Tootfinder

A Complete Characterization of Finite-Order Entire Solutions to Fermat-Type Partial Differential-Difference Systems in $\mathbb{C}^n$
Sujoy Majumder, Jhilik Banerjee, Abhijit Banerjee
https://arxiv.org/abs/2606.05240 https://arxiv.org/pdf/2606.05240 https://arxiv.org/html/2606.05240
arXiv:2606.05240v1 Announce Type: new
Abstract: The primary objective of this paper is to determine the explicit existence form and structure of finite-order entire solutions in $\mathbb{C}^n$ of the following system of Fermat-type partial differential-difference equations: \[\begin{cases} \left(\frac{\partial f_1\left(z\right)}{\partial z_1}\right)^{n_1} (f_2 \left(z c\right)-f_1(z) )^{m_1}= 1,
\medskip \left(\frac{\partial f_2\left(z\right)}{\partial z_1}\right)^{n_2} (f_1 \left(z c \right)-f_2(z) )^{m_2}= 1, \end{cases}\]
for different choices of the positive integers $n_1$, $n_2$, $m_1$, and $m_2$, where $c=(c_1,c_2,\ldots,c_n)$. We characterize the precise structure of finite-order transcendental entire solutions and extend the results of Xu et al. \cite{XLL1} from the setting of $\mathbb{C}^2$ to the more general space $\mathbb{C}^m$. In addition, several examples are presented to demonstrate the effectiveness and sharpness of the main results.
toXiv_bot_toot

EU Member States are deprioritising 'non-wires' solutions or non-fossil flexibility as alternatives for network expansion.
https://www.consilium.europa.eu/en/press/press-releases/20…

Without yet applying power, I have a suspect, and a new quest to find a part only exotic in this century. My hypothesis is when the signal clip on the "overdrive" phono socket came free, it could dangle touching a ground. Unreasonable because there shouldn't be any voltage on input wires, but that dangling clip could have touched anywhere, and falling over in the car (with a thump) likely didn't help.
Now, a new quest for a part not costing more than the part itself. I might have one in a crate of audio junk bits...
Oh and I now have 4 extra 3A 30mm should there be need 😊

Seattle-based Brinc Drones, which makes 911 response drones, raised $125M led by Motorola Solutions, bringing its total funding to more than $280M (Todd Bishop/GeekWire)
https://www.geekwire.com/2026/motorola-leads-125m…

Motorola leads $125M round for Brinc, fueling 911 drone expansion amid U.S. import crackdown
Seattle-based 911 drone maker Brinc raised $125 million led by Motorola Solutions, at a valuation the company says has nearly doubled from a year ago. The funding will support expanded manufacturing and a new Seattle headquarters and factory later this year.

Quebec hydropower is now flowing to New York City—1.25 GW of clean electricity displacing fossil generation.
Meanwhile, Twelve launched America's first commercial e-jet fuel plant, turning CO2 and renewable power into synthetic jet fuel.
And China brought online a massive solar-battery-hydrogen complex to power industry with renewables.
Real infrastructure. Real progress. Today.
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Weekly Climate Solutions Digest
Welcome Everything here is about systems learning to work together at scale. Like the season’s long light, these links extend our reach, quiet but decisive, so that what once felt distant starts to feel close. Here is what moved this week. Top Climate Solutions Of The Week Progress showed

Following a blockbuster IPO earlier this month,
Elon Musk’s SpaceX experienced a rude awakening.
The rocket company’s shares have now been sliding for four consecutive days,
wiping out nearly all the gains the public offering had initially made.
Now the broader stock market is experiencing a similar and intensifying sell-off.
S&P 500 futures slid 1.6 percent on Tuesday,
while Nasdaq 100 futures dropped 2.8 percent, on track to wipe out over $1 trillio…

Tech Stocks Are Abruptly Collapsing
The global stock market is experiencing an intensifying sell-off, intensifying fears of a bursting AI bubble.

#goodmorning
I spent yesterday loosing myself in my IT setup and still don't really know if I'm following a good solution. But I've learned a bit about Forgejo...

So the Canadian government is cracking down on anti-semitism (CBC: #israel #palestine #canada #cdnpoli #canpoli

“Awake! for Morning in the Bowl of Night
Has flung the Stone that puts the Stars to Flight:        
And Lo! The Hunter of the East has caught                        
The Sultan’s Turret in a Noose of Light”
(Edward FitzGerald and the Rubšiyšt of Omar Khayyšm, 1st edition 1859)
#Poetry #Translation

There's a general feeling that Judges shouldn't be able to make sentencing decisions that deviate from guidelines, except for the circumstances where it *would* be appropriate. How to identify those circumstances is the tricky part.
AI maybe?