Tootfinder

Hidden Higher-Order Vulnerabilities in Simplicial Complexes Revealed by Branch-Consistent Functional Robustness
Kaiming Luo
https://arxiv.org/abs/2603.24286 https://arxiv.org/pdf/2603.24286 https://arxiv.org/html/2603.24286
arXiv:2603.24286v1 Announce Type: new
Abstract: Robustness of higher-order networks is often quantified by the instantaneous smallest positive eigenvalue of the Hodge $1$-Laplacian under simplex deletion. We show that this observable is generically ill-defined: along a deletion trajectory, eigenvalue branches can switch, so the quantity being monitored may correspond to different nonharmonic modes at different steps. The primary issue is therefore definitional rather than algorithmic. We resolve it by fixing the first nonharmonic branch of the intact complex and following that same branch throughout the damage process, which defines a branch-consistent functional robustness. Triangle sensitivities then follow directly from first-order perturbation theory, making the resulting mode-sensitive deletion protocol a consequence of the observable itself rather than an independent heuristic. Across synthetic and empirical clique complexes, removing only a small fraction of triangles is sufficient to drive the tracked mode to collapse, while graph-level observables remain unchanged because the $1$-skeleton is exactly preserved. The same framework also reveals bridge-like localization of functionally critical simplices and provides a compact predictor of dynamical timescales.
toXiv_bot_toot

In the time I've been offline, I've been doing a lot and feeling a lot more mentally healthy. I've been exploring nomadnet a bit, looking at reticulum. I'm definitely going to go back to my break and being online much less regularly.
I actually totally forgot about the anniversary of the shooting, which is the first time that's happened since... uh... the shooting, I think.
I've definitely realized that, on some level, I've definitely used Mastodon (and formerly Twitter) as a coping mechanism, often in order to deal with the stressful things that I've found out about on Mastodon or Twitter.
But, again, none of those things really change our core job: build community. And that's part of what I've been neglecting, and what I can focus on more when I'm not spending as much time talking to people all over the world indirectly. Like, I can just chat directly with folks and talk about this shit.
Yeah, I do think there's value in this community. I don't think it's really screaming into the void (at least, not most of the time). But I know that I need the balance to be way farther on the side of direct engagement with comrades doing and building.
So that's what I'm gonna go back to. I feel as though it's a good sign that with all the writing about getting shot that I've been doing, and all the thinking about that, that the actual anniversary of the shooting I'm actually just thinking about bread.
And that seems like a good note to leave on. I'm gonna go back to some hacker shit.