daily

2026-07-21
1

Claude Fable produced a counterexample to the Jacobian Conjecture

Hacker News · original → · 8/10 · AI: Claude model disproves Jacobian Conjecture
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy)…

hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0) Jul 20, 2026 · 2:19 AM UTC 1,470 4,306 34,942 22,048,203 wolframalpha.com/input?i=Det… jacobian determinant in wolfram alpha 19 33 1,219 722,413 wolframalpha.com/input?i=%28… wolframalpha.com/input?i=%28… evaluating at two of those points in wolfram alpha 12 20 821 537,078

2

As a kid in the 80s, I spent a lot of time in arcades. I recently decided that I wanted one in my home.

r/gaming · original → · 8/10 · Retro gaming: home arcade cabinet collection
[image →] The top picture is my living room. On the far left is the Iconic Arcade Street Fighter II cabinet. It currently has 20 total classic Capcom games across fighting, shmup, beat ’em up, and…
[image →]

The top picture is my living room. On the far left is the Iconic Arcade Street Fighter II cabinet. It currently has 20 total classic Capcom games across fighting, shmup, beat ’em up, and action genres- several versions of Street Fighter, Final Fight, GigaWing1/2, Bionic Commando, Progear, Knights of the Round, etc.

Then left to right in the main spread:

  • an Atari Centipede cabinet (with a trackball) that also has Millipede, Missile Command, Asteroids, Major Havoc, Crystal Castles, and 30ish original Atari 2600 games
  • a Return of the Jedi cabinet with the yoke style controls that also has the original Star Wars and Empire Strikes Back games in old-school vector graphics
  • a 2 player WWF Wrestlefest cabinet with two classic WWF wrestling games as well as Super Dodgeball , Acrobatic Dog Fight, and The Big Pro Wrestling
  • a Dragon’s Lair cabinet that also has DL2: Time Warp and Space Ace
  • a Mortal Kombat II cabinet that has all four 90s arcade versions of MK (1/2/3/Ultimate 3) as well as 10 other classics- Paperboy, Gauntlet, Rampage, Toobin’, Bubbles, Joust, Defender, Root Beer Tapper, Wizard of Wor, and Klax
  • an OG PacMan cabinet with five other variants- PacMan Plus, Pacmania, PacLand, Super PacMan, and Pac and Pal.
  • a Class of 81 cabinet featuring Ms. PacMan and Galaga with 10 other games- Dig Dug, Dig Dug II, Galaga 88, Galaxian, Mappy, Rally-X, Rolling Thunder, Rompers, Tower of Druaga, and King & Balloon (some of these are also on the PacMan cabinet).

Of course, like I do with everything I do in my life, it’s all gas, no brakes so there’s now overflow which has ended up in a bedroom, as can be seen in the bottom right image:

  • an NBA Jam cabinet with an updated Tournament Edition and a similar third game, NBA Hang Time, which they released after they lost access to the NBA Jam trademark
  • a Terminator 2 cabinet which only has the one game but allows for two player simultaneous play with the light guns
  • a Big Buck Hunter cabinet with five different game variations all based around the large shotgun light guns
  • a Fast & the Furious cabinet that has two different versions of this frantic racing game with driving style controls: steering wheel, gas and brake pedals, and gear shifter

YOLO!

edit: just to clarify, these are not original cabinets. These are reproductions. The Street Fighter cabinet (9/10 scale) is by Iconic Arcade and everything else (~3/4 scale) is by Arcade 1up/Basic Fun.

submitted by /u/vsully360
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3

Rescue near shipping lane off Hook Head

Wexford Local · original → · 7/10 · Local Wexford: maritime rescue near Hook Head
[image →]HOOK HEAD, Co. Wexford. By Dan Walsh Fethard RNLI assisted two people yesterday (Sunday) after their 17-foot boat broke down one nautical mile off Hook Head. The Irish Coast Guard requested…
[image →]
HOOK HEAD, Co. Wexford.

By Dan Walsh

Fethard RNLI assisted two people yesterday (Sunday) after their 17-foot boat broke down one nautical mile off Hook Head.

The Irish Coast Guard requested the volunteer crew to launch their inshore lifeboat at 11.32am from Slade and proceed to the scene.

Once on scene, the crew observed that while the two onboard were safe and well, the boat having broken down, could not make any safe onward progress.

Due to the vessel’s proximity to a shipping lane and with other vessels in the area, the helm made the decision that the safest course of action was to tow the boat with the two onboard, to the nearest port at Duncannon.

Speaking following the call out, Fethard RNLI Helm John Colfer said; “Due to the potential hazard with other vessels in the area and the nearby shipping lane, the tow was essential and we were happy to help the motorboaters out.

“We would encourage anyone planning a trip to sea to always go prepared. Always let someone know where you are going and when you are due back. Always wear a lifejacket or suitable flotation device for your activity and always carry a means of communication such a VHF radio or mobile phone in a waterproof pouch.

“If you get into difficulty or see someone else in trouble, call 999 or 112 and ask for the Coast Guard,” advised Mr Colfer.

4

Enniscorthy water supply restored

Wexford Local · original → · 7/10 · Local Wexford: infrastructure/utilities affecting residents
[image →] By Dan Walsh UPDATE, Monday 9 pm; Uisce Éireann has completed repairs to the burst watermain in Enniscorthy and surrounding areas. Water supply is now restoring to affected customers as…

By Dan Walsh

UPDATE, Monday 9 pm; Uisce Éireann has completed repairs to the burst watermain in Enniscorthy and surrounding areas. Water supply is now restoring to affected customers as the network refills.

Uisce Éireann crews are working to repair a major burst and restore water supply to customers in Enniscorthy and surrounding areas today (Monday) but repairs should be completed by the afternoon.

The burst occurred overnight, and crews are currently onsite excavating the damaged section of the network and assessing options to bypass the affected area in order to restore water to some customers as quickly as possible while repair works continue.

In a statement to WexfordLocal.com Padraig Lyng, Water Operations Manager, Wexford, said: “Our crews have been working since early this morning to repair the burst and restore water supply to customers as quickly as possible. We understand the inconvenience that a loss of water supply causes for homes, businesses and the wider community in Enniscorthy and surrounding areas, and we thank customers for their patience while these essential repairs are carried out.”

Repairs are currently expected to be completed later today. Typically, it can take two to three hours following repairs for normal water supply to be restored to all customers as the network recharges. Customers at the end of the network or on higher ground may experience a longer restoration time.

5

Human mathematicians are being outcounterexampled

Hacker News · original → · 7/10 · AI: LLMs disproving mathematical conjectures
It’s been an interesting few weeks for counterexamples. This post is basically my perspective of what has been going on in the world of formalization, AI tools and, in particular, counterexamples.…

It’s been an interesting few weeks for counterexamples. This post is basically my perspective of what has been going on in the world of formalization, AI tools and, in particular, counterexamples. Unit distance Two months ago today (20th May 2026), ChatGPT disproved Erdős’ Unit Distance conjecture in discrete geometry. This is now old news but I had to start somewhere. The announcement was accompanied with testimonies by human mathematicians, many of whom I knew and a few of whom I trusted, saying that they believed the argument (they had been given early access to it and had checked it). The basic structure of the proof is that a profound theorem in number theory due to Golod and Shafarevich from the 1960s could be used to construct a counterexample to the conjecture. It is now 9 years since I had a mid-life crisis, realised I no longer trusted many human mathematicians when it comes to technical details, discovered Lean, and started to argue that interactive theorem provers should play an important role in the future of mathematics. So of course my first question was “is the counterexample formalized in Lean”. The answer was “no”. But under a week later (26th May 2026), I got an email from Fields Medallist Mike Freedman. Mike is now the Chief Science Officer for Logical Intelligence, a company cofounded by Turing Award winner and “godfather of AI” Yan LeCun. Mike informed me that their system had autoformalized the entire ChatGPT-generated paper in Lean and could I take a look. I looked, and my post-doc Thomas Browning looked too. And indeed this was what Logical Intelligence had done: they had formalized precisely the statement that the profound theorem of number theory implied the Erdős counterexample. Breakthrough LLM-generated mathematics being formalized in real time. Interesting data point. Of course there is an elephant in the room here though, the profound theorem of number theory which takes 100+ pages to prove (it needs huge chunks of global class field theory, a theory developed at the beginning of the 20th century and for which there are still no short proofs; it is proving difficult to compress). In 2025 I had run a Clay Summer School with Richard Hill on the formalization of class field theory, and one year later we have nearly done the local case (it is the current PhD project of my student Edison Xie); the global case remained open, and indeed in 2025 formalizing global class field theory seemed like a fantasy. One month later, on June 26th 2026, my perception of what was possible again changed. Boris Alexeev announced on the Lean Zulip that he had steered ChatGPT to a complete formalization of the Erdős counterexample, assuming nothing beyond the axioms of mathematics. Boris works at OpenAI and had used their new model Sol to do the autoformalization. Boris made the code public and it did not take long for me to realise that somewhere within all this AI-generated (and sometimes horrible, although sometimes decent) code was indeed a proof of some really hard theorems in global class field theory. Also of interest to me was that Sol had generated 1.2 million lines of Lean code in the three weeks that it had worked on the project. Lean’s fantastic (declaration of conflict of interest: I am a maintainer) mathematics library mathlib is only 2.3 million lines of code, and took nine years to write. Perhaps it was at this point that the penny really dropped for me — large AI-generated developments of mathematics are inevitable. One cannot trust AI-generated code so I ran it in a sandbox on my machine (malicious Lean code can run arbitrary commands on your computer — Lean is a programming language, after all). Indeed, it was proving nontrivial theorems about the cohomology of number fields. Wow. Group schemes of order n A week after Boris’ revelation, in early July, I was thinking hard about how to run my Formalizing Fermat workshop. This workshop was sponsored by Logos Research, who, like Logical Intelligence (and Harmonic and Axiom AI and Moonshot AI and…) have a tool which can autoformalize mathematics — translating it from human language into Lean — building on mathlib. Logos told me that they were only going to allow 5 people at a time to use their system during the workshop, and there were 25 attendees, so I told all attendees that I would buy them a Claude Max subscription for a month, so they had something to experiment with when it wasn’t their turn for Logos’ tool. The workshop was 6th to 10th July, and the Claude Max subscription would give attendees access to Claude Fable, at least until Tuesday 7th, when it was being switched off. When OpenAI got wind of what I was doing, they also offered all attendees free ChatGPT Pro access for a month; this was a big deal because ChatGPT Sol was coming out on the 9th. So basically all attendees would have access to Sol and Fable for 4 out of the 5 days of the workshop, and Logos’ tool for the entire week. In fact Fable access was not removed on the 7th so we were in even better shape. I was not sure how good Logos’ tool was going to be, but I wanted a development of the theory of finite flat group schemes in Lean for my ongoing proof of Fermat’s Last Theorem, so I put uploaded some classic papers in the area to Fable and ChatGPT, and got them together to write down an exposition of the theory in natural language. I passed this pdf document over to Logos the day before the workshop, and on the first day of the workshop they said that one of the claims in the pdf was false and they had found an explicit counterexample. Another counterexample! I took a look and indeed the LLM-generated pdf was simply wrong at some point when describing a standard construction; false alarm. I had missed this myself though when reading through the pdf. Interesting how AI had again found a counterexample. I fixed the pdf. I thought it was interesting that the AI didn’t just say “I don’t quite follow this argument”, it instead said “here is a proof that this argument is simply wrong”, a much more powerful statement. With the development of the theory of finite flat group schemes back on track, I could relax back into the FLT workshop. On Tuesday 7th July I sat opposite Akhil Mathew at lunch; Akhil is a professor of mathematics at UChicago and he was an attendee who had been experimenting with the tools available. We talked about potential questions which AI could work on, and Akhil raised the old question of Grothendieck about whether every finite free group scheme of order n was killed by n. Deligne had proved the result in the commutative case, and Grothendieck had proved it when the base was reduced; Rene Schoof had proved it in more cases, and there had even been a paper by Emiliano Torti published last year, proving it in even more generality. I said that I thought that this was a fabulous thing to get AI thinking about. The day after the workshop finished, on Saturday 11th July, I got a DM from Akhil telling me that Sol had found a counterexample. He sent me a 12 page pdf. I immediately replied saying that I was not reading AI-generated informal mathematics and could he please formalize the entire thing in Lean. Four hours later he replied again, saying that Fable had autoformalized the entire thing. I scanned over the 1076-line Lean file, checking that the code did not delete all the files on my hard drive (Lean is a programming language, so it can do this). Convinced that it was only theorems, I then compiled it on my laptop and it took me under 5 minutes in total to check that (a) the statement of the claimed theorem used only concepts in mathlib (and thus things like HopfAlgebra can be trusted to mean what mathematicians think of as Hopf algebras) (b) the statement of the claimed theorem was that there was a counterexample and (c) the proof compiled. At this point I knew that we had a counterexample — a group scheme of order 4 which was not killed by 4. I suggested to Akhil that he make a PR to mathlib with the counterexample — which he did. I would have also suggested to him that he draft a press release saying that a machine had solved a 60-year-old question of Grothendieck in algebraic geometry, but somehow by this point I was almost becoming immune to all of this. It wasn’t clear to me that the media would even be able to distinguish between “machine resolves question due to Erdős” and “machine resolves question due to Grothendieck” even though I personally found the latter far more interesting. Of course the Grothendieck counterexample was far far easier than the Erdős one (a thousand lines, not a million), all I’m saying is that it’s an area of mathematics that I personally find more interesting. I pointed out to Akhil that machines seemed to be getting very good at finding counterexamples and suggested that he try the Hodge conjecture next. Modularity lifting theorems I think it’s worth stepping back at this point and surveying what the attitudes of human experts to these sorts of things are. On Tuesday (14th July) I went to work at Imperial and the Grothendieck counterexample was the talk of lunch. A member of the faculty (who I won’t name) said to me that the fact that the counterexample was so easy to find just indicated that humans had not spent enough time thinking about the problem, implying that a 60-year-old question of Grothendieck was not actually that interesting to work on. I didn’t tell him that at some point earlier in my career I had spent a week working hard on the problem. In my mind my colleague is just going through the five stages of grief; right now they seem to be in the denial phase. After lunch I met with my PhD student Andrew Yang, who had been working on formalizing a modularity lifting theorem in Lean, something which is crucial to my FLT work. Andrew had come to the Logos FLT workshop and now had access to both Sol and Fable. He told me that using these tools he had written 250K lines of Lean code which basically completely finished the project in what was I guess a 2 week period. A few days earlier I had got an email from a professor in the maths department here at Imperial, expressing surprise that some of our graduate students were paying $200 per month to access models such as Sol and Fable. He said that he thought that these people were crazy. I did not immediately respond. But after meeting with Andrew I emailed the professor back and told him that in my opinion, any PhD student who was not paying $200 per month to access these tools was crazy. In fact during the workshop I learnt from Harvard PhD student Bryan Wang that Harvard were already giving free Fable access to all PhD students, post-docs and faculty at Harvard. The Jacobian Conjecture But back to Akhil. I am not sure if he took my idea to disprove the Hodge conjecture seriously. But it looks like he had deeply understood that, with these extraordinary new AI tools, counterexamples might be low-hanging fruit right now. He had discussed with Levent Alpöge the idea of finding more counterexamples in algebraic geometry, and 12 hours ago Levent posted on X that Fable had found a counterexample to the Jacobian Conjecture. This is a big deal — this is a famous question in algebraic geometry which had been open for 100 years and which many people had thought about. It was apparently solved during the 2026 World Cup Final. I woke up today to a DM from Akhil saying “shall I make another PR?” but this time he was too late — Paul Lezeau had already formalized the counterexample manually and had made a PR to DeepMind’s Formal Conjectures repo. Mathlib does not contain a large list of conjectures in mathematics, but DeepMind’s repo does. The importance of formalization of conjectures by humans is that if humans are agreed that a Lean statement does faithfully capture the idea behind a conjecture, then checking that (possibly AI-generated) Lean code does comprise a proof or disproof of the conjecture is a triviality. Congratulations to Levent, thanks to Akhil for suggesting the problem to him, and thanks to DeepMind for already having formalized the statement and thus making formal verification of the counterexample a triviality. The Jacobian conjecture is resolved! Wow! The next step in that work is for humans to understand exactly what is going on with the example. For the true value of work like this is to give humans better understanding of mathematics. Indeed Akhil has been working on trying to understand the Grothendieck counterexample in a way which is far deeper than “here is a random presentation of a random ring and a random calculation which shows that something doesn’t work”. What we need next is the insight which can be drawn from these extraordinary examples. What a time to be alive. Dear Kevin, Thanks for this article. You write that you are “not reading AI-generated informal mathematics” but also that “the next step in that work is for humans to understand exactly what is going on with the example.” How do we do this without reading the informal AI output? We are surely not going through a thousand-line Lean file? LikeLike I actually find it easier to go through the formal output than the informal output. With the formal output, there is no danger of imagining things or misinterpreting the argument. Most reasonable Lean developments are organized into logical progressions of lemmas, and most of the lemmas might even be obvious to someone well versed in the field (who can also read Lean, of course), leaving only a small amount of actual argumentation to read. LikeLike “A few days earlier I had got an email from a professor in the maths department here at Imperial, expressing surprise that some of our graduate students were paying $200 per month to access models such as Sol and Fable. He said that he thought that these people were crazy. I did not immediately respond. But after meeting with Andrew I emailed the professor back and told him that in my opinion, any PhD student who was not paying $200 per month to access these tools was crazy.” With due respect, I find this comment disgusting. Among other problems, this money will be used for the gigantic V-sign to future generations that is building lots of extra gas power plants to supply new data centers. I won’t judge people for doing it any more than for eating red meat, and especially not in such a toughly competitive academic system, but if you think it’s crazy not to give 10% of your salary to unethical companies if it might hurt your career, then we are fundamentally not operating on the same set of values. LikeLiked by 2 people With the caveat that the internet and years of social media encourage us to make kneejerk responses, my instinct is to concur with JAS’s comment/reply. Aside from views one may (or may not) have about the companies building and selling these tools, the sentiment that Kevin candidly admits to is not a mentality that I want to see encouraged among those doing a PhD. LikeLike There are possibly political or social welfare reasons why one should resist the AI takeover of mathematics. But, from a strict utilitarian standpoint, these tools make you much more than 10% more productive, and are well worth the cost. I worry about the social implications of handing over a large portion of our resources to AI companies, and the equity and access concerns for people from countries where $200 is a lot of money. Also, there is evidence that AI companies are subsidizing the present cost of subscription access and that the true cost is much higher than what we pay. But, for now, if you’re a graduate student at Harvard or Imperial, the economic argument is persuasively in favor of spending the money to subscribe to AI. LikeLike you should inform your opinion on actual numbers, data centers use a small fraction of electricity and water compared to, say agriculture. so if you’re the kind of person who judges people for eating red meat, you need to dish out that judgement proportionally for AI users. i’ve given the exact same advice to graduate students months ago, pay for the best models, especially now that they are still affordable. contribute to proving the use case (at this point, is there even any doubt?), and get your department / advisor to pay for the models going forward. LikeLike idk if this is satisfactory but here’s how GPT interpreted the Jacobian example. Take P1xP2->P3 (Union of divisors on P1 say), remove ramification locus and remove a hyperplane of P3 which is tangent to a point of the map P1->P3 (tripling the divisor) but not osculating (multiplicity exactly two). Then the preimage is A3 by direct computation. LikeLike On a more constructive note than my previous comment/post: in the hope that some people who follow this blog as part of their interest in/commitment to formalization are also interested in understanding algebraic geometry, I want to give a signal boost to https://sbseminar.wordpress.com/2026/07/20/the-new-counterexample-to-the-jacobian-conjecture/ so that some maths discussion takes place there. LikeLike

6

Agent swarms and the new model economics

Hacker News · original → · 7/10 · AI: agent swarms and model economics
Agent swarms and the new model economics Earlier this year, we ran experiments to test the limits of scaling agents to cooperate toward a goal. Our hypothesis was that this would unlock a new tier…

Agent swarms and the new model economics Earlier this year, we ran experiments to test the limits of scaling agents to cooperate toward a goal. Our hypothesis was that this would unlock a new tier of task scale and complexity. The flagship project was a long-running swarm building a web browser from scratch. It succeeded as a proof of concept, but fell far short of polished software. That work was deliberately empirical. We started from a blank canvas and hill-climbed toward a stable, effective system. Since then, our goal has been to understand the agent swarm well enough to engineer it deliberately. To test that progress, we returned to a task the old swarm had struggled with: building SQLite from scratch, in Rust, from nothing but its documentation. Our initial results have been promising. We ran the old and new swarms on the same task, with the same models and the same time budget, and measured how much of a held-out SQL test suite each could pass. The new swarm did better in every model configuration. Using Grok 4.5, it reached 80% in four hours, while the old swarm spiraled and had to be paused before its second hour. We also varied which models did which jobs. In some runs, one model handled everything while in others, a frontier model planned while a fast, inexpensive model carried out the work. Every mix produced similar quality, but the costs varied enormously.1 Trees and leaves Descriptions of large tasks naturally take the shape of trees, with a goal at the root that subdivides recursively into basic units of work. Our swarm has two roles, both organized around that same tree-like decomposition: - Planner agents, powered by the smartest models, split a goal into pieces and delegate them. - Worker agents, generally powered by faster and less expensive models, execute those pieces. The design is a superset of more rigid orchestration systems. Rather than imposing a fixed topology on the problem, the swarm’s shape grows to cover the problem’s contours, and compute and context scale in proportion to the task’s complexity. We think this is why the design generalizes to tasks as diverse as building a browser, solving math problems, and optimizing GPU kernels. We’ve also used it internally to find and fix vulnerabilities in open-source software, raise test coverage on our own codebase, and generate billions of tokens of synthetic training data. What the tree does for memory When a single agent takes on a complete task, it has to walk the entire tree itself, descending to each leaf while holding its ancestors, its current position, and the wider goal in context the whole time. We think this explains why long-running single agents drift. They can either focus on the work in front of them and lose sight of the bigger picture, or hold the big picture and do a worse job on the piece. In a swarm, a planner never implements, so its context never fills with low-level detail, and a worker never plans, so it can spend all its context on one narrow piece of work. We suspect the ability to scale the agent swarm comes from this context efficiency, more than from parallelism itself. That efficiency is present in the swarm at every scale, which is why this decomposition helps agent performance even on moderately sized tasks. There are echoes of this structure elsewhere. The economist Ronald Coase, asking why firms exist at all, argued that coordination costs grow faster than the work itself, so organizations settle into tiers of bounded units rather than letting everyone talk to everyone. A version control system for agents In an earlier post about the swarm, we noted that tools like Git and Cargo rely on coarse locks for concurrency control. This is fine for one developer but unworkable for the volume of work produced by hundreds of concurrent agents. The browser swarm from earlier this year peaked at roughly 1,000 commits per hour on Git. The new system peaks at around 1,000 commits per second. To facilitate this rate of activity, we built a new version control system (VCS) from scratch. Throughput was not the only reason to own this layer. Every change in the system passes through the VCS, so it is where collisions first become visible, and several of the coordination mechanisms in the next section are implemented directly inside of it. Failure modes at 1,000 commits per second Human engineering teams have standard coordination mechanisms like code review, ownership, standups, and merge queues. Those systems work at human tempo, but at the commit-rate of the swarm, we see failure modes that human teams don’t routinely encounter. Split-brain design Two planners, unaware of each other, implement the same concept in different ways in different parts of the codebase. We fixed this through prompting. Planners make design decisions themselves rather than delegating them, and we require them to ensure that no two delegated subtrees decide the same question. Contention between planners A harder form of contention is when two planners know about each other and fight through back-and-forth changes over the same files. The problem is two pictures of reality, and merge tooling can't fix a disagreement. Instead, we have agents record decisions in shared design docs. Code that depends on a decision carries a compile-checked reference back to its doc. When planners unknowingly contradict each other, a reconciler merges the docs and the references propagate the resolution downstream. Merge conflicts Within the swarm, agents constantly collide on the same files. In order to resolve a collision they would have to stop, absorb the other agent's context, and merge around it. Worker agents are bad at this and, in practice, either overwrite the other change or abandon their own. To fix this, we created a system where a neutral third-party agent intervenes on merge conflicts and resolves them on behalf of all parties. Its only goal is to be impartial and efficient, similar to the way merge queues work in engineering teams. Megafiles Some files are particularly popular places for agents to work. Each agent might add only a small amount of code, and no single agent is responsible for keeping the files small. These “megafiles” choke everything. They’re expensive to transport, diff, and merge, and become the site of constant collisions. To fix this, we gave worker agents a way to flag bloated files. Once flagged, we block new commits and an outside agent decomposes the overgrown file into smaller modules. Ossification Agents have learned, from working in existing codebases with humans in the loop, not to touch core code even when it needs to change. To fix this, we license intentional breakage. An agent that judges a core change worthwhile can make a focused patch outside its scope and leave a comment explaining why it did it. The compiler carries the change through the rest of the system, and everything depending on the old design fails to build. Each agent that hits one of those errors finds the comment, reads the reasoning, and updates its own piece of work to match. Review lenses In a system that is both long-running and multi-agent, errors accumulate, and the swarm needs a way to correct itself before small mistakes become foundational. We experimented with many kinds of review lenses, such as giving a review agent the worker's full transcript, or only its output, or nothing but the codebase. We also tried reviewers running on different models, with different training and a different personality. No single lens catches everything, but decorrelated lenses stack, the way self-driving systems reach above-human reliability without any single perfect component. The compute spent on review is high return, since review is much cheaper than the work it audits. We suspect this stacked review system was a major contributor to the sustained quality of the runs. Letting agents shape the environment Stigmergy is the mechanism by which swarm organisms like ants and termites coordinate without direct communication. They shape the environment, and the environment shapes the next organism. We had encoded rules like “keep notes” and “document decisions” in earlier runs because they seemed obviously good. In retrospect, they were letting agents institutionalize knowledge for their future selves and teammates. We pushed this further with an experiment in self-authored, shared context we call the Field Guide. It’s a folder owned entirely by the agents, whose index.md is automatically injected into every agent at start. It is the agents’ job to curate what goes into the guide and their only constraint is a line budget. The underlying logic of the guide is that model weights are frozen, so it’s precisely surprise encounters that are worth capturing so the next agent trajectory is shorter. The Field Guide is an early experiment with promising results. We’d expect the benefits to be even larger on codebases agents don’t fully own. Training models to write for their successors, where better capture leads to better rewards, is an interesting follow-up area of research. The SQLite experiment We instructed the new version of the swarm, equipped with all the improvements described above, to implement the whole of the 835-page SQLite manual in Rust. We withheld the source code, test suites, SQLite binary, and internet access. To measure progress, we graded against sqllogictest, a test suite from the SQLite project built to check that different database engines return the same results for the same queries. It contains millions of queries with known correct answers, and the grade is the fraction the swarm's database gets right. Progress shows up as a rising curve over the course of a run. The swarm was never told the suite existed. After each run, we manually reviewed the code and the run itself, checking for cheating and shortcuts, and confirming the system was built out evenly, rather than just in the places where the tests look. As you read the curves, keep in mind that agents chose their own strategies. Some built broad foundations and scored low for hours before a late spike while others went deep on one area, scored early, then plateaued while filling in the rest. Trends matter more than exact scores at exact moments. Results across model mixes We tested four configurations spanning capability and cost: - GPT-5.5 as both planner and worker. A strong frontier model throughout.2 - Grok 4.5 as both planner and worker. Our cost-efficient frontier model, as a comparison point. - Opus 4.8 as planner and Composer 2.5 as worker. Frontier judgment paired with efficient execution. - Fable 5 as planner and Composer 2.5 as worker. To see whether a next-tier planner makes the hybrid more or less worthwhile. The new harness outperformed the old in every mix. The Fable 5 hybrid passed about two-thirds of the suite within the first hour. By the four-hour cutoff, the new runs sat between 73% and 85%, while the old runs ranged from 11% to 77%. The old Grok 4.5 run was paused before its two-hour mark (more below). Every new configuration went on to pass 100% of the suite. In the future we’d like to run the full N×N matrix of planner-worker combinations. For this cycle, the comparison that matters is between harness versions, and the behavioral differences turned out to be much larger than the score differences suggest. A deep dive into the runs Starting with the simplest measure of activity, we can see how the rate of commits varied for Grok 4.5 under the old harness versus the new. The old run produced 68,000 commits in its first two hours, roughly 70 times the new run's pace. One reading is that it was more productive. Another is that most of those commits were busywork (thrash, contention, churn). The merge conflict data points to the latter interpretation. The old run accumulated more than 70,000 conflicts before we paused it, accelerating rather than stabilizing, while the new run logged fewer than a thousand over its full four hours. The conflicts concentrated where files grew largest. In the old run, the biggest files kept growing for the entire run and its single hottest file collected 7,771 conflicts, touched by 1,173 different agents. In the new run, the most contested file in the whole codebase saw 47. The old swarm's biggest coordination failure — split-brain, or planners duplicating each other's work — showed up in the package structure. Rust code is organized into packages called crates, and in a project like this, each crate is roughly one major component. The old run sprawled to 54 crates, including three separate SQL packages. The new run settled on nine crates early and never added another. All of this shows up in the final codebase. In the Fable 5 mix, both the old and new swarms ultimately passed the full suite, but the old one needed 64,305 lines of engine code and the new one did it in 9,908. The Opus mix shows the same shape with 19,013 lines at a 97% grade under the old harness, and 4,645 lines at 100% under the new harness. Model economics We said at the top that every model mix produced similar quality while the costs varied enormously, from $1,339 for the Opus 4.8 hybrid to $10,565 for GPT-5.5 alone. The token data shows where that difference comes from. The structure of the spend was consistent across every run, with workers carrying at least 69% of the tokens, and over 90% in most. But the dollars split differently than the tokens, because planner tokens cost more. In the Opus 4.8 and Composer 2.5 mix, the Opus-as-planner produced a small fraction of the tokens but roughly two-thirds of the cost, while Composer-as-worker handled the vast majority of the tokens for the remaining third of the cost. Few moments in a large task genuinely require frontier intelligence, such as the original decomposition, the design decisions, and certain trade-offs. Once a frontier planner has collapsed the ambiguity into a detailed, explicit instruction, less expensive models simply have to follow it. This is a huge potential source of cost savings. In the run that used GPT-5.5 for both planners and workers, the workers alone cost $9,373. In the run where Opus 4.8 did the planning and Composer 2.5 did the work, the entire worker fleet cost $411. One detail worth noting comes from comparing the two hybrid runs. The Fable 5 planner ran up a slightly smaller bill than the Opus 4.8 planner, despite roughly twice the per-token price, because it used far fewer planning tokens. But the Fable run's workers went through several times as many tokens, and the run as a whole came out substantially more expensive. Specs as prompts Each jump in AI capability has raised the level of abstraction at which an engineer can work. Autocomplete let engineers work one line of code at a time. Early models raised that to a block of code, and agents raised it to a file or a feature. With swarms, the unit of work becomes the spec. For that to work, the swarm has to actually follow the spec, which is what much of this post is about. We gave the swarm 835 pages of prose and it came back with a database. What was scarce in this experiment, and what we expect to be scarce in software engineering going forward, is the right description of intent. Seen this way, the swarm starts to resemble a compiler. A compiler translates source code down to machine code through a series of intermediate steps. The swarm does something similar with intent. Planners parse a goal into task trees, then lower it step by step into executable work. The difference is that a compiler preserves meaning at every step while the swarm is probabilistic at every one. Everything described in this post exists to close that gap. We invite you to explore the swarm's output. The codebase from the solo Opus 4.8 run is public at github.com/cursor/minisqlite. Based on our initial glance it looks great, but we have not done a deeper manual analysis. Take your own look, and tell us what you find. - To get a sense of solo frontier costs, we also ran Opus 4.8 and Fable 5 on their own. We graded those runs only informally, so we draw no conclusions about their quality here, though from experience we would expect both models to do well. Their costs are shown in the chart as the hatched bars. ↩ - We had wanted GPT-5.6 Sol as the frontier configuration. The new model appears more sensitive to literal and emphasized wording than the others we tested, and we encountered runaway spirals unlike anything the other models produced. There wasn’t time to tune prompts for a model that arrived so recently, and tuning for one model while leaving the rest untouched would have made the comparison inaccurate, so we fell back to GPT-5.5. ↩

7

Seeing So Many "I've Lost Interest in Gaming" Posts Made Me Think

r/gaming · original → · 7/10 · Gaming: mid-life adult maintaining gaming hobby
I am almost 35 and, honestly, I never lost my joy for gaming. I think my reasons are pretty simple. First, gaming should never be your only hobby. Your body needs physical activity, too. Second,…

I am almost 35 and, honestly, I never lost my joy for gaming. I think my reasons are pretty simple.

First, gaming should never be your only hobby. Your body needs physical activity, too. Second, never buy five games at once when you know you do not have time to play them all. Do not build a backlog. I only play one game at a time, maybe two if the second one is something smaller and more mindless.

Another rule I have is to never play for more than two hours, even if I want to keep going. Leave yourself wanting more next time. Stop before you get bored, or at least when you feel yourself starting to get bored. I also think gaming works much better as a weekend hobby, almost like a reward for getting your work done, spending time with your family, going to the gym, cycling, or doing whatever else matters in your life.

Especially after a certain age, there is just too much life to fill every free hour with gaming. You need to give your body and mind what they need and treat gaming as something you earn, not something you do all day. You are not in college anymore, and if you have a job and a family, spending six hours gaming every day probably is not a great idea.

The only time I ever got seriously bored of gaming was when I was unemployed for four or five months while my wife was working. I had too much free time, jumped from game to game, played a ridiculous amount, completely burned myself out, and eventually stopped gaming for a few months. Once I got my routine back, so did my enjoyment.

The moments when I enjoy gaming the most are Saturdays. I finish work for the week, spend a nice morning with my family and kid, go to the gym or ride my bike, come home, eat a good meal, and then give myself two hours just for gaming. My mind is at peace, my body is tired, my stomach is full, and I have nothing else to think about. Those sessions are amazing. I try to do that at least twice a week, three times if I am lucky. Sometimes I also play on my Steam Deck for 30 minutes when I have some spare time.

There are so many great games coming out every year, with even more on the way, and I still have older games I want to play and some favorites I want to replay. Gaming feels stronger than ever to me.

I keep seeing posts from people in their late 20s and 30s saying that they have lost their passion for gaming, and I genuinely wonder how common my experience is. Are there other people around my age who still enjoy gaming just as much as they always did? What keeps it fun for you?

submitted by /u/molym
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8

Reverse-engineering is cheap now

Simon Willison · original → · 7/10 · AI: coding agents for home device automation
20th July 2026 I keep hearing anecdotes from people who used coding agents to reverse-engineer and automate devices in their homes. I think this is an interesting illustration of the impact of the…

20th July 2026 I keep hearing anecdotes from people who used coding agents to reverse-engineer and automate devices in their homes. I think this is an interesting illustration of the impact of the reduced cost of writing code. Prior to agents, it was entirely possible to reverse-engineer home devices. The problem was the ROI - was it really worth all of that effort? More importantly, any experienced programmer knows that undocumented, unstable APIs like that may well change or break in the future. Is that initial work worth the effort if you're committing yourself to a frustrating cycle of maintenance in the future? Coding agents change that equation entirely. The effort to get a simple automation working has dropped, as has the cost of trying and failing to get it to work. Since the code is so cheap, the idea of having to maintain it in the future - or throw it away and start again - carries way less psychological baggage. Recent articles - Kimi K3, and what we can still learn from the pelican benchmark - 16th July 2026 - The new GPT-5.6 family: Luna, Terra, Sol - 9th July 2026 - sqlite-utils 4.0, now with database schema migrations - 7th July 2026

Items scoring 7/10 or above from 11 sources, scored by claude-haiku-4-5-20251001 on relevance to my interests. At most 3 per source.

Scoring categories & sources
  1. Local Wexford or South East Ireland news
  2. Irish or EU-wide affairs affecting citizens broadly: elections, new laws or policy being debated, cost of living, education — especially impacts on mid-life adults or teenagers. Never courts/crime stories.
  3. Irish news on a topic relevant to my interests
  4. Work and tech topics: networking, AI, Kubernetes, platforms, SaaS
  5. AI news including critical or anti-AI perspectives
  6. Gaming: PC gaming, indie gaming, retro gaming
  7. General interests: gardening, woodwork, cycling, fitness, travel
  8. Comics

Sources: Breaking News Ireland, Wexford Local, Hacker News, r/gaming, r/pcgaming, r/antiAI, r/indiegaming, Lenny's Newsletter, One Useful Thing, Newcomer, Simon Willison

Comics

Arthurian Connector

XKCD · view →
Most coffee shops have a descendant of Sophia of Hanover on staff for this, but just as I was about to ask for help, a previously unknown heir of Uther Pendragon who was ordering a muffin tripped on my laptop cord.

Most coffee shops have a descendant of Sophia of Hanover on staff for this, but just as I was about to ask for help, a previously unknown heir of Uther Pendragon who was ordering a muffin tripped on my laptop cord.