We are all hav­ing to keep re­vis­ing up­wards our as­sess­ments of the math­e­mat­i­cal ca­pa­bil­i­ties of large lan­guage mod­els. I have just made a fairly large re­vi­sion as a re­sult of ChatGPT 5.5 Pro, to which I am for­tu­nate to have been given ac­cess, pro­duc­ing a piece of PhD-level re­search in an hour or so, with no se­ri­ous math­e­mat­i­cal in­put from me.

The back­ground is that, as has been widely re­ported, LLMs are now ca­pa­ble of solv­ing re­search-level prob­lems, and have man­aged to solve sev­eral of the Erdős prob­lems listed on Thomas Bloom’s won­der­ful web­site. Initially it was pos­si­ble to laugh this off: many of the “solutions” con­sisted in the LLM notic­ing that the prob­lem had an an­swer sit­ting there in the lit­er­a­ture al­ready, or could be very eas­ily de­duced from known re­sults. But lit­tle by lit­tle the laugh­ter has be­come qui­eter. The mes­sage I am get­ting from what other math­e­mati­cians more in­volved in this en­ter­prise have been say­ing is that LLMs have got to the point where if a prob­lem has an easy ar­gu­ment that for one rea­son or an­other hu­man math­e­mati­cians have missed (that rea­son some­times, but not al­ways, be­ing that the prob­lem has not re­ceived all that much at­ten­tion), then there is a good chance that the LLMs will spot it. Conversely, for prob­lems where one’s ini­tial re­ac­tion is to be im­pressed that an LLM has come up with a clever ar­gu­ment, it of­ten turns out on closer in­spec­tion that there are prece­dents for those ar­gu­ments, so it is still just about pos­si­ble to com­fort one­self that LLMs are merely putting to­gether ex­ist­ing knowl­edge rather than hav­ing truly orig­i­nal ideas. How much of a com­fort that is I will not dis­cuss here, other than to note that quite a lot of per­fectly good hu­man math­e­mat­ics con­sists in putting to­gether ex­ist­ing knowl­edge and proof tech­niques.

I de­cided to try some­thing a lit­tle bit dif­fer­ent. At least in com­bi­na­torics, there are quite a lot of pa­pers that in­ves­ti­gate some rel­a­tively new com­bi­na­to­r­ial pa­ra­me­ter that leads nat­u­rally to sev­eral ques­tions. Because of the sheer num­ber of ques­tions one can ask, the au­thors of such pa­pers will not nec­es­sar­ily have the time to spend a week or two think­ing about each one, so there is a de­cent prob­a­bil­ity that at least some of them will not be all that hard. This makes such pa­pers very valu­able as sources of prob­lems for math­e­mati­cians who are do­ing re­search for the first time and who will be hugely en­cour­aged by solv­ing a prob­lem that was of­fi­cially open. Or rather, it used to make them valu­able in that way, but it looks as though the bar has just been raised. It is no longer enough that some­body asks a prob­lem: it needs to be hard enough for an LLM not to be able to solve it.

In any case, a lit­tle over a week ago I de­cided to see how ChatGPT 5.5 Pro would fare with a se­lec­tion of prob­lems asked by Mel Nathanson in a pa­per en­ti­tled Diversity, Equity and Inclusion for Problems in Additive Number Theory. Nathanson has a re­mark­able record of be­ing in­ter­ested in prob­lems and the­o­rems that have later be­come ex­tremely fash­ion­able, which has led him to write a se­ries of ex­tremely well timed and there­fore highly in­flu­en­tial text­books. In this pa­per, he ar­gues for the in­ter­est of sev­eral other prob­lems, some of which I will now briefly de­scribe.

If is a set of in­te­gers, then its sum­set is de­fined to be . For a pos­i­tive in­te­ger , the –fold sum­set, de­noted , is de­fined to be . Nathanson is in­ter­ested in the pos­si­ble sizes of given the size of . To that end one can de­fine a set to be the set of all such that there ex­ists a set with and .

An ob­vi­ous first ques­tion to ask is sim­ply “What is ?” When , the an­swer is the set of all in­te­gers be­tween and . It is an easy ex­er­cise to show that if , then , so this re­sult is say­ing that all sizes in be­tween can be re­al­ized. However, it is not true in gen­eral that can take every size be­tween its min­i­mum and max­i­mum pos­si­bil­i­ties, and we do not cur­rently have a com­plete de­scrip­tion of .

Another nat­ural ques­tion one can ask, and this is where ChatGPT came in, is how large a di­am­e­ter you need if you want a set with and hav­ing pre­scribed sizes. (Of course, the size of must be­long to .) Nathanson showed that for every there is a sub­set of with and , and asked whether the bound could be im­proved. ChatGPT 5.5 Pro thought for 17 min­utes and 5 sec­onds be­fore pro­vid­ing a con­struc­tion that yielded a qua­dratic up­per bound, which is clearly best pos­si­ble. It wrote up its ar­gu­ment in a slightly ram­bling LLM-ish style, so I asked if it could write the ar­gu­ment up as a LaTeX file in the style of a typ­i­cal math­e­mat­i­cal preprint. After two min­utes and 23 sec­onds it gave me that, af­ter which I spent some time con­vinc­ing my­self that the ar­gu­ment was cor­rect.

The ba­sic idea be­hind both Nathanson’s ar­gu­ment and ChatGPT’s was that in or­der to ob­tain a set of a given size with a sum­set of a given size, it is use­ful to build it out of a Sidon set, which means a set with sum­set of max­i­mal size (that is not quite the usual de­f­i­n­i­tion but it is the sim­plest to use in this dis­cus­sion), and an arith­metic pro­gres­sion. Also, for a bit of fine tun­ing one can take an ad­di­tional point near the arith­metic pro­gres­sion. Then if one plays around with the var­i­ous pa­ra­me­ters, one finds that one can ob­tain sets of all the sizes one wants. Nathanson does­n’t ex­press his ar­gu­ment this way (it is Theorem 5 of this pa­per), in­stead giv­ing an in­duc­tive ar­gu­ment, but I think, with­out hav­ing checked too care­fully, that if one un­rav­els his ar­gu­ment, one finds that ef­fec­tively that is what he ends up with, and the Sidon set in ques­tion con­sists of pow­ers of 2. ChatGPT ob­tained its im­prove­ment by sim­ply us­ing a more ef­fi­cient Sidon set — it is well known that one can find Sidon sets of qua­dratic di­am­e­ter. (One might ask why Nathanson did­n’t do that in the first place: I think it is be­cause the ob­vi­ous idea of us­ing a more ef­fi­cient Sidon set be­comes ob­vi­ous only af­ter one has re­described his in­duc­tive con­struc­tion. Is that what ChatGPT did? It is very hard to say.)

Next, I asked ChatGPT to see whether it could do the same for a closely re­lated ques­tion, where in­stead of look­ing at the size of the sum­set, one looks at the size of the re­stricted sum­set, which is de­fined to be . Unsurprisingly, it was able to do that with no trou­ble at all. I got it to write both re­sults up in a sin­gle note, to avoid a cer­tain amount of du­pli­ca­tion. If you are cu­ri­ous, you can see the note here.

I then asked what it could do for gen­eral . I was much less op­ti­mistic that it would man­age to do any­thing in­ter­est­ing, be­cause the proof for makes fun­da­men­tal use of the fact (due to Erdős and Szemerédi) that we know ex­actly which sizes we need to cre­ate. If we don’t know what the set is, then it seems that we are forced to start with a hy­po­thet­i­cal set with and and build out of it a set of small di­am­e­ter with the same prop­erty. As it hap­pens, I still don’t know how to get round that dif­fi­culty (I’m men­tion­ing that just to demon­strate that my math­e­mat­i­cal in­put was zero, and I did­n’t even do any­thing clever with the prompts), but Nathanson men­tioned in his pa­per a re­mark­able pa­per of Isaac Rajagopal, a stu­dent at MIT, who must have got round the dif­fi­culty some­how, be­cause he had man­aged to prove an ex­po­nen­tial de­pen­dence of on for each fixed .

I’ll leave the pre­vi­ous para­graph there, but Isaac has sub­se­quently ex­plained to me that that is­n’t re­ally the dif­fi­culty. His ar­gu­ment gives a com­plete de­scrip­tion of when is suf­fi­ciently large, and if one wants to prove a poly­no­mial de­pen­dence for fixed , then as­sum­ing that is suf­fi­ciently large is clearly per­mit­ted. The real dif­fi­culty is that con­struct­ing the sets with given sum­set sizes was sig­nif­i­cantly more com­pli­cated, and nec­es­sar­ily so be­cause the de­gree of the poly­no­mial grows with , and one there­fore needs more and more pa­ra­me­ters to de­fine the sets.

In any case, the task faced by ChatGPT was not to solve the prob­lem from scratch, but to see whether it was pos­si­ble to tighten up Isaac Rajagopal’s ar­gu­ment. Here’s what hap­pened.

After 16 min­utes and 41 sec­onds, it came back with an ar­gu­ment that claimed to have im­proved the up­per bound from ex­po­nen­tial in to ex­po­nen­tial in for any .

I asked it to write that in preprint form too, which took it a fur­ther 47 min­utes and 39 sec­onds.

That preprint would have been hard for me to read, as that would have meant care­fully read­ing Rajagopal’s pa­per first, but I sent it to Nathanson, who for­warded it to Rajagopal, who said he thought it looked cor­rect.

Both ChatGPT and Rajagopal spec­u­lated a lit­tle on what might need to be done to push things fur­ther and get a poly­no­mial bound, so I got greedy and asked ChatGPT to give that a go.

After 13 min­utes and 33 sec­onds it told me it felt op­ti­mistic about the ex­is­tence of such an ar­gu­ment but there were a cou­ple of tech­ni­cal state­ments that needed check­ing.

I asked it to check them.

After 9 min­utes and 12 sec­onds it got back to me with the check hav­ing been done, so I asked for this too to be writ­ten in preprint form.

After 31 min­utes and 40 sec­onds the “preprint” was ready. Here it is.

Isaac Rajagopal looked at it and de­clared it to be al­most cer­tainly cor­rect. It was clear that he meant this not just at a line-by-line level but at the level of ideas.

Isaac made some very in­ter­est­ing re­marks about the na­ture of what the ad­di­tional ideas were that ChatGPT con­tributed. Since, as I have al­ready said, my math­e­mat­i­cal in­put was zero, I in­vited him to write a guest sec­tion to this post. Just be­fore we get to that, I want to raise a ques­tion (that will un­doubt­edly have been raised by oth­ers as well), which is sim­ple: what should we do with this kind of con­tent? Had the re­sult been pro­duced by a hu­man math­e­mati­cian, it would def­i­nitely have been pub­lish­able, so I think it would be wrong to de­scribe it as AI slop. On the other hand, it seems point­less even to think about putting it in a jour­nal, since it can be made freely avail­able, and no­body needs “credit” for it (except that Isaac de­serves plenty of credit for cre­at­ing the frame­work on which ChatGPT could build). I un­der­stand that arXiv has a pol­icy against ac­cept­ing AI-written con­tent, which makes good sense to me. So maybe there should be a dif­fer­ent repos­i­tory where AI-produced re­sults can live. But var­i­ous de­ci­sions would need to be made about how it was or­ga­nized. I my­self think that one would prob­a­bly want to have some kind of mod­er­a­tion process, so that re­sults would be in­cluded only if a hu­man math­e­mati­cian was pre­pared to cer­tify that they were cor­rect — or, bet­ter still, that they had been for­mal­ized by a proof as­sis­tant — and per­haps also that they an­swered a ques­tion that had been asked in a hu­man-writ­ten pa­per. On the other hand, I would­n’t want a mod­er­a­tion process that cre­ated vast amounts of work (unless the work was it­self done by AI, but there are ob­vi­ous dan­gers in go­ing down that route). Anyway, un­til these ques­tions are an­swered, this re­sult is avail­able from the link above, and per­haps, now that LLMs are so good at lit­er­a­ture search, that will be enough to make it find­able by any­one who wants to know whether Nathanson’s prob­lem has been solved.

Isaac’s eval­u­a­tion of what ChatGPT achieved

With just a few prompts, ChatGPT was able to im­prove the up­per bound on (which I will de­fine very soon) from ex­po­nen­tial in to poly­no­mial in . While its first im­prove­ment of the bound, from ex­po­nen­tial in to ex­po­nen­tial in , was a rou­tine mod­i­fi­ca­tion of my work, the im­prove­ment to poly­no­mial in is quite im­pres­sive. To do this, ChatGPT came up with an idea which is orig­i­nal and clever. It is the sort of idea I would be very proud to come up with af­ter a week or two of pon­der­ing, and it took ChatGPT less than an hour to find and prove, us­ing sim­i­lar meth­ods to those in my own proof. My goal is to ex­plain that idea, in a man­ner that will be di­gestible to my friends who are com­puter sci­ence ma­jors as well as my math ma­jor friends.

The prob­lem of bound­ing is closely re­lated to a prob­lem I worked on at the Duluth REU (Research Experience for Undergrads) pro­gram, of de­ter­min­ing . In par­tic­u­lar, is the set of pos­si­ble -fold sum­set sizes , where can be cho­sen to be any set of in­te­gers. is the min­i­mal such that we can achieve all of the val­ues of us­ing -element sets . I spent last sum­mer ex­plic­itly char­ac­ter­iz­ing the set for large , by con­struct­ing sets such that achieves all sizes which I could not rule out as im­pos­si­ble. So, can be up­per-bounded by op­ti­miz­ing my con­struc­tions.

I con­structed these sets by com­bin­ing smaller com­po­nent sets which are sim­pler to an­a­lyze. Some of these com­po­nents are the geo­met­ric se­ries

for var­i­ous val­ues of and . Unfortunately, the el­e­ments of and are ex­po­nen­tially large in terms of . So, I asked ChatGPT (through Tim) whether there ex­ist sets of el­e­ments which have sim­i­lar sum­set sizes to these geo­met­ric se­ries, but con­tain only num­bers of poly­no­mial size in : I had no idea if this was pos­si­ble, or how to be­gin con­struct­ing such sets. ChatGPT came back with an an­swer, con­struct­ing sets and which be­have like “half a geo­met­ric se­ries squeezed into a poly­no­mial in­ter­val,” which is coun­ter­in­tu­itive. Before I dis­cuss the con­struc­tion of and , I will ex­plain the im­por­tant prop­er­ties of the sum­set sizes of and which they recre­ate.

For , a set is called a set if the only so­lu­tions to

with in are the “trivial” so­lu­tions, by which I mean that one side of the equa­tion is a re­order­ing of the other side. If is a set of size , then el­e­ments of cor­re­spond ex­actly to choices of el­e­ments of , with rep­e­ti­tion al­lowed. Using “stars and bars,” one can see that and this is the max­i­mum pos­si­ble value of among sets of size . So, an­other de­f­i­n­i­tion is that is a set if . Sidon sets, which Tim dis­cussed, are ex­actly sets.

To make things more con­crete, let us as­sume that in (1). Then, is a set, but it is not a set be­cause of the re­la­tions

for any choice of in . In par­tic­u­lar, , as these re­la­tions are the only ones pre­vent­ing from be­ing a set. lacks the re­la­tions in (2) be­cause is not in . So, is a set, but it is not a set be­cause of the re­la­tions

for any choices of in . This gives re­la­tions, and one can check that . To sum­ma­rize, we have seen that

(a) is a set.

(b) is a lin­ear func­tion of .

(c) is a set.

(d) is a qua­dratic func­tion of .

ChatGPT was able to find sets and of el­e­ments which sat­isfy (a)-(d), but whose el­e­ments all have poly­no­mial size in . The con­struc­tion of and uses -dissociated sets, which are sets where the only so­lu­tions to

with and in are the “trivial” so­lu­tions, i.e. and one side of the equa­tion is a re­order­ing of the other side. For , it is pos­si­ble to con­struct an -dissociated set , where is ap­prox­i­mately , and in par­tic­u­lar poly­no­mial in . Constructions of such a us­ing fi­nite fields date back to Singer (1938) and Bose–Chowla (1963) and are de­scribed in Appendix 1. Define

and

In hind­sight, I have good in­tu­ition for the con­struc­tion of and . All of the re­la­tions in (2) and (3) are formed by com­bin­ing one or two re­la­tions of the form . There are ap­prox­i­mately re­la­tions of the form in and , and ap­prox­i­mately such re­la­tions in and . There are few other low-or­der re­la­tions in and , and sim­i­larly in and be­cause is -dissociated. So, and man­age to con­tain half as many -relations as their geo­met­ric se­ries coun­ter­parts, while also con­tain­ing few low-or­der re­la­tions.

We now see why (a)-(d) hold with and re­placed by and , re­spec­tively. For con­crete­ness, we as­sume that and , so con­tains no non­triv­ial re­la­tions as in (4) with . Then, is a set, but it is not a set be­cause of the re­la­tions

for any choice of in . If we let , we can check that is lin­ear in . In par­tic­u­lar, (a) and (b) hold with re­placed by , and the lin­ear func­tion re­placed by . We can also see that is a set, but it is not a set be­cause of the re­la­tions

for any in . If we let , we can check that is qua­dratic in . In a sim­i­lar man­ner, (c) and (d) hold with re­placed by , and the qua­dratic func­tion re­placed by .

Even though I can mo­ti­vate it in ret­ro­spect, ChatGPT’s idea to use -dissociated sets to con­trol re­la­tions of or­der at most feels quite in­ge­nious. As far as I can tell, this idea is com­pletely orig­i­nal.

ChatGPT’s proof that its con­struc­tion pro­duces the de­sired val­ues of is very sim­i­lar to my proof that the sets which I con­struct achieve all pos­si­ble val­ues of , af­ter re­plac­ing and by and , re­spec­tively. Properties (a)-(d) cap­ture many of the im­por­tant prop­er­ties of and (or and ) which are used in this proof. The fi­nal con­struc­tions in­volve com­bin­ing the sets and (or and in my pa­per) for each value of be­tween and with an­other set which is the union of an arith­metic pro­gres­sion and a point. Intuitively, and (or and ) have large sum­sets, while arith­metic pro­gres­sions have small sum­sets, so it is plau­si­ble that one could get sets which achieve all the medium-sized sum­sets by com­bin­ing them. However, the proof of this is quite in­volved, and it oc­cu­pies Section 4 of my pa­per and the en­tirety of the ChatGPT preprint. In Appendix 2, I work out the de­tails of the ChatGPT con­struc­tion to show that for suf­fi­ciently large,

For com­par­i­son, it is easy to see that is at least on the or­der of , and it is un­known what the real value is. In Appendix 3, I give de­tails of the cor­re­spon­dence be­tween my pa­per and the ChatGPT preprint, which will be help­ful for those who want to read ei­ther.

Finally, I want to ex­press my deep grat­i­tude to Tim for al­low­ing me to con­tribute to this blog. I am still stunned by the co­in­ci­dence that the prob­lem he chose to put into ChatGPT 5.5 Pro led him to my pa­per on the arXiv.

Tim on what this means for math­e­mat­i­cal re­search

I would judge the level of the re­sult that ChatGPT found in un­der two hours to be that of a per­fectly rea­son­able chap­ter in a com­bi­na­torics PhD. It would­n’t be con­sid­ered an amaz­ing re­sult, since it leant very heav­ily on Isaac’s ideas, but it was def­i­nitely a non-triv­ial ex­ten­sion of those ideas, and for a PhD stu­dent to find that ex­ten­sion it would be nec­es­sary to in­vest quite a bit of time di­gest­ing Isaac’s pa­per, look­ing for places where it might not be op­ti­mal, fa­mil­iar­iz­ing one­self with var­i­ous al­ge­braic tech­niques that he used, and so on.

It seems to me that train­ing be­gin­ning PhD stu­dents to do re­search, which has al­ways been hard (unless one is lucky enough, as I have of­ten been, to have a stu­dent who just seems to get it and there­fore does­n’t need in any sense to be trained), has just got harder, since one ob­vi­ous way to help some­body get started is to give them a prob­lem that looks as though it might be a rel­a­tively gen­tle one. If LLMs are at the point where they can solve “gentle prob­lems”, then that is no longer an op­tion. The lower bound for con­tribut­ing to math­e­mat­ics will now be to prove some­thing that LLMs can’t prove, rather than sim­ply to prove some­thing that no­body has proved up to now and that at least some­body finds in­ter­est­ing.

I would qual­ify that state­ment in two ways though. First, there is the ob­vi­ous point that a be­gin­ning PhD stu­dent has the op­tion of us­ing LLMs. So the task is po­ten­tially eas­ier than prov­ing some­thing that LLMs can’t prove: it is prov­ing some­thing in col­lab­o­ra­tion with LLMs that LLMs can­not man­age on their own. I have done quite a lot of such col­lab­o­ra­tion re­cently and found that LLMs have made use­ful con­tri­bu­tions with­out (yet) hav­ing game-chang­ing ideas.

A sec­ond point is that I don’t know how much of what I have said gen­er­al­izes to other ar­eas of math­e­mat­ics. Combinatorics tends to be quite fo­cused on prob­lems: you start with a ques­tion and you rea­son back from the ques­tion or if you rea­son for­wards you do so very much with the ques­tion in mind. In other ar­eas there can be much more of an em­pha­sis on for­wards rea­son­ing: you start with a cir­cle of ideas and see where it leads. To do it suc­cess­fully, you need to have some way of dis­crim­i­nat­ing be­tween in­ter­est­ing ob­ser­va­tions and un­in­ter­est­ing ones, and it is­n’t ob­vi­ous to me what LLMs would be like at that.

Of course, every­thing I am say­ing con­cerns LLMs as they are right now. But they are de­vel­op­ing so fast that it seems al­most cer­tain that my com­ments will go out of date in a mat­ter of months. It is also al­most cer­tain that these de­vel­op­ments will have a pro­foundly dis­rup­tive ef­fect on how we go about math­e­mat­i­cal re­search, and es­pe­cially on how we in­tro­duce new­com­ers to it. Somebody start­ing a PhD next aca­d­e­mic year will be fin­ish­ing it in 2029 at the ear­li­est, and my guess is that by then what it means to un­der­take re­search in math­e­mat­ics will have changed out of all recog­ni­tion.

I some­times get emails from peo­ple who are in­ter­ested in do­ing math­e­mat­i­cal re­search but are not sure whether that makes sense any more as an as­pi­ra­tion. I have a view on that ques­tion, but it may very well change in re­sponse to fur­ther de­vel­op­ments. That view is that there is still a great deal of value in strug­gling with a math­e­mat­ics prob­lem, but that the era where you could en­joy the thrill of hav­ing your name for­ever as­so­ci­ated with a par­tic­u­lar the­o­rem or de­f­i­n­i­tion may well be close to its end. So if your aim in do­ing math­e­mat­ics is to achieve some kind of im­mor­tal­ity, so to speak, then you should un­der­stand that that won’t nec­es­sar­ily be pos­si­ble for much longer — not just for you, but for any­body. Here’s a thought ex­per­i­ment: sup­pose that a math­e­mati­cian solved a ma­jor prob­lem by hav­ing a long ex­change with an LLM in which the math­e­mati­cian played a use­ful guid­ing role but the LLM did all the tech­ni­cal work and had the main ideas. Would we re­gard that as a ma­jor achieve­ment of the math­e­mati­cian? I don’t think we would.

So what is the point of strug­gling with a dif­fi­cult math­e­mat­ics prob­lem? One an­swer is that it can be very sat­is­fy­ing to solve a prob­lem even if the an­swer is al­ready known, but I don’t think that is a suf­fi­cient rea­son to spend sev­eral years of your life on this pe­cu­liar ac­tiv­ity. A bet­ter an­swer is that by solv­ing hard prob­lems you get an in­sight into the prob­lem-solv­ing process it­self, at least in your area of ex­per­tise, in a way that you sim­ply don’t if all you do is read other peo­ple’s so­lu­tions. One con­se­quence of this is that peo­ple who have them­selves solved dif­fi­cult prob­lems are likely to be sig­nif­i­cantly bet­ter at us­ing solv­ing prob­lems with the help of AI, just as very good coders are bet­ter at vibe cod­ing than not such good coders, or peo­ple who have a solid grasp of how to do ba­sic arith­metic are likely to be more skilled at us­ing cal­cu­la­tors (and es­pe­cially at notic­ing when an an­swer feels off). Mathematics is a highly trans­fer­able skill, and that ap­plies to re­search-level math­e­mat­ics as well. By do­ing re­search in math­e­mat­ics, you may not get the same re­wards as your equiv­a­lents a gen­er­a­tion ago, but there is a good chance that you will be equip­ping your­self very well for the world we are about to ex­pe­ri­ence.

Appendix 1 (Isaac)

We will con­struct an -dissociated set , where is ap­prox­i­mately . This con­struc­tion is a very mi­nor mod­i­fi­ca­tion of Bose–Chowla (1963)’s con­struc­tion of a set, which I learned about from this pa­per. For what­ever rea­son, the GPT preprint (Lemma 3.1) uses a dif­fer­ent, less ef­fi­cient con­struc­tion us­ing mo­ment curves.

Let be a prime, let , let be the fi­nite field with el­e­ments and fix a gen­er­a­tor of , so that is equal to . Define a set of el­e­ments

Then, each el­e­ment cor­re­sponds to a unique value of , by tak­ing . Now an ad­di­tive re­la­tion of the form in (4) with can be re­framed by tak­ing pow­ers of as

As is a de­gree- ex­ten­sion of and is a gen­er­a­tor of as an -extension, this means that does not sat­isfy any nonzero poly­no­mi­als in of de­gree . So, both sides of (6) are iden­ti­cal as poly­no­mi­als in and thus the ad­di­tive re­la­tion in (4) is triv­ial. So, is -dissociated, and of course one can prune a few el­e­ments to re­duce to size .

Appendix 2 (Isaac)

Fix con­stants such that (in my pa­per I ar­bi­trar­ily chose ). Let the two sets in (5) be called and . Let de­note the set of in­te­gers sat­is­fy­ing . Similarly to my pa­per, the con­struc­tions of such that achieves the de­sired sizes will com­bine sets of the fol­low­ing four types:

One rea­son that this con­struc­tion needs to be com­pli­cated is that we need to cre­ate at least many sets. To do this, we vary pa­ra­me­ters and in the do­main and pa­ra­me­ters and in the do­main . We can choose to be slightly big­ger than , and then the above con­struc­tion gives us dif­fer­ent sets where can be made ar­bi­trar­ily small. So, if we were to re­move any of the above pa­ra­me­ters from the con­struc­tion, and not change the oth­ers, this con­struc­tion would no longer cre­ate many sets. In com­par­i­son, Nathanson’s con­struc­tion when only needs to cre­ate sets. He does this by com­bin­ing a Sidon set, an arith­metic pro­gres­sion, and one ex­tra value, and vary­ing the size of the arith­metic pro­gres­sion and the ex­tra value in ranges of size .

We want to com­bine sets , which are given by , for the val­ues of , for the val­ues of , and a set. By Appendix 1, for all , there ex­ists a -dissociated set of di­am­e­ter . By the con­struc­tions of and , we can take each , where . Let have ba­sis vec­tors . To com­bine , we can de­fine as

Similarly to my Lemma 4.9, this con­struc­tion en­sures that the gen­er­at­ing func­tion prod­uct holds, which is the iden­tity that both my pa­per and the GPT preprint use (see ei­ther pa­per for a de­f­i­n­i­tion of these gen­er­at­ing func­tions). By (the stan­dard) Lemma 2.3 of the GPT preprint, is Freiman-isomorphic of or­der to a sub­set of . Therefore, for suf­fi­ciently large (the whole con­struc­tion re­lies on this for the same rea­sons as in my pa­per),

Appendix 3 (Isaac)

In Section 4.2 of my pa­per, I use a dif­fer­ent, sim­pler con­struc­tion to con­struct sets achiev­ing the val­ues in which have , for some small . These sets are sub­sets of , mean­ing that all el­e­ments have poly­no­mial size in . This is ob­served in Section 5 of the GPT preprint.

Section 4.3 of my pa­per car­ries out the con­struc­tion which com­bines many com­po­nents in­clud­ing and . This cor­re­sponds to Sections 2, 3, 4, and 6 of the GPT preprint. This sec­tion has a lot of mov­ing parts; I give an out­line in Section 4.3.1.

In Section 4.3.2, I de­scribe how the dif­fer­ent com­po­nents will be com­bined, us­ing a con­struc­tion which I call the dis­joint union, and in­tro­duce gen­er­at­ing func­tions as a book­keep­ing tool to keep track of the sum­set sizes of a set . This cor­re­sponds to Section 2 and Section 4 of the GPT preprint.

In Section 4.3.3, I com­pute the gen­er­at­ing func­tion of each of the com­po­nent sets, in­clud­ing (Lemma 4.15) and (Lemma 4.17). This cor­re­sponds to Section 3 and Section 6.1 of the GPT preprint. In par­tic­u­lar, is com­puted in Lemma 3.3 and is com­puted in Lemma 3.4. Once these gen­er­at­ing func­tions have been com­puted, the re­main­der of the proof is al­most iden­ti­cal in my pa­per and in the GPT preprint.

In Section 4.3.4, I put all the pieces to­gether to show that as we range over the sets which I have con­structed, the val­ues of will as­sume all of the el­e­ments of . The key idea is to show that the set of all val­ues of forms an in­ter­val, and con­tains num­bers both smaller than and equal to .

Tags: ai, math­e­mat­ics

This en­try was posted on May 8, 2026 at 4:40 pm and is filed un­der Computing, Straight maths. You can fol­low any re­sponses to this en­try through the RSS 2.0 feed. You can leave a re­sponse, or track­back from your own site.

Thirty years ago, Brewster Kahle founded the Internet Archive with an am­bi­tious goal: Universal Access to All Knowledge. Today, that mis­sion con­tin­ues to grow with an ex­cit­ing new chap­ter: the launch of the Internet Archive Switzerland, a non-profit foun­da­tion based in St. Gallen.

The Internet Archive Switzerland, on­line at https://​in­ter­netarchive.ch/, is a newly-formed Swiss non-profit foun­da­tion that will op­er­ate in­de­pen­dently within its na­tional con­text. Its ef­forts will ini­tially fo­cus on pre­serv­ing en­dan­gered archives from around the world and col­lect­ing the gen­er­a­tive AI wave that is cur­rently upon us all. With a UNESCO con­fer­ence planned for November 2026 in Paris, Internet Archive Switzerland is tak­ing a con­crete step to ex­plore how en­dan­gered archives can be pro­tected.

In par­al­lel, the Swiss foun­da­tion is work­ing in part­ner­ship with the School of Computer Science at the University of St. Gallen, on the Gen AI Archive pro­ject led by Prof. Dr. Damian Borth. Together, they aim to be­gin archiv­ing AI mod­els, which is an emerg­ing fron­tier for preser­va­tion.

The choice of St. Gallen is no co­in­ci­dence. With a thou­sand-year tra­di­tion of archiv­ing and schol­ar­ship, the city of­fers a fit­ting home for this next phase of dig­i­tal preser­va­tion. Its strong aca­d­e­mic en­vi­ron­ment—in­clud­ing col­lab­o­ra­tion with the University of St. Gallen—makes it an ideal place to es­tab­lish a 21st cen­tury mem­ory or­ga­ni­za­tion.

“St. Gallen is a very suit­able place to take the preser­va­tion of our uni­ver­sal knowl­edge a step fur­ther. Stability and in­no­va­tion go hand in hand here and are em­bed­ded in a deep un­der­stand­ing of the im­por­tance of cul­tural her­itage,” said Roman Griesfelder, the ex­ec­u­tive di­rec­tor of Internet Archive Switzerland.

Internet Archive Switzerland joins a grow­ing group of mis­sion-aligned or­ga­ni­za­tions, along­side Internet Archive, Internet Archive Canada, and Internet Archive Europe. Together, these in­de­pen­dent li­braries strengthen a shared vi­sion: build­ing a dis­trib­uted, re­silient dig­i­tal li­brary for the world.

Contact Internet Archive SwitzerlandRoman Griesfelder, ex­ec­u­tive di­rec­to­rof­fice@in­ter­netarchive.ch

Welcome

Welcome toIn­t­er­net Archive Switzerland.

Universal Access to ALL Knowledge.

Internet Archive Switzerland is an in­de­pen­dent Swiss foun­da­tion, which is op­er­at­ing as an non-profit or­gan­i­sa­tion based in Sankt Gallen. Our pri­mary goal is: Universal Access to All Knowledge.

Together with like-minded part­ners we col­lect and pre­serve dig­i­tal in­for­ma­tion for learn­ing and re­search. Our ob­jec­tive is to en­sure peo­ple can find any kind of help­ful dig­i­tal ma­te­ri­als, to­day and in the fu­ture.

Although at first glance one might think that the dig­i­tal con­tent avail­able on the in­ter­net is in­ex­haustible and end­lessly grow­ing, it is also ev­i­dent that dig­i­tal in­for­ma­tion is ac­tu­ally short-lived.

We are fac­ing con­stant changes in file for­mats, sud­den fail­ure of stor­age me­dia, rapid dele­tion processes (accidental or de­lib­er­ate) and an in­creas­ing ten­dency of hid­ing knowl­edge be­hind pay­walls. All of this jeop­ar­dises easy ac­cess to in­for­ma­tion, learn­ing and the shap­ing of opin­ions on the ba­sis of facts.

All of this has led us to launch two ini­tia­tives in the foun­da­tion’s early stages: We are part­ner­ing with the University of St. Gallen to build the Gen Artificial Intelligence (AI) Archive, pre­serv­ing to­day’s AI mod­els for fu­ture gen­er­a­tions. And through our Endangered Archives ini­tia­tive, we in­vite global part­ners to ex­plore ways of res­cu­ing vul­ner­a­ble col­lec­tions from con­flict, dis­as­ter, and sup­pres­sion be­fore they are lost.

Projects

What we are WORKING on.

Project 01 · Research

Gen AI Archive

Artificial Intelligence, Generative AI, and Large Language Models (LLMs) are fun­da­men­tally re­shap­ing how hu­man­ity cre­ates and shares knowl­edge. To doc­u­ment this evo­lu­tion, the University of St. Gallen and Internet Archive Switzerland part­ner in pre­serv­ing to­day’s most pro­found mod­els for fu­ture gen­er­a­tions in the Gen AI Archive.

Project 02 · Preservation

Endangered Archives

Cultural her­itage and his­tor­i­cal records world­wide face ever grow­ing threats from con­flict, in­sta­bil­ity, and nat­ural dis­as­ters. To pre­vent the loss of this col­lec­tive mem­ory, Internet Archive Switzerland seeks to es­tab­lish an ini­tia­tive called Endangered Archives. In co­op­er­a­tion with UNESCO and other well es­tab­lished or­gan­i­sa­tions we aim to res­cue vul­ner­a­ble ma­te­ri­als by pro­vid­ing a se­cure dig­i­tal haven.

About

The foun­da­tion.

Organization

An in­de­pen­dent non profit foun­da­tion in St. Gallen, Switzerland. Mission-aligned with the Internet Archive, Internet Archive Canada and Internet Archive Europe, and a com­mon goal: Universal Access to All Knowledge.

Our char­ter states (excerpt): “The pur­pose of the Foundation is to ad­vance the preser­va­tion and uni­ver­sal ac­ces­si­bil­ity of all knowl­edge as in­spired by the United Nations Universal Declaration of Human Rights (Articles 19, 26, and 27) and the United Nations’s Sustainable Development Goal 4, which strives to en­sure in­clu­sive and eq­ui­table qual­ity ed­u­ca­tion and pro­mote life­long learn­ing op­por­tu­ni­ties for all.

Board & Advisers

Executive Director

Roman Griesfelder

Internet Archive Switzerland is led by Roman Griesfelder as Executive Director. Roman is an Austrian cit­i­zen and has been liv­ing in Switzerland since 1998. The so­ci­ol­o­gist and busi­ness ad­min­is­tra­tor has been work­ing for many years in se­nior roles as pro­ject man­ager and man­age­ment con­sul­tant, among other things, be­fore hold­ing lead­ing po­si­tions at cul­tural in­sti­tu­tions in Switzerland. His wide-rang­ing in­ter­ests con­verge at the points where so­cial, cul­tural and tech­no­log­i­cal de­vel­op­ments in­ter­sect and af­fect the lives of many peo­ple, or even just a few in­di­vid­u­als.

Location

St. Gallen.

47.4245° N · 9.3767° E

St. Gallen is no stranger to the idea that pre­serv­ing the record is a form of civic re­spon­si­bil­ity. Its archival tra­di­tion stretches back over a thou­sand years — a fit­ting sym­bolic home for this new chap­ter of the Internet Archive.

The ex­is­tence of the Abbey Archives proves that, with con­vic­tion and per­se­ver­ance, it is pos­si­ble to pre­serve the foun­da­tions of our knowl­edge about so­ci­ety. This con­vic­tion mo­ti­vates the Internet Archive Switzerland to em­bark boldly on its mis­sion and to pur­sue it un­wa­ver­ingly.

We are also de­lighted to be part­ner­ing with the University of St. Gallen to es­tab­lish the world’s first com­pre­hen­sive AI archive.

Blog

Latest NEWS.

May 5, 2026 • 5 min­utes of read­ing

Internet Archive Switzerland Launches in St. GallenA Thousand Years of Memory, and a New Chapter

On May 5th, 2026, Internet Archive Switzerland cel­e­brates its launch at the ex­hi­bi­tion hall of the Abbey Archives of St. Gallen, one of the old­est con­tin­u­ously ac­tive archives in the world. We are grate­ful to Peter Erhart and the Abbey Archives of St. Gallen for host­ing us: two in­sti­tu­tions, one a mil­len­nium old and one…

Read more: Internet Archive Switzerland Launches in St. Gallen

May 5, 2026 • 5 min­utes of read­ing

Internet Archive Switzerland Launches in St. Gallen

A Thousand Years of Memory, and a New Chapter

On May 5th, 2026, Internet Archive Switzerland cel­e­brates its launch at the ex­hi­bi­tion hall of the Abbey Archives of St. Gallen, one of the old­est con­tin­u­ously ac­tive archives in the world. We are grate­ful to Peter Erhart and the Abbey Archives of St. Gallen for host­ing us: two in­sti­tu­tions, one a mil­len­nium old and one…

pub­lished 5/6/2026

OpenAI posted a tech­ni­cal blog a few days ago. This blog post trig­gered me more than it should have. I urge to slap my meaty fin­gers on the key­board.

You should NOT copy OpenAI.

I don’t think you should use WebRTC for voice AI. WebRTC is the prob­lem.

Me

Like 6 years ago I wrote a WebRTC SFU at Twitch. Originally we used Pion (Go) just like OpenAI, but forked af­ter bench­mark­ing re­vealed that it was too slow. I ended up rewrit­ing every pro­to­col, be­cause of course I did!

Just a year ago, I was at Discord and I rewrote the WebRTC SFU in Rust. Because of course I did! You’re prob­a­bly notic­ing a trend.

Fun Fact: WebRTC con­sists of ~45 RFCs dat­ing back to the early 2000s. And some de-facto stan­dards that are tech­ni­cally drafts (ex. TWCC, REMB). Not a fun fact when you have to im­ple­ment them all.

You should con­sider me a Certified WebRTC Expert. Which is why I never, never want to use WebRTC again.

Product Fit

I’m go­ing to cheat a lit­tle bit and start with the hot takes be­fore they get cold. Don’t worry, we’ll get right back to talk­ing about the OpenAI blog post and load bal­anc­ing, I promise.

WebRTC is a poor fit for Voice AI.

But that seems counter-in­tu­itive? WebRTC is for con­fer­enc­ing, and that in­volves speak­ing? And ro­bots can speak, right?

WebRTC is too ag­gres­sive

Let’s say I pull up my OpenAI app on my phone. I say hi to Scarlett Johansson Sky and then I ut­ter:

should I walk or drive to the car wash?

should I walk or drive to the car wash?

WebRTC is de­signed to de­grade and drop my prompt dur­ing poor net­work con­di­tions.

wtf my dude

WebRTC ag­gres­sively drops au­dio pack­ets to keep la­tency low. If you’ve ever heard dis­torted au­dio on a con­fer­ence call, that’s WebRTC bay­bee. The idea is that con­fer­ence calls de­pend on rapid back-and-forth, so paus­ing to wait for au­dio is un­ac­cept­able.

…but as a user, I would much rather wait an ex­tra 200ms for my slow/​ex­pen­sive prompt to be ac­cu­rate. After all, I’m pay­ing good money to boil the ocean, and a garbage prompt means a garbage re­sponse. It’s not like LLMs are par­tic­u­larly re­spon­sive any­way.

But I’m not al­lowed to wait. It’s im­pos­si­ble to even re­trans­mit a WebRTC au­dio packet within a browser; we tried at Discord. The im­ple­men­ta­tion is hard-coded for real-time la­tency or else.

UPDATE: Some WebRTC folks are claim­ing this is a skill is­sue. It might be pos­si­ble to en­able au­dio NACKs, but we could­n’t fig­ure out the cor­rect SDP mung­ing. Either way, the WebRTC jit­ter buffer is ag­gres­sively small.

And yes, Voice AI agents will even­tu­ally get the la­tency down to the con­ver­sa­tional range. But re­duc­ing la­tency has trade-offs. I’m not even sure that pur­posely de­grad­ing au­dio prompts will ever be worth it.

TTS is faster than real-time

You speak into the mi­cro­phone, it gets sent to one of OpenAI’s bil­lion servers, and then a GPU pre­tends to talk to you via text-to-speech. Neato.

Let’s say it takes 2s of GPUs to gen­er­ate 8s of au­dio. In an ideal world, we would stream the au­dio as it’s be­ing gen­er­ated (over 2s) and the client would start play­ing it back (over 8s). That way, if there’s a net­work blip, some au­dio is buffered lo­cally. The user might not even no­tice the net­work blip.

But nope, WebRTC has no buffer­ing and ren­ders based on ar­rival time. Like se­ri­ously, time­stamps are just sug­ges­tions. It’s even more an­noy­ing when video en­ters the pic­ture.

To com­pen­sate for this, OpenAI has to make sure pack­ets ar­rive ex­actly when they should be ren­dered. They need to add a sleep in front of every au­dio packet be­fore send­ing it. But if there’s net­work con­ges­tion, oops we lost that au­dio packet and it’ll never be re­trans­mit­ted.

OpenAI is lit­er­ally in­tro­duc­ing ar­ti­fi­cial la­tency, and then ag­gres­sively drop­ping pack­ets to “keep la­tency low”. It’s the equiv­a­lent of screen shar­ing a YouTube video in­stead of buffer­ing it. The qual­ity will be de­graded.

Fun fact: WebRTC ac­tu­ally adds la­tency. It’s not much, but WebRTC has a dy­namic jit­ter buffer that can be sized any­where from 20ms to 200ms (for au­dio). This is meant to smooth out net­work jit­ter, but none of this is needed if you trans­fer faster than real-time.

Ports Ports Ports

Okay but let’s talk about the tech­ni­cal meat of the OpenAI ar­ti­cle. We’re no longer on a boat, but let’s talk about ports.

When you host a TCP server, you open a port (ex. 443 for HTTPS) and lis­ten for in­com­ing con­nec­tions. The TCP client will ran­domly se­lect an ephemeral port to use, and the con­nec­tion is iden­ti­fied by the source/​des­ti­na­tion IP/ports. For ex­am­ple, a con­nec­tion might be iden­ti­fied as 123.45.67.89:54321 -> 192.168.1.2:443.

But there’s a mi­nor prob­lem… client ad­dresses can change. When your phone switches from WiFi to cel­lu­lar, oops your IP changes. NATs can also ar­bi­trar­ily change your source IP/port be­cause of course they can.

Whenever this hap­pens, bye bye con­nec­tion, it’s time to dial a new one. And that means an ex­pen­sive TCP + TLS hand­shake which takes at least 2 – 3 RTTs. The users def­i­nitely no­tice the net­work hic­cup when you’re live stream­ing.

WebRTC tried to solve this is­sue but made things worse. Seriously.

A WebRTC im­ple­men­ta­tion is sup­posed to al­lo­cate an ephemeral port for each con­nec­tion. That way, a WebRTC ses­sion can iden­ti­fied by the des­ti­na­tion IP/port only; the source is ir­rel­e­vant. If the source IP/port changes, oh hey that’s still Bob be­cause the des­ti­na­tion port is the same.

But as OpenAI cor­rob­o­rates, this causes is­sues at scale be­cause…

Servers only have a lim­ited num­ber of ports avail­able.

Firewalls love to block ephemeral ports.

Kubernetes lul

You could prob­a­bly abuse IPv6 to work around this, but IDK I never tried. Twitch did­n’t even sup­port IPv6…

Hacks by Necessity

So most ser­vices end up ig­nor­ing the WebRTC spec­i­fi­ca­tions. Because of course they do. We mux mul­ti­ple con­nec­tions onto a sin­gle port in­stead.

At Twitch I lit­er­ally hosted my WebRTC server on UDP:443. That’s sup­posed to be the HTTPS/QUIC port, but ly­ing meant we could get past more fire­walls. Like the Amazon cor­po­rate net­work, which blocked all but ~30 ports.

Discord uses ports 50000 – 50032, one for each CPU core. As a re­sult it gets blocked on more cor­po­rate net­works. But like, if you’re on a Discord voice call on the Amazon cor­po­rate net­work, you prob­a­bly won’t be there much longer any­way.

HOWEVER, HUGE PROBLEM.

WebRTC is ac­tu­ally a bunch of stan­dards in a trench­coat, and 5 of those go over UDP di­rectly. It’s not hard to fig­ure out which pro­to­col a packet is us­ing, but we need to fig­ure out how to route each packet.

STUN: We can choose a unique ufrag and route on it.

SRTP/SRTCP: The browser chooses a ran­dom ssrc (u32)… which we can usu­ally route based on.

DTLS: Uh oh. We pray that RFC9146 gets wide­spread sup­port.

TURN: IDK I’ve never im­ple­mented it.

So OpenAI only uses STUN:

No pro­to­col ter­mi­na­tion: Relay parses only STUN head­ers/​ufrag; it uses cached state for sub­se­quent DTLS, RTP, and RTCP, keep­ing pack­ets opaque.

No pro­to­col ter­mi­na­tion: Relay parses only STUN head­ers/​ufrag; it uses cached state for sub­se­quent DTLS, RTP, and RTCP, keep­ing pack­ets opaque.

It’s a pos­i­tive way of say­ing:

We re­ally hope the user’s source IP/port never changes, be­cause we broke that func­tion­al­ity.

We re­ally hope the user’s source IP/port never changes, be­cause we broke that func­tion­al­ity.

While it’s im­pres­sive load bal­anc­ing any­thing at OpenAI scale, their cus­tom load bal­anc­ing is a hack. But a nec­es­sary hack, be­cause the core pro­to­col is at fault.

Fun fact: Browsers can ran­domly gen­er­ate the same ssrc. If there is a col­li­sion, and no source IP/port map­ping is avail­able, Discord at­tempts to de­crypt the packet with each pos­si­ble de­cryp­tion key. If the key worked, hey we iden­ti­fied the con­nec­tion!

Round Trips and U

The OpenAI blog post starts with 3 re­quire­ments, one of them is:

Fast con­nec­tion setup so a user can start speak­ing as soon as a ses­sion be­gins

Fast con­nec­tion setup so a user can start speak­ing as soon as a ses­sion be­gins

lol

It takes a min­i­mum of 8* round trips (RTT) to es­tab­lish a WebRTC con­nec­tion. While we try to run CDN edge nodes close enough to every user to min­i­mize RTT, it adds up.

Signaling server (ex. WHIP):

1 for TCP

1 for TLS 1.3

1 for HTTP

Media server:

1 for ICE (with server)

2 for DTLS 1.2

2 for SCTP

* It’s com­pli­cated to com­pute, be­cause some pro­to­cols can be pipelined to avoid 0.5 RTT. Kinda like half an A-Press.

All of this non­sense is be­cause WebRTC needs to sup­port P2P. It does­n’t mat­ter if you have a server with a sta­tic IP ad­dress, you still need to do this dance.

It’s ex­tra de­press­ing when the sig­nal­ing and me­dia server are run­ning on the same host/​process. You end up do­ing two re­dun­dant and ex­pen­sive hand­shakes. It’s like walk­ing AND dri­ving your car to the car wash.

Forking the Protocol

Fun Fact: This was orig­i­nally go­ing to be a Fun Fact, but it gets its own sec­tion now.

WebRTC prac­ti­cally en­cour­ages you to fork the pro­to­col. There’s so many lim­i­ta­tions that I’ve barely scratched the sur­face. The browser im­ple­men­ta­tion is owned by Google and tai­lor made for Google Meet, so it’s also an ex­is­ten­tial threat for con­fer­enc­ing apps.

Sad Fact: That’s why every con­fer­enc­ing app (except Google Meet) tries to shove a na­tive app down your throat. It’s the only way to avoid us­ing WebRTC.

OpenAI def­i­nitely has the debt fund­ing to do this. But I think they should also throw the baby out with the bath wa­ter. Don’t fork WebRTC, re­place it with some­thing that has browser sup­port.

Fun Fact: Discord has forked WebRTC so hard that na­tive clients only im­ple­ment a tiny frac­tion of the pro­to­col. No more SDP/ICE/STUN/TURN/DTLS/SCTP/SRTP/etc. But we still have to im­ple­ment every­thing for web clients.

But What Instead?

If not WebRTC, then what should you use for Voice AI?

Honestly, if I was work­ing at OpenAI, I’d start by stream au­dio over WebSockets. You can lever­age ex­ist­ing TCP/HTTP in­fra­struc­ture in­stead of in­vent­ing a cus­tom WebRTC load bal­ancer. It makes for a bor­ing blog post, but it’s sim­ple, works with Kubernetes, and SCALES.

I think head-of-line block­ing is a de­sir­able user ex­pe­ri­ence, not a li­a­bil­ity. But the fated day will come and drop­ping/​pri­or­i­tiz­ing some pack­ets will be nec­es­sary. Then I think OpenAI should copy MoQ and uti­lize WebTransport, be­cause…

QUIC FIXES THIS

Remember the round trip dis­cus­sion? Good times. Here’s how many RTTs it takes to es­tab­lish a QUIC con­nec­tion:

1 for QUIC+TLS

But that was an easy one. Let’s dive into the deeper de­tails of QUIC that you would­n’t know about un­less you’re a turbo QUIC nerd (it me).

Connection ID

Remember that link to RFC9146? In the DTLS sec­tion? That you did­n’t click? Good times. The idea is lit­er­ally copied from QUIC.

QUIC ditches source IP/port based rout­ing. Instead, every packet con­tains a CONNECTION_ID, which can be 0 – 20 bytes long. And most im­por­tantly for us: it’s cho­sen by the re­ceiver.

So our QUIC server gen­er­ates a unique CONNECTION_ID for each con­nec­tion. Now we can use a sin­gle port and still fig­ure out when the source IP/port changes. When it does, QUIC au­to­mat­i­cally switches to the new ad­dress in­stead of sev­er­ing the con­nec­tion like TCP.

But if your gut re­ac­tion is: “how dare they! this is a waste of bytes!” These bytes are very im­por­tant, keep read­ing u nerd.

Stateless Load Balancing

I glossed over this, but OpenAI’s load bal­ancers (like most) de­pend on shared state. Even if you have a sticky packet router, load bal­ancers can still restart/​crash. Something has to store the map­ping from source IP/port -> back­end server.

They’re us­ing a Redis in­stance to store the map­ping of source IP/port to back­end server. Simple and easy, I ap­prove.

The European Parliamentary Research Service (EPRS) has warned that vir­tual pri­vate net­works (VPNs) are in­creas­ingly be­ing used to by­pass on­line age-ver­i­fi­ca­tion sys­tems, de­scrib­ing the trend as “a loop­hole in the leg­is­la­tion that needs clos­ing.”

The warn­ing comes as gov­ern­ments across Europe and else­where con­tinue ex­pand­ing on­line child-safety rules that re­quire plat­forms to ver­ify users’ ages be­fore grant­ing ac­cess to adult or age-re­stricted con­tent.

VPNs are pri­vacy tools de­signed to en­crypt in­ter­net traf­fic and hide a user’s IP ad­dress by rout­ing con­nec­tions through re­mote servers. While widely used for le­git­i­mate pur­poses such as pro­tect­ing com­mu­ni­ca­tions, avoid­ing sur­veil­lance, and en­abling se­cure re­mote work, reg­u­la­tors are in­creas­ingly con­cerned that the same tech­nol­ogy al­lows mi­nors to cir­cum­vent re­gional age checks.

The EPRS notes that VPN us­age surged af­ter manda­tory age-ver­i­fi­ca­tion laws took ef­fect in coun­tries in­clud­ing the United Kingdom and sev­eral US states. In the UK, where on­line ser­vices are now re­quired to pre­vent chil­dren from ac­cess­ing harm­ful con­tent, VPN apps re­port­edly dom­i­nated down­load charts af­ter the law came into force.

— European Parliamentary Research Service (@EP_EPRS) May 6, 2026

The doc­u­ment ex­plic­itly frames VPNs as a reg­u­la­tory gap, stat­ing that some pol­i­cy­mak­ers and child-safety ad­vo­cates be­lieve VPN ac­cess it­self should re­quire age ver­i­fi­ca­tion. England’s Children’s Commissioner has also called for VPN ser­vices to be re­stricted to adults only.

However, forc­ing users to ver­ify their iden­tity be­fore ac­cess­ing VPN ser­vices could sig­nif­i­cantly weaken anonymity pro­tec­tions and cre­ate new risks around sur­veil­lance and data col­lec­tion. VPN providers and other pri­vacy ad­vo­cates have al­ready ex­pressed their ob­jec­tions to this ap­proach in a let­ter sent to the UK pol­i­cy­mak­ers.

Last month, re­searchers found mul­ti­ple se­cu­rity and pri­vacy flaws in the European Commission’s of­fi­cial age-ver­i­fi­ca­tion app shortly af­ter its re­lease. The app, pro­moted as a pri­vacy-pre­serv­ing tool un­der the DSA frame­work, was dis­cov­ered stor­ing sen­si­tive bio­met­ric im­ages in un­en­crypted lo­ca­tions and ex­pos­ing weak­nesses that could al­low users to by­pass ver­i­fi­ca­tion con­trols en­tirely.

The EPRS pa­per ac­knowl­edges that age ver­i­fi­ca­tion re­mains tech­ni­cally dif­fi­cult and frag­mented across the EU. Current sys­tems based on self-de­c­la­ra­tion, age es­ti­ma­tion, or iden­tity ver­i­fi­ca­tion are de­scribed as rel­a­tively easy for mi­nors to by­pass. The re­port high­lights emerg­ing ap­proaches, such as “double-blind” ver­i­fi­ca­tion sys­tems used in France, where web­sites re­ceive only con­fir­ma­tion that a user meets age re­quire­ments with­out learn­ing the user’s iden­tity, while the ver­i­fi­ca­tion provider does not see which web­sites the user vis­its.

At the same time, reg­u­la­tors are be­gin­ning to ad­dress VPN use di­rectly in leg­is­la­tion. Utah re­cently be­came the first US state to en­act a law ex­plic­itly tar­get­ing VPN use in on­line age ver­i­fi­ca­tion. The state’s SB 73 de­fines a user’s lo­ca­tion based on phys­i­cal pres­ence rather than ap­par­ent IP ad­dress, even if VPNs or proxy ser­vices are used to mask it.

The EPRS sug­gests VPN providers may face in­creas­ing scrutiny as the EU re­vises cy­ber­se­cu­rity and on­line safety leg­is­la­tion, not­ing that fu­ture up­dates to the EU Cybersecurity Act could in­tro­duce child-safety re­quire­ments aimed at pre­vent­ing VPN mis­use to by­pass le­gal pro­tec­tions.

If you liked this ar­ti­cle, be sure to fol­low us on X/Twitter and also LinkedIn for more ex­clu­sive con­tent.

In the early 1960s, Fred Brooks man­aged the de­vel­op­ment of IBM’s System/360 com­puter sys­tems. After it was done he penned his thoughts in the book The Mythical Man-Month which be­came one of the most in­flu­en­tial books on soft­ware de­vel­op­ment af­ter its pub­li­ca­tion in 1975. Reading it in 2026, we’ll find some of it out­dated, but it also re­tains many lessons that are still rel­e­vant to­day.

The book con­tains Brooks’s law: “Adding man­power to a late soft­ware pro­ject makes it later.” The is­sue here is com­mu­ni­ca­tion, as the num­ber of peo­ple grows, the num­ber of com­mu­ni­ca­tion paths be­tween those peo­ple grows ex­po­nen­tially. Unless these paths are skill­fully de­signed, then work quickly falls apart.

Perhaps my most en­dur­ing les­son from this book is the im­por­tance of con­cep­tual in­tegrity

I will con­tend that con­cep­tual in­tegrity is the most im­por­tant con­sid­er­a­tion in sys­tem de­sign. It is bet­ter to have a sys­tem omit cer­tain anom­alous fea­tures and im­prove­ments, but to re­flect one set of de­sign ideas, than to have one that con­tains many good but in­de­pen­dent and un­co­or­di­nated ideas.

I will con­tend that con­cep­tual in­tegrity is the most im­por­tant con­sid­er­a­tion in sys­tem de­sign. It is bet­ter to have a sys­tem omit cer­tain anom­alous fea­tures and im­prove­ments, but to re­flect one set of de­sign ideas, than to have one that con­tains many good but in­de­pen­dent and un­co­or­di­nated ideas.

He ar­gues that con­cep­tual in­tegrity comes from both sim­plic­ity and straight­for­ward­ness - the lat­ter be­ing how eas­ily we can com­pose el­e­ments. This point of view has been a strong in­flu­ence upon my ca­reer, the pur­suit of con­cep­tual in­tegrity un­der­pins much of my work.

The an­niver­sary edi­tion of this book is the one to get, be­cause it also in­cludes his even-more in­flu­en­tial 1986 es­say “No Silver Bullet”.

GrapheneOS has re­leased a new up­date that fixes a re­cently dis­closed Android VPN by­pass vul­ner­a­bil­ity ca­pa­ble of leak­ing a user’s real IP ad­dress.

The leak hap­pens even when Android’s “Always-On VPN” and “Block con­nec­tions with­out VPN” pro­tec­tions were en­abled.

The is­sue, dis­closed last week by se­cu­rity re­searcher “lowlevel/Yusuf,” af­fected Android 16 and stemmed from a newly in­tro­duced QUIC con­nec­tion tear­down fea­ture in Android’s net­work­ing stack. In its lat­est re­lease, GrapheneOS says it has “disable[d] reg­is­terQuic­Connec­tion­Close­P­a­y­load op­ti­miza­tion to fix VPN leak,” ef­fec­tively neu­tral­iz­ing the at­tack vec­tor on sup­ported Pixel de­vices.

GrapheneOS is a pri­vacy- and se­cu­rity-fo­cused Android-based op­er­at­ing sys­tem pri­mar­ily de­vel­oped for Google Pixel de­vices. The pro­ject is widely used by pri­vacy-con­scious con­sumers, jour­nal­ists, ac­tivists, and en­ter­prise users seek­ing stronger ap­pli­ca­tion sand­box­ing, ex­ploit mit­i­ga­tions, and re­duced re­liance on Google ser­vices.

According to Yusuf’s tech­ni­cal write-up, the vul­ner­a­ble API al­lowed or­di­nary ap­pli­ca­tions with only the au­to­mat­i­cally granted INTERNET and ACCESS_NETWORK_STATE per­mis­sions to reg­is­ter ar­bi­trary UDP pay­loads with sys­tem_server.

When the ap­p’s UDP socket was later de­stroyed, Android’s priv­i­leged sys­tem_server process would trans­mit the stored pay­load di­rectly over the de­vice’s phys­i­cal net­work in­ter­face rather than through the VPN tun­nel. Because sys­tem_server op­er­ates with el­e­vated net­work­ing priv­i­leges and is ex­empt from VPN rout­ing re­stric­tions, the packet by­passed Android’s VPN lock­down pro­tec­tions en­tirely.

The re­searcher demon­strated the flaw on a Pixel 8 run­ning Android 16 with Proton VPN en­abled along­side Android’s lock­down mode. The app re­port­edly leaked the de­vice’s ac­tual pub­lic IP ad­dress to a re­mote server de­spite VPN pro­tec­tion be­ing fully en­abled.

Google in­tro­duced a fea­ture that al­lows ap­pli­ca­tions to grace­fully ter­mi­nate QUIC ses­sions when sock­ets are un­ex­pect­edly de­stroyed. However, the im­ple­men­ta­tion ac­cepted ar­bi­trary pay­loads with­out val­i­dat­ing whether they were le­git­i­mate QUIC CONNECTION_CLOSE frames and did not ver­ify whether the orig­i­nat­ing ap­pli­ca­tion was re­stricted to VPN-only traf­fic.

The re­searcher re­ported the is­sue to Android’s se­cu­rity team, which clas­si­fied it as “Won’t Fix (Infeasible)” and “NSBC” (Not Security Bulletin Class), stat­ing that it did not meet the thresh­old for in­clu­sion in Android se­cu­rity ad­vi­sories. The re­searcher ap­pealed the de­ci­sion, ar­gu­ing that any ap­pli­ca­tion could leak iden­ti­fy­ing net­work in­for­ma­tion us­ing only stan­dard per­mis­sions, but Google main­tained its po­si­tion, au­tho­riz­ing pub­lic dis­clo­sure on April 29.

GrapheneOS re­sponded by dis­abling the un­der­ly­ing op­ti­miza­tion en­tirely in re­lease 2026050400.

Beyond the VPN leak fix, the lat­est re­lease also in­cludes the full May 2026 Android se­cu­rity patch level, mul­ti­ple hard­ened_­mal­loc im­prove­ments, Linux ker­nel up­dates across Android’s 6.1, 6.6, and 6.12 branches, and a back­ported fix for CVE-2026 – 33636 in libpng. The up­date ad­di­tion­ally ships newer Vanadium browser builds and ex­panded Dynamic Code Loading re­stric­tions.

The re­searcher noted that stock Android users could tem­porar­ily mit­i­gate the is­sue man­u­ally through ADB by dis­abling the close_quic_­con­nec­tion DeviceConfig flag. However, that workaround re­quires de­vel­oper ac­cess and may not per­sist in­def­i­nitely if Google re­moves the fea­ture flag in fu­ture up­dates.

If you liked this ar­ti­cle, be sure to fol­low us on X/Twitter and also LinkedIn for more ex­clu­sive con­tent.

I like the Internet. I am old enough to re­mem­ber the pre-In­ter­net era and de­spite the younger gen­er­a­tions pin­ing for those sim­pler days, I was there. Paper maps were ab­solutely hor­ri­ble, just you and a com­pass in your car on the side of the road in the mid­dle of the night try­ing to fig­ure out where you are and where you are go­ing. Once when dri­ving from Michigan to Florida I got so lost in the mid­dle of the night in Kentucky that I had to pull over to sleep and wait for the sun so I could fig­ure out where I was. I awoke to an old man star­ing un­blink­ingly into my car, shirt­less, breath­ing heavy enough to fog the win­dows. To say I floored that 1991 Honda Civic is an un­der­state­ment.

You would leave your house and then just dis­ap­pear. This is pre­sented as kind of ro­man­tic now, as if we were just free spir­its on the wind and could stop and re­ally watch a sun­set. In prac­tice it was mostly an an­noy­ing game of at­tempt­ing to guess where peo­ple were. You’d call their job, they had left. You’d call their house, they weren’t home yet. Presumably they were in tran­sit but you ac­tu­ally had no idea. As a child my re­sponse to peo­ple ask­ing me where my par­ents were was of­ten a shrug as I re­sumed at­tempt­ing to eat my weight in shoplifted candy or make home­made na­palm with gaso­line and sty­ro­foam. Sometimes I shud­der as a par­ent re­mem­ber­ing how young I was putting pen­nies on train tracks and hid­ing dan­ger­ously close so that we could get the cool squished penny af­ter­wards.

Cassettes are the worst way to lis­ten to mu­sic ever in­vented. Tapes squealed. Tapes slowed down for no rea­son, like they were de­pressed. Multiple times in my life I would set off on a long road trip, pop in a tape, and within fif­teen min­utes watch as it shot from the deck un­spooled like the guts from the tauntaun in Star Wars. You’d then spend forty-five min­utes at a Sunoco try­ing to wind it back in with a Bic pen know­ing in your heart you were per­form­ing CPR on a corpse. Then you’d put it back in the player out of pure stub­born­ness, and it would chew it­self again im­me­di­ately, and you’d drive the next six hours in si­lence with your own thoughts, which were not as good as Pearl Jam.

So I am, mostly, grate­ful for the bounty the in­ter­net has pro­vided. But there is some­thing wrong, deeply wrong, with what we built. The wrong­ness was there at the start. It was baked into the foun­da­tion by peo­ple who told them­selves a story about free­dom, and that story was a lie, and we are all, every one of us, pay­ing their tab.

To un­der­stand what hap­pened we need to go back to the 90s.

A Declaration of the Independence of Cyberspace

One of the first and most clas­sic ex­am­ples of the ide­ol­ogy that pow­ered and con­tin­ues to power tech is the clas­sic “A Declaration of the Independence of Cyberspace” by John Perry Barlow writ­ten in 1996. You can find the full text here. I re­mem­ber think­ing it was ge­nius when I first read it. I was young enough that I also thought “Snow Crash” was a se­ri­ous po­lit­i­cal doc­u­ment. Today the Declaration reads like one of those sov­er­eign cit­i­zen TikToks where some­one in traf­fic court is claim­ing diplo­matic im­mu­nity un­der mar­itime law.

It helps to know who Barlow was. Barlow was a Grateful Dead lyri­cist. He was also a Wyoming cat­tle rancher. He was also, briefly, the cam­paign man­ager for Dick Cheney’s first run for Congress. (You did not mis­read that.) He spent his later years as a fix­ture at Davos, the World Economic Forum, where the very wealthy gather each January to re­mind each other that they are in­ter­est­ing. It was at Davos, in February 1996, fu­eled by cham­pagne and griev­ance over the Telecommunications Act, that Barlow banged out the Declaration on a lap­top and emailed it to a few hun­dred friends. From there it be­came, some­how, one of the found­ing doc­u­ments of the mod­ern in­ter­net.

These in­creas­ingly hos­tile and colo­nial mea­sures place us in the same po­si­tion as those pre­vi­ous lovers of free­dom and self-de­ter­mi­na­tion who had to re­ject the au­thor­i­ties of dis­tant, un­in­formed pow­ers. We must de­clare our vir­tual selves im­mune to your sov­er­eignty, even as we con­tinue to con­sent to your rule over our bod­ies. We will spread our­selves across the Planet so that no one can ar­rest our thoughts.

Many of the pil­lars of “modern Internet” are here. Identity is­n’t a fixed con­cept based on gov­ern­ment ID but is a more fluid con­cept. We don’t need cen­tral­ized con­trol or re­ally any form of con­trol be­cause those things are un­nec­es­sary. It was this and the fa­mous ear­lier “Cyberspace and the American Dream: A MagnaCarta for the Knowledge Age” that laid a fa­mil­iar foun­da­tion for a lot of the cul­ture we now have. [link]

The Magna Carta is also our in­tro­duc­tion to the (now fa­mil­iar) creed of “catch up or get left be­hind”. The adop­tion of new tech­nol­ogy must be done at the ab­solute fastest speed pos­si­ble with no reg­u­la­tions or checks. You don’t need to worry about the con­se­quences of tech­nol­ogy be­cause these prob­lems cor­rect them­selves. If you told me the fol­low­ing was writ­ten two weeks ago by OpenAI I would have be­lieved you.

If this analy­sis is cor­rect, copy­right and patent pro­tec­tion of knowl­edge (or at least many forms of it) may no longer be un­nec­es­sary. In fact, the mar­ket­place may al­ready be cre­at­ing ve­hi­cles to com­pen­sate cre­ators of cus­tomized knowl­edge out­side the cum­ber­some copy­right/​patent process

The cum­ber­some copy­right/​patent process. Cumbersome to whom, ex­actly? This is al­ways the move. The thing your in­dus­try would pre­fer not to deal with is re­framed as an ob­so­lete bur­den. Your re­fusal to do it is re­branded as in­no­va­tion. Your in­abil­ity to imag­ine a world where you don’t get ex­actly what you want be­comes a man­i­festo.

Winner Saw It Coming

So there are dozens of these pieces and they all read the same. If you don’t reg­u­late these tech­nolo­gies hu­man­ity will only ben­e­fit. Education, health­care, in­dus­try, etc. We don’t need reg­u­la­tions be­cause the trans­for­ma­tion from the medium of pa­per to dig­i­tal has trans­formed the hu­man spirit. But one was ex­tremely sur­pris­ing to me. Langdon Winner wrote some­thing al­most prophetic back in 1997. You can read it here.

He coins the term cy­ber­lib­er­tar­i­an­ism (or at least is the first men­tion of it I could find) and then goes on to de­scribe an al­most eerily ac­cu­rate set of events.

In this per­spec­tive, the dy­namism of dig­i­tal tech­nol­ogy is our true des­tiny. There is no time to pause, re­flect or ask for more in­flu­ence in shap­ing these de­vel­op­ments. Enormous feats of quick adap­ta­tion are re­quired of all of us just to re­spond to therequire­ments the new tech­nol­ogy casts upon us each day. In the writ­ings of cy­ber­lib­er­tar­i­ans those able to rise to the chal­lenge are the cham­pi­ons of the com­ing mil­len­nium. The rest are fated to lan­guish in the dust.

Characteristic of this way of think­ing is a ten­dency to con­flatethe ac­tiv­i­ties of free­dom seek­ing in­di­vid­u­als with the op­er­a­tionsof enor­mous, profit seek­ing busi­ness firms. In the Magna Cartafor the Knowledge Age, con­cepts of rights, free­doms, ac­cess, andown­er­ship jus­ti­fied as ap­pro­pri­ate to in­di­vid­u­als are mar­shaledto sup­port the machi­na­tions of enor­mous transna­tional firms.We must rec­og­nize, the man­i­festo ar­gues, that “Government does­not own cy­ber­space, the peo­ple do.” One might read this as asug­ges­tion that cy­ber­space is a com­mons in which peo­ple have­shared rights and re­spon­si­bil­i­ties. But that is def­i­nitely not wherethe writ­ers carry their rea­son­ing.What “ownership by the peo­ple” means, the Magna Cartainsists, is sim­ply “private own­er­ship.” And it even­tu­ally be­comesclear that the pri­vate en­ti­ties they have in mind are ac­tu­ally large,transna­tional busi­ness firms, es­pe­cially those in com­mu­ni­ca­tions.Thus, af­ter prais­ing the mar­ket com­pe­ti­tion as the path­way to abet­ter so­ci­ety, the au­thors an­nounce that some forms of compe-tition are dis­tinctly un­wel­come. In fact, the writ­ers fear that the­gov­ern­ment will reg­u­late in a way that re­quires ca­ble com­pa­niesand phone com­pa­nies to com­pete. Needed in­stead, they ar­gue,is the re­duc­tion of bar­ri­ers to col­lab­o­ra­tion of al­ready large firms,a step that will en­cour­age the cre­ation of a huge, com­mer­cial,in­ter­ac­tive mul­ti­me­dia net­work as the for­merly sep­a­rate kinds of­com­mu­ni­ca­tion merge.

What “ownership by the peo­ple” means, the Magna Cartainsists, is sim­ply “private own­er­ship.” And it even­tu­ally be­comesclear that the pri­vate en­ti­ties they have in mind are ac­tu­ally large,transna­tional busi­ness firms, es­pe­cially those in com­mu­ni­ca­tions.Thus, af­ter prais­ing the mar­ket com­pe­ti­tion as the path­way to abet­ter so­ci­ety, the au­thors an­nounce that some forms of compe-tition are dis­tinctly un­wel­come. In fact, the writ­ers fear that the­gov­ern­ment will reg­u­late in a way that re­quires ca­ble com­pa­niesand phone com­pa­nies to com­pete. Needed in­stead, they ar­gue,is the re­duc­tion of bar­ri­ers to col­lab­o­ra­tion of al­ready large firms,a step that will en­cour­age the cre­ation of a huge, com­mer­cial,in­ter­ac­tive mul­ti­me­dia net­work as the for­merly sep­a­rate kinds of­com­mu­ni­ca­tion merge.

In all he lays out 4 pil­lars of this ide­ol­ogy.

Technological de­ter­min­ism. The new tech­nol­ogy is go­ing to trans­form every­thing, it can­not be stopped, and your only job is to keep up. Stewart Brand’s ac­tual quote, which Winner pulls out and lets sit there like a body on dis­play, is “Technology is rapidly ac­cel­er­at­ing and you have to keep up.” There’s no room to ask whether we want any of this. The wave is com­ing. Surf or drown.

It does not oc­cur to any­one in this dis­course that ‘drown’ is a choice the wave is mak­ing, not a nat­ural law. Waves do not have in­ten­tions. Destroying your liveli­hood and leav­ing you to rot is­n’t a re­quire­ment of the nat­ural or­der as much as that would con­ve­nient.

Radical in­di­vid­u­al­ism. The point of all this tech­nol­ogy is per­sonal lib­er­a­tion. Anything that gets in the way of the in­di­vid­ual max­i­miz­ing them­selves be it gov­ern­ment, reg­u­la­tion, so­cial oblig­a­tion, your an­noy­ing neigh­bors, is an ob­sta­cle to be re­moved. Winner notes, with what I imag­ine was a very dry ex­pres­sion, that the writ­ers of the “Magna Carta for the Knowledge Age” cited Ayn Rand ap­prov­ingly. In 1994. As in­tel­lec­tual ground­ing. For a doc­u­ment about com­put­ers.

There is some­thing deeply funny about a move­ment claim­ing to in­vent the fu­ture and ground­ing its case in a Russian émi­gré’s air­port nov­els about steel barons in love with their own re­flec­tions.

Free-market ab­so­lutism. Specifically the Milton Friedman, Chicago School, sup­ply-side fla­vor. The mar­ket will sort it out. Regulation is theft. Wealth is virtue. George Gilder, who co-wrote the Magna Carta, had pre­vi­ously writ­ten a book called Wealth and Poverty that helped sell Reaganomics to the masses. He then wrote Microcosm, which ar­gued that mi­cro­proces­sors plus dereg­u­lated cap­i­tal­ism would lib­er­ate hu­man­ity. He was very se­ri­ous about this.

Don’t worry, Gilder is still out there. He loves the blockchain and crypto now. He now writes about how Bitcoin will save the soul of cap­i­tal­ism, which it is some­how do­ing while also de­stroy­ing the planet. Both can be true in his cos­mol­ogy. The ide­ol­ogy is flex­i­ble like that.

A fan­tasy of com­mu­ni­tar­ian out­comes. This is the part that should make you laugh out loud. After es­tab­lish­ing that gov­ern­ment is bad, reg­u­la­tion is theft, and the in­di­vid­ual is sov­er­eign, the cy­ber­lib­er­tar­i­ans then promise that the re­sult of all this will be… rich, de­cen­tral­ized, har­mo­nious com­mu­nity life. Negroponte: “It can flat­ten or­ga­ni­za­tions, glob­al­ize so­ci­ety, de­cen­tral­ize con­trol, and help har­mo­nize peo­ple.” Democracy will flour­ish. The gap be­tween rich and poor will close. The lion will lie down with the lamb, and the lamb will have a Pentium II.

We also have the ad­van­tage of hind­sight and know, with­out ques­tion, that all of these pre­dicted out­comes were wrong. Not ‘directionally wrong’ or ‘wrong in the de­tails.’ Wrong the way it would be wrong to pre­dict that if you set your kitchen on fire, the re­sult will be a ren­o­va­tion.

You have to hold these four ideas in your head at the same time to see the trick. The cy­ber­lib­er­tar­i­ans wanted you to be­lieve that rad­i­cal in­di­vid­u­al­ism plus dereg­u­lated cap­i­tal­ism plus in­evitable tech­nol­ogy would pro­duce com­mu­ni­tar­ian utopia. This is, on its face, in­sane. It is the eco­nomic equiv­a­lent of claim­ing that if every­one punches each other re­ally hard, even­tu­ally we’ll all be hug­ging.

But Winner’s sharpest ob­ser­va­tion, the one I keep com­ing back to, is­n’t about any of the four pil­lars in­di­vid­u­ally. It’s about the move un­der­neath them. He writes:

“Characteristic of this way of think­ing is a ten­dency to con­flate the ac­tiv­i­ties of free­dom seek­ing in­di­vid­u­als with the op­er­a­tions of enor­mous, profit seek­ing busi­ness firms.”

This is the en­tire game. This is how “don’t tread on me” be­comes “Meta should be al­lowed to do what­ever it wants.” This is how the rights of the lone hacker work­ing in their garage be­come in­dis­tin­guish­able from the rights of a multi­na­tional with a mar­ket cap larger than most coun­tries’ GDP. The Magna Carta lit­er­ally ar­gues that the gov­ern­ment should re­duce bar­ri­ers to col­lab­o­ra­tion be­tween ca­ble com­pa­nies and phone com­pa­nies in the name of in­di­vid­ual free­dom and so­cial equal­ity. Winner caught this in 1997.

That is why ob­struct­ing such col­lab­o­ra­tion — in the cause of forc­ing a com­pe­ti­tion­be­tween the ca­ble and phone in­dus­tries — is so­cially elit­ist. To the ex­tent it pre­vents col­lab­o­ra­tion be­tween the ca­ble in­dus­try and the phone com­pa­nies, pre­sent fed­eral pol­icy ac­tu­ally thwarts the Administration’s own goals of ac­cess and em­pow­er­ment.

What makes the es­say un­com­fort­able to read now is that Winner was­n’t even pre­dict­ing the fu­ture. He was just de­scrib­ing what was al­ready hap­pen­ing and not­ing where it would ob­vi­ously lead. He saw the me­dia merg­ers and asked the ques­tion no­body in the in­dus­try wanted to an­swer: what hap­pened to the pre­dicted col­lapse of large cen­tral­ized struc­tures in the age of elec­tronic me­dia? Where, ex­actly, did the de­cen­tral­iza­tion go? He saw that the cy­ber­lib­er­tar­i­ans were go­ing to de­liver the op­po­site of every­thing they promised, and that they were go­ing to keep get­ting paid to promise it any­way.

He was writ­ing be­fore Google. Before Facebook. Before the iPhone. Before YouTube. Before Twitter, Bitcoin, Uber, AirBnB, OpenAI, and the en­tire app econ­omy. Before any of the ac­tual ex­am­ples that would even­tu­ally prove him right ex­isted. He just looked at the peo­ple do­ing the talk­ing, lis­tened to what they were say­ing, and wrote down where it ended. It is not a long es­say. He did­n’t need a long es­say. The fu­ture was right there on the page, in their own words. He just had to read it back to them.

The es­say closes with a ques­tion that has, to my knowl­edge, never been se­ri­ously an­swered by the in­dus­try it was aimed at:

“Are the prac­tices, re­la­tion­ships and in­sti­tu­tions af­fected by peo­ple’s in­volve­ment with net­worked com­put­ing ones we wish to fos­ter? Or are they ones we must try to mod­ify or even op­pose?”

Twenty-eight years later, the in­dus­try still treats this ques­tion as some­where be­tween naive and sedi­tious. It’s the ques­tion Barlow’s de­c­la­ra­tion was specif­i­cally de­signed to make unask­able. And it re­mains, to this day, the only ques­tion that ac­tu­ally mat­ters.

Caveat emp­tor

When you look at these early for­ma­tive writ­ings, so much of what we see now be­comes clear. The cy­ber­lib­er­tar­ian deal was al­ways the same: you’re on your own. The in­dus­try would build the in­fra­struc­ture, take the prof­its, and shove every con­se­quence, every harm, every cost, every re­spon­si­bil­ity, onto some­body else.

There is no greater ex­am­ple to me than the mod­er­a­tor. Anyone who has ever mod­er­ated a fo­rum or a sub­red­dit knows that adding the word “cyber” to a space does­n’t sud­denly turn peo­ple into bet­ter hu­mans. People are still peo­ple. They flame each other, they post slurs, they doxx, they ha­rass, they spam, they post CSAM, they rad­i­cal­ize each other, they grief, they co­or­di­nate, they lie. A space with hu­mans in it re­quires gov­er­nance.

They pro­duce, with fright­en­ing reg­u­lar­ity, the ex­act be­hav­ior any kinder­garten teacher could have pre­dicted. Then they act sur­prised.

But the cy­ber­lib­er­tar­ian model re­quired pre­tend­ing it was un­fore­see­able. The plat­forms could­n’t ac­knowl­edge that they needed gov­er­nance be­cause ac­knowl­edg­ing it would mean ac­knowl­edg­ing re­spon­si­bil­ity, and ac­knowl­edg­ing re­spon­si­bil­ity would mean ac­knowl­edg­ing li­a­bil­ity, and ac­knowl­edg­ing li­a­bil­ity would mean the en­tire eco­nomic model col­lapses. So in­stead the in­dus­try in­vented a beau­ti­ful fic­tion: gov­er­nance hap­pens, but it hap­pens by magic, per­formed by vol­un­teers, for free, who we will si­mul­ta­ne­ously rely on and mock.

Reddit is run by un­paid mod­er­a­tors. Wikipedia is run by un­paid ed­i­tors. Stack Overflow was run by un­paid ex­perts and is now a ghost town. On TikTok and Twitter it is the un­know­able “algorithm” that is the cause of and so­lu­tion to every prob­lem backed by capri­cious mod­er­a­tors who de­light in stop­ping free speech. Unless you don’t like it, then it’s neg­li­gence mod­er­a­tion in de­fense of your en­e­mies.

Open source is run by un­paid main­tain­ers hav­ing ner­vous break­downs. The plat­forms col­lect the rent. The peo­ple do­ing the ac­tual work of mak­ing the plat­forms liv­able get noth­ing, and when they ask for any­thing like recog­ni­tion, tools, ba­sic pro­tec­tion from ha­rass­ment, they’re told they’re power-trip­ping nerds who should touch grass.

This is also the crypto story, just with the masks off. What if we made worse money on pur­pose, money that by­passed every pro­tec­tion con­sumers had won over the pre­vi­ous cen­tury, money that could­n’t be re­versed when stolen, money that funded ran­somware at­tacks on hos­pi­tals and pump-and-dumps tar­get­ing peo­ple’s re­tire­ment ac­counts? The cy­ber­lib­er­tar­ian an­swer was: that’s free­dom. The losses were real. People killed them­selves. Hospitals had to turn away pa­tients. The ar­chi­tects be­came bil­lion­aires and bought yachts and now sit on the boards of AI com­pa­nies, where they are rein­vent­ing the same con with a new vo­cab­u­lary.

Now Winner got one thing wrong, and it’s worth paus­ing on, be­cause it’s the most in­ter­est­ing wrin­kle in all of this. What ac­tu­ally hap­pened was weirder and worse. The cy­ber­lib­er­tar­i­ans be­came the cor­po­ra­tions. They did­n’t sell out. They did­n’t be­tray their prin­ci­ples for the first of­fer of money. They sim­ply scaled un­til their prin­ci­ples be­came in­con­ve­nient, and then they stopped men­tion­ing them.

Once the plat­forms got large enough to be un­stop­pable, once they cap­tured enough of the reg­u­la­tory ap­pa­ra­tus to write their own rules, the lib­er­tar­ian rhetoric got qui­etly shelved like a col­lege poster you took down be­fore your in-laws came over. Meta no longer pre­tends it stands for free speech and seem­ingly takes de­light in putting its thumb on the scale. TikTok users have in­vented an en­tire eu­phemistic shadow lan­guage to evade au­to­mated cen­sor­ship like “unalive,” “le dol­lar bean,” “graped” that would have made 1996 Barlow weep into his bolo tie.

Copyright and patents mat­ter when they’re Apple’s copy­right and patents. Or Googles. Or OpenAIs. Go try to make a Facebook+ web­site and see how quickly Meta is ca­pa­ble of re­spond­ing to con­tent it finds ob­jec­tion­able.

Cyberlibertarianism was the lad­der. Once they were on the roof, they kicked it away and started charg­ing ad­mis­sion to look at the view.

So the Internet is Doomed?

Remember I like the Internet. I said it in the be­gin­ning and it is still true. I love the Fediverse, I love weird Discords about small table­top RPGs I’m in. I spend hours in the Mister FPGA fo­rums. There are cor­ners that are good. But they’re mostly good be­cause they’re not big enough to be worth break­ing up.

It feels in­creas­ingly like I’m hang­ing out in the old neigh­bor­hood dive bar af­ter most of the reg­u­lars have moved away. The light­ing is the same. The bar­tender re­mem­bers your or­der. But you can hear your­self think now, and that’s mostly be­cause the room is half empty and the juke­box fi­nally died. The new clien­tele is from out of town. They are tak­ing pic­tures of the menu.

If we want to have a se­ri­ous con­ver­sa­tion about why we are in the sit­u­a­tion we’re in, it is no longer pos­si­ble to pre­tend that the bro­ken ide­ol­ogy that put us on this tra­jec­tory is still some­how com­pat­i­ble with the harsh re­al­i­ties that sur­round us. It is not clear to me if democ­racy can sur­vive a dereg­u­lated Internet. A dereg­u­lated Internet filled with LLMs that can per­fectly im­per­son­ate hu­man be­ings pow­ered by un­reg­u­lated cor­po­ra­tions with zero eth­i­cal guide­lines seems like a some­what ob­vi­ous prob­lem. Like an episode of Star Trek where you the viewer are like “well clearly the Zorkians can’t keep the Killbots as pets.” It does­n’t take some gi­ant in­tel­lect to see the pretty fuck­ing ob­vi­ous prob­lem.

If we want to save the parts of the in­ter­net worth sav­ing, we have to evolve. We have to find some sort of eth­i­cal code that says: just be­cause I can do some­thing and it makes money, that is not suf­fi­cient jus­ti­fi­ca­tion to un­leash it on the world. Or, more sim­ply: just be­cause I want to do some­thing and you can­not ac­tively stop me, that does not make do­ing it a good idea. We have waited thirty years for the cy­ber­lib­er­tar­ian fu­ture to ar­rive and pro­duce the promised har­mo­nious com­mu­nity. It’s time to face the facts. It’s never com­ing. The bus left in 1996. The bus was never real.

People did not get bet­ter be­cause they went on­line. Giving every­one ac­cess to a raw, un­fil­tered pipeline of every fact and lie ever pro­duced did not turn them into bet­ter-ed­u­cated peo­ple. It broke them. It al­lowed them to choose the re­al­ity they now in­habit, like or­der­ing off a menu. If I want to be­lieve the world is flat, TikTok will gladly serve me that con­tent all day. Meta will rec­om­mend sup­port­ive groups. There will be hash­tags. There will be Discords. There will be a guy named Trent who runs a pod­cast. I will never have to face the deeply un­com­fort­able pos­si­bil­ity that I might be wrong about any­thing, ever, un­til the day I die, sur­rounded by peo­ple who agree with me about every­thing, in­clud­ing which of the other mourn­ers are se­cretly lizards.

That is the in­ter­net we built. It was not an ac­ci­dent. It was the prod­uct of a spe­cific ide­ol­ogy, writ­ten down by spe­cific peo­ple, at a spe­cific cock­tail party in Davos, in 1996. Winner watched it hap­pen and told us where it was go­ing. We did not lis­ten. There is still time, maybe, to start.

🗓️ 2026 – 05-08 • Tagged /web, /opinions, /meta=only

I don’t like peo­ple adding track­ing stuff to URLs. Still less do I like peo­ple adding track­ing stuff to my URLs.

https://​chris­mor­gan.info/​no-query-strings?ref=ex­am­ple.com? Did I ask? If I wanted to know I’d look at the Referer header; and if it is­n’t there, it’s prob­a­bly for a good rea­son. You abuse your users by adding that to the link.

https://​chris­mor­gan.info/​no-query-strings?ut­m_­source=ex­am­ple&utm_&c.? Hey! That one’s even worse, UTM pa­ra­me­ters are for me to use, not you. Leave my URLs alone.

So I’ve de­cided to try a blan­ket ban for this site: no unau­tho­rised query strings.

At pre­sent I don’t use any query strings. If I ever start us­ing any query strings, I’ll al­low only known pa­ra­me­ters. (In past times I used ?t=… and ?h=… cache-bust­ing URLs for stylesheet URLs; and I de­cided I’m okay break­ing such re­quests; there should­n’t be any le­git­i­mate ones.)

Want to see what hap­pens if you add a query string? Go ahead, try it.

It’s my web­site: I can do what I want with it.

And you can do what you want with yours!

This is cur­rently im­ple­mented in my Caddyfile.