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A note concerning the ($S_3$) condition for roots in mixed characteristic
Prashanth Sridhar
https://arxiv.org/abs/2506.09072 https://…

A note concerning the ($S_3$) condition for roots in mixed characteristic
The goal of this note is to record the following curious fact: let $S$ be an unramified regular local ring of mixed characteristic $p>0$. Let $L$ denote the quotient field of $S$ and $K=L(ω)$ with $ω^p\in L$. Let $R$ denote the integral closure of $S$ in $K$. Then $R$ is Cohen-Macaulay if and only if $R$ satisfies Serre's condition $(S_3)$, i.e., the obstruction to the Cohen-Macaulayness of $R$ is in codimension three.

This https://arxiv.org/abs/2501.16144 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Survey of the Holroyd-Talbot Conjecture
A family of sets is intersecting if every pair of its members has an element in common. Such a family of sets is called a star if some element is in every set of the family. Given a graph $G$, let $μ(G)$ denote the size of the smallest maximal independent set of $G$. In 2005, Holroyd and Talbot conjectured the following generalization of the Erdős-Ko-Rado Theorem: for $1\le r\le μ(G)/2$, there is a maximum size intersecting family of independent $r$-sets that is a star. In this paper we pres…

The Trump administration deported a 31-year-old Salvadoran man minutes after a federal appeals court barred his removal while his case proceeded, the government admitted in a court filing this week.
In its filing, the government denied that it had violated the order from the U.S. Court of Appeals for the Second Circuit, in New York, instead blaming “a confluence of administrative errors.”
The government had previously given the court what the judges called “express assurance” that…

Trump Officials Deported Another Man Despite Court Order
A federal appeals panel ordered officials not to deport a 31-year-old to El Salvador. Minutes later, it happened anyway. The government blamed “administrative errors.”

Battery electric vehicles had a market share of 18% last month in Germany; sales 45% higher than in May 2024.
China's BYD up 824%, easily surpassing Tesla (down 36%), but still only 4% share in Germany's BEV market.
https://www.

When was the first middle-finger used to denote contempt in a (mainstream) film? I don't know but there is an instance of it in Sergio Leone's 1971 Giù la testa (Duck, You Sucker / A Fistful of Dynamite).
This was perpetrated by Rod Steiger. In this film he and James Coburn also make a solid case that Keanu Reeves' accent in Bram Stoker's Dracula was not even close to being the worst in film history.

I spend $100 a month on Bandcamp instead of #11.99 a month on Spotify because I support artists.
#BandcampFriday

Omfg, as much as I have mixed feelings about setting up ecommerce stores of any kind, Freewebstore is another level of nightmare.
Simulated chatbot "conversations" that make onboarding / offboarding annoyingly lengthy. GIVE ME OLD-FASHIONED FORMS GOD DAMMIT.
UX that treats me like a toddler while trying way too hard to upgrade me to a paid plan.
Oh, and of course. AI. AI this, AI that 😓 😡
Never, never, never again.

I've been working on a full calendar app upgrade to the Discordian date widget I made years ago for Android. It's nearly ready for release, just got a bug or three to fix first.
#discordianism #discordiancalendar

I read "Then I Am Myself the World: What Consciousness Is and How to Expand It" by Christof Koch.
Interesting book which spends like 8 or 9 chapters detailing all the experiments which prove beyond much doubt that consciousness, and self awareness, is a thing done by a brain.
It describes how perception is a construction of a description, has a chapter called "computational mind"
And then spends the last two chapters describing why he thinks the mind can't be computed, because drugs have made him think experience is some kind of magic associated with highly interconnected causal structures.
Apparently, he thinks, once things become interconnected enough they become able to cause things independently of the physics running those connections.
Which is crazy, obviously. There's nothing causal in direct connections between neurons that isn't equally causal in modeled connections between virtual neurons.
All his evidence in the book from neural MRI scans to the effects of psychedelic drugs and symptoms of strokes and disease point to the brain simulating a virtual reality which is the basis of perception.
That simulated world in which we live is full of colour and shape and sounds and emotions and millions of mental constructs that are built to be correlated by the senses with the outside world, but are not equal to the world itself. We live in a dream constructed to correlate with reality.
But then instead of taking the next step: That consciousness itself is a property of a simulated being inside that mental model of the universe, a property which the brain simulates and applies to the virtual self that's doing the experiencing inside that model, he jumps towards some magic implying pan-psychism or that sufficiently interconnected networks become causally self-complete for some reason nobody can fathom.
Sure, colour and shape and emotions are all made up by the brain but experience can't be! For some reason.
You see in truth dualism is false, in that there is no spirit realm in which ghosts animate the matter of the body somehow.
Yet also, dualism is true, in that there is a simulated mental reality which we live in, computed by the brain in which all perception and experience are created, which is related-to but separate-from the unfolding complicated dance of energy that is the universe our bodies interact with.
People take some DMT trip, and the model of the universe emulated by their brain collapses and breaks. Their virtual simulated self inside their mind has these experiences of being one with the universe or the experience of feeling dead yet conscious or whatever, and these hippies think that the broken down simulated experience is real and reflects how consciousness is more fundamental than the atoms that make up the neurons in their brain.
Instead of realizing it shows them that their experienced universe is a simulacrum, they think they get a more direct experience of reality somehow. A consciousness more pure than any mere base atom.
"Then I am myself the world" is a great title. Everything you ever experience is created and simulated in your brain like a dream, the whole universe is inside your head. Even the fact of experience itself.
But that isn't the conclusion Koch reaches somehow, he just jumps from describing the evidence that this is so straight into ascribing super-causal magic consciousness to particular arrangements of atoms that integrated information theory suggest have high correlation, and thinks therefore conciousness is itself the entire universe.
Ah well, fun book. I like arguing in my head with authors that are wrong.
#reading #books #consciousness #thenIAmMyselfTheWorld