Tootfinder

Constructing crowded Hausdorff $P$-spaces in set theory without the axiom of choice
Eleftherios Tachtsis, Eliza Wajch
https://arxiv.org/abs/2510.11935 https://

Constructing crowded Hausdorff $P$-spaces in set theory without the axiom of choice
For an infinite set $X$, a closed under finite unions family $\mathcal{Z}$ with $[X]^{<ω}\subseteq\mathcal{Z}\subseteq\mathcal{P}(X)$, and any $\mathcal{A}\subseteq\mathcal{P}(X)$, the topology $τ_{\mathcal{A}}[\mathcal{Z}]=\{V\in\mathcal{A}: (\forall x\in V)(\exists z\in \mathcal{Z})(x\cap z=\emptyset \wedge \{y\in\mathcal{A}: x\subseteq y\subseteq X\setminus z\}\subseteq V)\}$ on $\mathcal{A}$ is investigated to give answers to the following open problem in various models of $\mathbf{ZF}$ o…

this is an incredibly funny sentence
"the thin films are fairly thin"
well what else would they be, robert? thick? if they were thick they'd be called thick films!!

I grew up with a lot of male cousins who loved watching sports. I understand that some people enjoy gambling for emotions, but I don't.
That's why I like books. Instead of gambling for feelings, a book takes my emotions on a journey, rips them to shreds in the middle in an unpredictable way, then grinds my feelings into a fine paste that they feed to their goat, which is sacrificed in a bloody feral ceremony whose carnage further defiles said emotional residue
Or you can …

I tried vibecoding again. Gave Opus 4.5 what I thought was a fairly hard assignment: generate a TypeScript compiler transform, using ts-patch, to let me mark functions with a magic decorator to make the compiler inline all calls to them.
It one-shot a basic implementation.
Getting to a higher-quality implementation required guidance from me – at times it had bad instincts – but when I gave guidance, it was competent at following it.
Overall, I'm spooked.

PCIe / FPGA folks: the ThunderScope people are chasing a strange issue where the TS PCIe card appears to work properly on AMD hosts (even with fairly long lossy channels like OCuLink cables or >1 foot riser ribbons) but is failing to train the link at all (i.e. not even coming up as gen1 x1) on Intel hosts.
Ideas on root cause / fixes? I haven't scoped the training yet, as soon as I get an updated unit in my lab I will.

I'm #ActuallyAutistic, and I love this woman deeply. I have been a huge fan of her music, especially my special interest in her song “Loin d’ici” (ESC Version) since May 14, 2016.
But now, watching Taylor Swift, Cœur de Pirate, and other artists slowly take her place feels like an unspoken farewell, like a song fading softly into the distance. It’s as if she herself is tell…

Wow. RIP Ace. One of the first to inspire me to play.
Still remember flipping through the TV channels randomly and stumbling on a KISS concert, being blown away by the guitar bursting into flames during a solo and rising out of his hands into the rafters.
#kiss #AceFrehley

ACE FREHLEY Dead At 74
Original KISS guitarist Ace Frehley has died at the age of 74. The news of his passing comes just hours after TMZ.com reported that the musician was hospitalized on life support after he suffered a brain bleed when he took a fall in his studio a couple weeks ago. Frehley's family issued the followin...

"Only nine countries doing well on municipal waste recycling, EU auditors say"
#EU #EuropeanUnion #Recycling

EU countries falling behind on municipal waste recycling, auditors say
The European Court of Auditors says a frail recycling industry, poor funding management and insufficient funds are all major obstacles.

Declared extinct in 2025: A look back at some of the species we lost https://news.mongabay.com/short-article/2025/12/declared-extinct-in-2025-a-look-back-at-some-of-the-species-weve-lost/

Declared extinct in 2025: A look back at some of the species we lost
Some species officially bid us farewell this year. They may have long been gone, but following more recent assessments, they’re now formally categorized as extinct on the IUCN Red List, considered the global authority on species’ conservation status. We may never see another individual of these species ever again. Or will we? Slender-billed curlew This […]

"Declared extinct in 2025: A look back at some of the species we lost"
#Animals #Nature

Declared extinct in 2025: A look back at some of the species we lost
Some species officially bid us farewell this year. They may have long been gone, but following more recent assessments, they’re now formally categorized as extinct on the IUCN Red List, considered the global authority on species’ conservation status. We may never see another individual of these species ever again. Or will we? Slender-billed curlew This […]