Tootfinder

Fundamental and homogeneous bases of Hopf algebras built from nonsymmetric operads
Samuele Giraudo
https://arxiv.org/abs/2507.02165 https://

Fundamental and homogeneous bases of Hopf algebras built from nonsymmetric operads
We introduce new partial order structures on the underlying sets of free nonsymmetric operads. These posets involve decorated ordered rooted trees, and their terminal intervals are lattices. These lattices are not graded, not self-dual, and not semi-distributive, but they are EL-shellable, and their Mbius functions take values in $\{-1, 0, 1\}$. They admit sublattices on the families of $m$-Fuss-Catalan objects and of forests of trees. This latter order structure is used to construct two new ba…

I have my share of issues with Parkrose Permaculture, but she has a lot of things I do strongly agree with. I can't stress enough that you never dehumanize your enemies. You can respond appropriately to violence. You can defend yourself from them by any means necessary. But you do not dehumanize them. You always limit your response to the minimum necessary to defend yourself.
There are a number of former Nazi skins who became antifascists after realizing they were wrong. Those folks tend to be some of the most dedicated because they feel a debt, and some of the most knowledgeable because they were there. Coming out of these types of cults, police included, is hard and takes time. A lot of us don't have the ability to work with them. But some do.
By repeatedly humanizing your opponent, you can break some of them. The #Seattle Police Department was not defunded but saw a massive reduction in numbers because their morale was destroyed. Some people will never change. Some people are broken and feel like they need the power. But if you change one person's mind, even give them something to think about, it's a crack. If even one cop quits, that's one less trained gun pointed at you in the future.
The 18 year old marines and federalized national guard troops out there are literally kids. A lot of them came from poor communities. They are being used in a way they haven't been trained to do, doing things they (should) have been told are not legal. They joined to get out of poverty, to go to college, or to "defend the American people" (regardless of how misguided that is). Few, if any, of them joined to abuse people. They will be especially open to persuasion.
Remind those troops that they are carrying out illegal orders, that they are being called on to violate their oath to protect the constitution, that they are suppressing the free speech of the fellow Americans they swore to defend. Remind them that the people they could be illegally arresting now are just like their parents, their neighbors, their families, the friends who didn't join. Remind them that this is the first step. They will be called on to kill Americans if they let this keep going.
Remind them ICE sleeps in hotels while they sleep on the ground. Remind them that their drunk and incompetent leadership thinks of them as disposable tools. Remind them that some of these people are out protesting *for them* against cuts to the VA and other services. Remind them that the people they're defending refuse to make college free so they can recruit from poor schools. Remind them that they will always be welcome when they're ready to join the side of freedom and justice.
When you dehumanize your enemies, you unify them. When you humanize your enemies, you can divide them. There is no weapon available to us right now so powerful as compassion.
https://youtu.be/YtWOYUDMsBw

The liberal obsession with optics serves the right and persuades no one. There is literally an active ethnic cleansing happening in the US right now, and the only thing that matters is making that as hard as possible to carry out.
Anarchists destroying intelligence assets saves lives. Every escooter thrown at a cop car is one less escort for a goon too afraid to kidnap random brown people without being flanked by a branch full of bad apples. Spray paint is not violence. Vandalism is not violence. Community self defense in all forms is legitimate.
Make no mistake, these raids are about changing demographics. Demographic trends have been shifting blue for a long time, and the right has, for a long time, been blaming "white replacement." Conspiracy theory aside, Democrats have also been relying on the growth of black and brown voters as a block. The nuances of whiteness as an identity are lost on the current administration and their supporters. They see that "white people will be a minority by 2050" and equate that with the "end of Western Civilization."
The only way to "save Western Civilization" is to change those demographics. Forced birth and forced removal are two sides of the same white nationalist objective. Of course they can't have due process, because they need to be able to kidnap anyone who they see as a threat to their demographic future.
They don't care about optics. The plan is to murder away any threat and flood everyone else with propaganda. There is no mythical middle. There's no one unconvinced. They know this, but they win when democrats buy that myth and save the police the work of policing the protests.
If your protest is 90% "peaceful," they'll take pictures of the 10% that isn't. If it's 99% peaceful, they'll shoot rubber bullets and teargas until someone throws a brick and take 100 pictures from a dozen angles. If its 100% "peaceful" and no one can be provoked, they'll generate pictures with AI or photoshop like they did during the George Floyd uprising and the pictures from the CHOP/CHAZ. Do you have literally no memory?
#USPol #FiftyFiftyOne #50501movenent #resistance #NoKingsDay #NoKingsDayOfAction

Extending Congruences for the number of smallest parts in overpartitions with smallest part even
Robson da Silva
https://arxiv.org/abs/2508.03971 https://a…

Extending Congruences for the number of smallest parts in overpartitions with smallest part even
In a recent paper, Jin, Liu, and Xia \cite{JLX} presented some modulo 4 congruences for $\overline{spt2}(n)$, the number of smallest parts in the overpartitions of $n$ where the smallest part is even and is not overlined. In this paper, we extend the list of such congruences in two directions. First, we prove some new individual congruences for $\overline{spt2}(n)$. Then, we provide a number of infinite families of Ramanujan-like congruences satisfied by $\overline{spt2}(n)$.