toXiv_bot_toot

A Tale of Two Compact Bosons
Christian Ferko, Vishnu Jejjala, Brandon Robinson
https://arxiv.org/abs/2608.06376 https://arxiv.org/pdf/2608.06376 https://arxiv.org/html/2608.06376
arXiv:2608.06376v1 Announce Type: new
Abstract: Neural network field theory (NN-FT) defines a field theory by a network architecture together with a probability density on its latent variables. For compact theories the local Gaussian sector is only part of the story: one must also sum over discrete topological sectors. We review a mixed continuous/discrete latent-variable construction and apply it to two compact bosons. For the Berezinskii--Kosterlitz--Thouless transition, a random Fourier feature spin-wave sampler supplemented by an explicit Coulomb gas vortex sector reproduces the Gaussian critical line below $T_c$, vortex proliferation above $T_c$, the essential singularity of the correlation length, and the Nelson--Kosterlitz jump. For the bosonic string, oscillator modes augmented by momentum--winding labels reproduce circle T-duality, Buscher transformations on constant toroidal backgrounds, self-dual current algebra enhancement, and a toy T-fold. The common lesson is that the same local neural sampler, paired with different discrete topological data, yields physically distinct compact theories. These proceedings are based on arXiv:2604.02313.
toXiv_bot_toot

Lee-Yang paradigm of phase transition in eigenstate thermalized systems
Yongjiang Xu, Weixin Sun, Chushun Tian, Huajia Wang
https://arxiv.org/abs/2608.13174 https://arxiv.org/pdf/2608.13174 https://arxiv.org/html/2608.13174
arXiv:2608.13174v1 Announce Type: new
Abstract: As phase transitions in isolated quantum systems remain elusive, here we show how a thermodynamic-like phase transition, falling into the Lee-Yang paradigm, can arise in systems displaying eigenstate thermalization. Specifically, we show that in holographic conformal field theories, the eigenstate expectation of the auto-correlation function can be mapped to the partition function ${\cal Z}_{{gauge}}(z)$ of a virtual interacting instanton gas, with the conformal mapping of the imaginary time: $z=1-e^{-\tau}$ and the central charge $c$ mimicking the instanton fugacity and volume, respectively. We find that akin to the Lee-Yang paradigm, for $c\to\infty$ a pair of complex conjugate zeros of ${\cal Z}_{{gauge}}(z)$ move to the real axis located at the famous forbidden singularity. Passing through the singularity the system transits from the low- to high-fugacity phase, accompanied by dramatic changes in scaling behaviors of the free energy and dominant microscopic configurations. Our findings indicate that physics of phase transitions from eigenstate thermalization is very rich.
toXiv_bot_toot

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
- Singularity of non-pluripolar cohomology classes
Duc-Bao Nguyen, Shuang Su, Duc-Viet Vu
https://arxiv.org/abs/2508.14669 https://mastoxiv.page/@arXiv_mathCV_bot/115065656430154433
- Analytic structure of $q$-pseudoconcave subsets of continuous graphs
Filippo Valnegri
https://arxiv.org/abs/2603.04967 https://mastoxiv.page/@arXiv_mathCV_bot/116181309294452296
- Non-symmetric vector dyson equations
Jiaoyang Huang, Zhonggen Su, Ruizhe Xu
https://arxiv.org/abs/2607.16333 https://mastoxiv.page/@arXiv_mathCV_bot/116956844212485469
- Cofinite Zeros of High Derivatives
Eric Hou
https://arxiv.org/abs/2607.20816 https://mastoxiv.page/@arXiv_mathCV_bot/116973837268195335
- Coefficient Problems for a Ma-Minda Convex Class Associated with the Normalized Arcsine Mapping
Shantanu Panja, Abhijit Banerjee, Jhilik Banerjee, Sujoy Majumder
https://arxiv.org/abs/2607.27293 https://mastoxiv.page/@arXiv_mathCV_bot/117013548331556229
- Skoda division theorem on compact K\"ahler manifolds for line bundles with singular hermitian met...
Jaehoon Jeong
https://arxiv.org/abs/2607.29669 https://mastoxiv.page/@arXiv_mathCV_bot/117030527056701741
- Classes of Holomorphic Multicomplex-Valued Functions Generated by Elliptic-Admissible Involutions
Nicolas Doyon, Pierre-Olivier Paris\'e, William Verreault
https://arxiv.org/abs/2211.13875
- Fast vanishing cycles on perturbations of complex weighted-homogeneous complete intersection germs
Dmitry Kerner, Rodrigo Mendes
https://arxiv.org/abs/2311.13423 https://mastoxiv.page/@arXiv_mathAG_bot/111458171750230260
toXiv_bot_toot

We've reached some kind of dystopia singularity, where you can't write dystopian fiction anymore because things are worse than the society you had imagined by the time you finish fleshing out the idea.

You know how everything in “AI” is always “almost there” or “the singularity is next year” or “in 3 years nobody has to work anymore”?
This is a specific type of scam, that many people fall for.
As always there’s a good Weizenbaum quote.
Translation: “People have the same attitude toward technology, especially toward computer technology: it's a kind of natural automatic necessity whose arrival cannot be averted. When experts talk about artificial intelligence, for example, they always talk about tomorrow, the day after tomorrow, and the day after that; very rarely do we hear about what has already been achieved to date.”

🇺🇦 #NowPlaying on #BBC6Music's #6MusicsJukebox
Jon Hopkins:
🎵 Singularity
#JonHopkins
https://jonhopkins.bandcamp.com/track/emerald-rush
https://open.spotify.com/track/4oZ2Xkline6CvRDebjbi8Q

Clever girl
#AI_armageddon #aisecurity #airisks #singularity

RE: https://infosec.exchange/@0xabad1dea/117015434798858894
Still laughing about this, the Anthropic chatbot saw the system date is 2026 and concluded that "this must be staged" (because the training data it's trained on probably ends in 2023 or whatever) and ignored the instruction that "you're in sandbox".
Truly the brightest minds of a generation working on this stuff. A veritable techbro brains singularity.