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How to solve cubic and quartic equations II: cubics

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Technical Difficulties

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One thing I find striking in the discourse between AI 2040 and its detractors is that the two seem to be locked in to totally incompatible worldviews of how fast and how much of a big deal AI progress is: * In AI 2040, every scenario sees superintelligence of some kind emerging by 2040, unless a herculean effort is made to completely stop it * Detractors say things like "AI 2040 is naive about human coordination ability and a threat to freedom", but don't seem to see any naivety in assuming that the ASI transition will just go well by default, don't seem to see ASI itself as a massive power concentrator risk, and don't seem to feel fear of humanity's "hard power" dropping to zero if ASIs can do literally every task better than we can. This stance makes total sense in a "AI is normal technology" world, zero sense in a world where superintelligence is possible by 2030 and almost guaranteed by 2040 I think my beliefs are: - If I was confident that (present-day-style) AI is normal technology, I would be in the detractor camp - If I was confident that superintelligence is coming in 2030 by default, I would be closer to the AI 2040 camp - it's naive, but every other option is naive squared? But my problem is that I feel great uncertainty and have no idea which of the two worlds (or some other third thing) we're living in? Hence why I continue to be open-minded about slowdowns/pauses, but also I feel very uncomfortable with the "open source bad, the good outcome is the one where our guys have controlling global dominance" push coming from some major AI companies and intellectuals - in a "normal" world that's the sort of thing that triggers every political alarm bell at the same time. A big reason why I have been advocating and trying my best to support the d/acc platform (rapid up-skilling in formal verification, cryptography, secure and open hardware, pandemic resistance and other defensive biotech, food and basic resource security, public epistemics, non-power-concentrating versions of physical security) is that these things are clearly worth doing in both worlds. The 2040 plan is already much more open source friendly (even mandating it! yay). It also includes "mutually assured compute destruction" ideas which (if they work) effectively give one of 2-5 actors the ability to trigger a global compute winter - as opposed to giving 1-5 actors the ability to selectively disenfranchise people they consider baddies while exempting themselves. This is also a big improvement. So I can see the earnest attempts to improve along the dimensions detractors criticize on ("does this concentrate power in big AI labs and superpower governments?"), and I appreciate this. I think many people don't appreciate enough the differences between different "kinds" of pause buttons, and how some concentrate power far more than others. Probably we can think harder and improve even more here. But on the "slowdown/pause or not" topic, there isn't a magic "escape the tradeoff" button. The Hansonian in me says: the winning deal is a deal which, from the perspective of both sides' present-day beliefs and knowledge, both sides would accept, though for different reasons. If the crux is AI progress speed, then identify a set of pre-agreed triggers for "okay, serious shit is happening" [super-pandemics? >25% unemployment? something involving slaughterbots?], and pre-agree that we become much more open-minded to the slowdown or pause thing if enough triggers come to pass within some timeframe. 2040 detractors (who clearly implicitly think that we'll see amazing speedup of progress from AI but think that what I call the "serious shit" category is overhyped) will accept expecting that the triggers don't come to pass, and AI worriers will accept expecting that they will. Pre-agreeing on the specific triggers means that once the triggers either hit or don't hit, there is stronger legitimacy around the idea that one side's worldview turned out more correct and we should be more inclined toward their program. If I were @elonmusk (or zuck, or...) I would re-tool twitter much more heavily into being a platform for helping to identify and make these kinds of grand win-win deals, so that we can bypass big-country governments and big-company CEOs and big nonprofit intellectuals and give more people a voice in the discussion. It's possibly one of the best things that social media _could_ do for humanity if it wanted to. But again, maybe this is also naive. Actually, probably it's naive. But currently, I see zero plans for how to deal with an ASI transition that are not naive. Perhaps humanity is stuck with a choice between naive and naive squared (or maybe even naive squared and naive cubed), so I feel inclined to cut some slack to people who are trying.

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🇪🇺 The EU is now for the 6th time trying to force Chat Control through which lets them scan ALL your private messages, photos and emails without a warrant Implictly showing the EU is not democratic and not about what the people of Europe want, because once a law is rejected, you just re-submit it un

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And ... we have a winner! My method when writing the post in 2024 was: I wrote it in Chinese, used qwen2.5 locally to translate it to English, then manually fixed all the bugs in the translation. Notice that the stylistic hints that his AI picked up on were intellectual habits and style of math and algorithm explanation, which bypassed my obfuscation strategy (which only covered prose) completely.

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The Extremely Lean Chain

Special thanks to Emile, Potuz, Anders Elowsson for initial feedback and review. The goal of this post will be to show how the Ethereum consensus chain, in the context of “Lean” upgrades (single-slot finality, recursive…

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There have recently been claims that AI text analysis will make online anonymity untenable. So let me cannibalize a piece of my own anonymity to do an experiment. At some point this decade, I wrote a published document of medium importance to Ethereum - I estimate ~200 to 2000 documents in Ethereum

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This year, the EF is decreasing its budget by roughly 40%, which entails some difficult decisions. The goal of the decreases was set out in the Treasury Management Policy last year: the EF is transitioning into being a long-term-oriented endowment-based organization, shifting from its pre-2026 average of spending ~15% of its remaining funds each year, toward a post-2030 target of ~5% per year. Often, when an organization goes through something like this, people try to pretend that nothing of great value was lost, that it is an efficiency increase, that the only people cut are unproductive dead weight, and everyone else stopped partying, studied the blade, entered cracked S-tier beast mode, and this was sufficient to make up for the downside. I will not try to pretend this. I respect my EF colleagues far too much to pretend that there was not much that is lost. They are brilliant people. They are dedicated engineers of whom some have worked on the Ethereum protocol for nearly a decade. They have brought a bright light to the Ethereum ecosystem with their code, their words, their warmth as human beings and their actions. My dearest hope is that they find a path that brings them fulfillment and happiness whether inside Ethereum or outside. Hopefully many will be able to bring their excellent talents and mindset to the wider Ethereum ecosystem, or the even wider CROPS world. Instead, I will try to explain what *are* some of the grand sacrifices being made. The Ethereum Strawmap is no small thing. It is an extremely ambitious undertaking seeking to replace and augment almost every part of the protocol - consensus, proofs, privacy, account model, state, and more. This is the third iteration of Ethereum, in the same way that the Merge was the second, even if the shipping style is less Big Bang and more one-piece-at-a-time. On top of this, the EF is increasing its role in the Access Layer. We are not compromising on Ethereum being a Deeply Impressive protocol, something worthy of its place in a world with quantum computing, rockets to Mars and powerful biotech and AI, and capable of meeting the challenges that this era will bring. Some of the deficit will be recovered through more work happening outside the EF. But not all. So what are the grand sacrifices that will enable a leaner effort to accomplish all of this? I will give a few examples (though far from an exhaustive list): * The multi-client model will shift in the direction of multiple clients existing less for _redundancy_, and more for _specialization_. Up to this point, redundancy has been the main security strategy: if one client has a bug, if it has less than 33%, the chain keeps going and does not even stop finalizing. We are increasingly exploring moving more pieces of the protocol to a different security strategy: AI-assisted formal verification. Some smaller pieces of Ethereum (eg. BLS libraries) have worked this way already for a long time. But soon many more parts of Ethereum will likely function on this model. This may greatly reduce resource requirements of shipping a large number of EIPs. The resources saved by client teams can ideally instead be used to better serve different specialized user needs, including EF Access Layer goals. * PSE (Privacy and Scaling Explorations) is winding down as a unit, and its underlying task (working on ZKP and related tech to support privacy and scaling) is shifting from an "exploration" strategy to a "build specific things we know are important" strategy, which requires less resources. * Devcon will likely over time become smaller-scale, somewhat more spartan, much lower-deficit than previous years, in addition to other changes in vision in line with the Mandate. * Fewer beyond-Ethereum megaprojects coming from EF. As I announced earlier this year, I am taking on some of the responsibility of doing projects in this category that I consider valuable with my personal funds. * EF institutional work is reducing in scope, specializing more specifically on creating replicable test cases of highly CROPS-friendly deployments, even if at smaller scale. These do not explain all departures; in some cases they do not explain departures at all and rather explain _reduced need for new spending_. But they are a large part of the strategy at play. In the longer term, I personally favor a "soft lean-and-done" approach to Ethereum: once the Strawmap is completed, generally stick to security fixes and small high-value changes, and have a much higher bar for considering new feature additions to the protocol. This allows Ethereum to remain capture-resistant without demanding very large budgets. Learn less from multimillion-line-of-code behemoth projects, more from bitcoin. The past years have been a challenging era for Ethereum. However, the ecosystem is adapting, both inside the EF and outside, and I am confident that Ethereum is very well-positioned to succeed and thrive.

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There have recently been claims that AI text analysis will make online anonymity untenable. So let me cannibalize a piece of my own anonymity to do an experiment. At some point this decade, I wrote a published document of medium importance to Ethereum - I estimate ~200 to 2000 documents in Ethereum are as or more important - not under my name. Find it. (I genuinely have no idea how easy or hard this is, will be very curious what comes out)

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Building index-tracking assets on top of options instead of debt

Special thanks to Vladimir Novakovski, Curve developers, and others for feedback and review. Suppose that you have some ticker T, which represents a price index denominated in ETH. For example, T could equal the USD/ETH…

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In an ideal world all software and hardware would have "nutrition labels" that provide a full list of trust dependencies - what math and which actors' honest behavior (and on what time scale) the system is relying on to provide its core functionality and implied guarantees. https://x.com/Fricoben/status/2059567691103371382

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Some of my perspective on where the @ethereumfndn is going. First of all, this is only my own view. The board is not just me, and I have no extra special powers on the board that the other board members do not. @aerugoettinea is the one executing much of this transition. My input has been largely on technical questions. The board is in the process of expanding, and my own power within the org will continue to decrease, which is honestly what I want. The 2025 era brought many important improvements to EF and its ability to execute. Many issues were resolved, and EF continues to benefit from its improved efficiency and greater focus on concrete goals to this day. And so with those problems resolved, early this year, the largest remaining hole that I perceived was something different nagging at me: I would regularly spot people saying things like "vitalik says these beautiful things about ethereum needing to be decentralized, and have privacy, and be a sanctuary technology, but why do the EF's actions not reflect that?" Now, you may have been hearing something different. You may not have been sensing a feeling of crisis at all, and maybe were hearing people saying that finally we were taking execution and BD seriously and the main task for us is to keep going that way and be even better and faster. Then probably there is genuine difference between you and me, in what kinds of criticism I take most seriously, and what kinds of critics through their criticism are most able to make me feel pain. As an analogy, let's briefly switch over to a different domain. One belief you can have about Google is that it is a success story, and has brought a lot of good to humanity in organizing the world's information. Another belief you can have about Google is that they had a beautiful idealistic beginning, but at some point the corruption of mainstream corporate attitudes seeped in, and they slowly bit by bit completely abandoned the "don't be evil" slogan. My belief on Google specifically is probably somewhere between the two. BUT, if you had taken me back in time to ~2008, and offered me a button to press to make Google one or two standard deviations more "dogmatic", eg. give Richard Stallman permanent veto power over some key policies, I would immediately press it. Why? Because a choice for one company is not a choice for the world, or even one country. Google existed and exists in the context of a technology industry generally drifting away from early idealistic don't-be-evil roots and toward greed for financial gain, totalizing visions of accelerated superintelligence, infiltration by sociopaths, and craven capitulation to (or worse, active participation in) government pressure for ideological control, surveillance and war. And so *one company* doing something different, positioning itself to be what George Bernard Shaw calls the Unreasonable Man, resisting the trend of the times, would have been better for freedom, balance of power and stability of society as a whole, than *all* large companies bending to dominant trends. This is a part of my version of pluralism. This line of thinking is not just mine, but I also is not too far off from what Aya and others had in mind with the Mandate. Now how does this all get to the role of the EF? EF is not a "center of Ethereum", rather EF is "one node, with a defined purpose, alongside other nodes". We've always said that the EF should be the latter, but many in the Ethereum ecosystem (and even within the EF) wanted us to be the former. Now, we are taking action to ensure that we will be the latter. This is particularly important because EF is a limited organization, with limited resources and limited organizational capacity. The EF has only ~0.16% of all ETH (less than many other individual ETH holders), whereas among other blockchains it's common for "the central foundation" to have 10-50%. Fiscally, the EF was originally designed to fulfill a limited work scope defined in the token sale docs and other pre-launch materials (building the chain software; getting through Frontier, Homestead, Metropolis, Serenity), which was fully completed in 2022; it was not designed to be an eternal steward. And so today, the EF is choosing to use its remaining resources to pursue longevity over breadth (yes, this means we sell less ETH). The EF focuses *specifically* on those activities critical to the success of ethereum as a censorship/capture-resistant, open, private and secure system, that would not happen otherwise. This means making hard choices, and in some cases even activities that we highly approve of and people that we highly respect becoming outside of the EF. People of great technical talent, public respect and even alignment with the mission and CROPS being outside of the EF is in fact necessary if we want important tasks to be able to attract outside capital. This also means the EF taking opinionated stands culturally. This is all intended in cooperation with all...

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vitalik.eth.limo

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GitHub - Verified-zkEVM/ArkLib: Formally Verified Arguments of Knowledge in Lean

Formally Verified Arguments of Knowledge in Lean. Contribute to Verified-zkEVM/ArkLib development by creating an account on GitHub.

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Keyed nonces are not just a way to add stronger in-protocol support for privacy solutions. They are also a potential first foray into a new state scaling strategy for Ethereum: create new types of storage that are more optimized for handling categories of use cases that we care about, with restrictions on their use that make them usable at extreme scale while preserving the protocol's decentralization. Let's zoom in on this case (in-protocol nullifiers). Let's say we get to 2000 TPS of privacy-preserving transactions onchain, for eight years. Then we get 2^11 tx/sec * 2^25 sec/year * 2^3 years = 2^39 [ie. 500 billion] nullifiers stored onchain (the challenge with nullifiers is that they are fundamentally not possible to prune). It's actually far easier to keep Ethereum decentralized if we have 500 billion nullifiers onchain in a dedicated nullifier store, than if we just let them grow in the current state. The reason is that the more restrictive structure of nullifiers (only used to check validity, and we can require the nullifier ID to be explicitly specified in the tx) enables more decentralized ways of handling them. This includes: * Sharding: each node (incl builders) can hold a small percentage of nullifiers, and make sure to have a connection to an honest peer in each other shard * Bloom filters: see this somewhat wacky idea here for reducing the VOPS requirement for nullifiers to ~8 bits per nullifier: https://docs.fileverse.io/d/020001fc0012#k=UT7Btd6tyqHgOj47t-TX06F8D6OpcpM_2PKdf7s4tGE Both techniques are not possible to use for dynamically accessible state. And so builders would have to download the full 16 TB to become viable (not just optimal, viable!), and privacy protocol users would not be able to use FOCIL without providing a Merkle branch proving that their nullifier is unspent, and there would be very few nodes capable of providing such a branch... Zooming back out, the moral of the story is that fully dynamic state is much harder to handle at extreme scale (tens to hundreds of TB) than state that is more controlled and restricted in how it can be used. And so if we can move the majority of usage into these more specialized forms of state (which we can make much cheaper in terms of gas), then we can keep Ethereum decentralized, and highly scalable, and keep the fully dynamic state available for applications (eg. defi) that really need its full functionality.

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