Tootfinder

CoLF Logic Programming as Infinitary Proof Exploration
Zhibo Chen (Carnegie Mellon University), Frank Pfenning (Carnegie Mellon University)
https://arxiv.org/abs/2510.12302 http…

CoLF Logic Programming as Infinitary Proof Exploration
Logical Frameworks such as Automath [de Bruijn, 1968] or LF [Harper et al., 1993] were originally conceived as metalanguages for the specification of foundationally uncommitted deductive systems, yielding generic proof checkers. Their high level of abstraction was soon exploited to also express algorithms over deductive systems such as theorem provers, type-checkers, evaluators, compilers, proof transformers, etc. in the paradigm of computation-as-proof-construction. This has been realized in l…

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[…] Paradoxically, the more a population grew, the more precious it became, as it offered a supply of cheap labour, and by lowering costs allowed a greater expansion of production and trade. In this infinitely open labour market, the ‘fundamental price’, which for Turgot meant a subsistence level for workers, and the price determined by supply and demand ended up as the same thing. A country was all the more commercially competitive for having at its disposal the virtual wealth that a large population represented.
Confinement was therefore a clumsy error, and an economic one at that: there was no sense in trying to suppress poverty by taking it out of the economic circuit and providing for a poor population by charitable means. To do that was merely to hide poverty, and suppress an important section of the population, which was always a given wealth. Rather than helping the poor escape their provisionally indigent situation, charity condemned them to it, and dangerously so, by putting a brake on the labour market in a period of crisis. What was required was to palliate the high cost of products with cheaper labour, and to make up for their scarcity by a new industrial and agricultural effort. The only reasonable remedy was to reinsert the population in the circuit of production, being sure to place labour in areas where manpower was most scarce. The use of paupers, vagabonds, exiles and émigrés of any description was one of the secrets of wealth in the competition between nations. […]
Confinement was to be criticised because of the effects it had on the labour market, but also because like all other traditional forms of charity, it constituted a dangerous form of finance. As had been the case in the Middle Ages, the classical era had constantly attempted to look after the needs of the poor by a system of foundations. This implied that a section of the land capital and revenues were out of circulation. In a definitive manner too, as the concern was to avoid the commercialisation of assistance to the poor, so judicial measures had been taken to ensure that this wealth never went back into circulation. But as time passed, their usefulness diminished: the economic situation changed, and so did the nature of poverty.
«Society does not always have the same needs. The nature and distribution of property, the divisions between the different orders of the people, opinions, customs, the occupations of the majority of the population, the climate itself, diseases and all the other accidents of human life are in constant change. New needs come into being, and old ones disappear.» [Turgot, Encyclopédie]
The definitive character of a foundation was in contradiction with the variable and changing nature of the accidental needs to which it was designed to respond. The wealth that it immobilised was never put back into circulation, but more wealth was to be created as new needs appeared. The result was that the proportion of funds and revenues removed from circulation constantly increased, while that of production fell in consequence. The only possible result was increased poverty, and a need for more foundations. The process could continue indefinitely, and the fear was that one day ‘the ever increasing number of foundations might absorb all private funds and all private property’. When closely examined, classical forms of assistance were a cause of poverty, bringing a progressive immobilisation that was like the slow death of productive wealth:
«If all the men who have ever lived had been given a tomb, sooner or later some of those sterile monuments would have been dug up in order to find land to cultivate, and it would have become necessary to stir the ashes of the dead in order to feed the living.» [Turgot, Lettre Š Trudaine sur le Limousin]
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(Michel Foucault, History of Madness)

I think we can actually prove that this constraint is the *only* constraint that can preserve freedom:
1. There will exist actors in a system who will wish to take advantage of others. Evolution drives survival and one strategy for increasing survival in an altruistic society is to become a parasite.
2. Expecting exploitative dynamics, a system needs to have a set of rules to manage exploitation.
3. If the set of rules is static it will lack the requisite variety necessary to manage the infinite possible behavior of humans so the system will fail.
4. If the system is dynamic then it must have a rule set about how it's own rules are updated. This would make the system recursive, which makes the system at least as complex as mathematics. Any system at least as complex as mathematics is necessarily either incomplete or inconsistent (Gödel's incompleteness theorem). If the system is incomplete, then constraints can be evaded which then allow a malicious agent to seize control of the system and update the rules for their own benefit. If constraints are incomplete, then a malicious agent can take advantage of others within the system.
5. Therefore, no social system can possibly protect freedom unless there exists a single metasystemic constraint (that the system must be optional) allowing for the system to be abandoned when compromised.
Oh, you might say, but this just means you have to infinitely abandon systems. Sure, but there's an evolutionary advantage to cooperation so there's evolutionary pressure to *not* be a malicious actor. So a malicious actor being able to compromise the whole system is likely to be a much more rare event. Compromising a system is a lot of work, so the first thing a malicious actor would want to do is preserve that work. They would want to lock you in. The most important objective to a malicious actor compromising a system would be to violate that metasystemic constraint, or all of their work goes out the window when everyone leaves.
And now you understand why borders exist, why fascists are obsessed with maintaining categories like gender, race, ethnicity, etc. This is why even Democrats like Newsom are on board with putting houseless people in concentration camps. And this is why the most important thing anarchists promote is the ability to choose not to be part of any of that.

Worrying new simulations show that a solar storm on par with the infamous Carrington Event
could potentially wipe out every single satellite orbiting our planet,
leaving us in a precarious and expensive predicament.
And experts say such a powerful solar storm is inevitable and will hit our planet sooner or later.
On Sept. 1, 1859, British astronomer Richard Carrington observed a brilliant flash of light coming from a gigantic sunspot that was about the same size as J…

The next solar superstorm could wipe out 'all our satellites,' new simulations reveal
New ESA simulations suggest that a solar storm on par with the 1859 Carrington Event could wreak havoc on Earth-orbiting satellites — and it is a question of "when," not "if" this will happen, experts say.

Black Holes with Accretion Disks as High-Energy Particle Colliders
Delilah E. A. Gates
https://arxiv.org/abs/2509.19435 https://arxiv.org/pdf/2509.19435

Black Holes with Accretion Disks as High-Energy Particle Colliders
In principle, rapidly rotating black holes (BHs) with accretion disks -- either prograde or retrograde -- could naturally act as high-energy particle colliders (HEPCs) because particles falling in from infinity that collide with particles in the disk near the BH horizon can exhibit center-of-mass (CM) energies beyond the capabilities of terrestrial instruments. However, we show that scattering can moderate the CM energy of near-horizon collisions. We find that rapidly rotating BHs with prograde…

Sharpness of the phase transition for constrained-degree percolation
Ivailo Hartarsky, Roger W. C. Silva
https://arxiv.org/abs/2509.16162 https://arxiv.org…

Sharpness of the phase transition for constrained-degree percolation
We consider constrained-degree percolation on the hypercubic lattice. Initially, all edges are closed, and each edge independently attempts to open at a uniformly distributed random time; the attempt succeeds if, at that instant, both end-vertices have degrees strictly less than a prescribed parameter. The absence of the FKG inequality and the finite energy property, as well as the infinite range of dependency, make the rigorous analysis of the model particularly challenging. In this work, we s…

Terahertz Quasi-BIC Metasurfaces for Ultra-Sensitive Biosensing and High-Speed Wireless Communications
Islam I. Abdulaal, Abdelrahman W. A. Elsayed, Omar A. M. Abdelraouf
https://arxiv.org/abs/2510.00357

Terahertz Quasi-BIC Metasurfaces for Ultra-Sensitive Biosensing and High-Speed Wireless Communications
Bound states in the continuum (BICs) have emerged as a revolutionary paradigm in terahertz (THz) photonics, enabling metasurfaces with theoretically infinite quality factors (Q-factors) and unprecedented light-matter control. This review synthesizes a decade of progress in THz-BIC research, tracing the evolution from foundational symmetry-protected designs to application-optimized quasi-BICs. We dissect multipolar origins, topological robustness, and symmetry-breaking strategies underpinning hi…