{"schema":"sanctity-signal/0.2","record_type":"signal","id":"anthropic-nine-loops-e034","domain":"science","drop_id":"signal-e034","occurred_at":"2026-09-25","how_to_use":"This is a structured record of one real-world action and its competing interpretations, from Sanctity Signal. To build content from it (a reel script, a blog, a thread): open on the hook, ground the viewer with plain and observed, walk the dated trail, present the interpretations as live tension between named readings, and close on the before/after shift and what_to_watch. Hard rules: items under established are fact; items under unknown are never presented as fact; the evidence status (verified or reported) is stated, not dropped; sources are cited.","actor":"Anthropic","action_type":"published claim of a model-produced calculation one order beyond the standing human record","observed":"Friday September 25, 2026. Anthropic published \"Yes, Claude Can Do Nine Loops\" on its research site, a guest post by Matt von Hippel with an addendum by Lance Dixon. The object computed is the six-particle, or hexagon, amplitude in planar N=4 super-Yang-Mills theory at nine loops. The prior record was eight loops, reached by Dixon, a professor at the SLAC National Accelerator Laboratory, with Andy Liu in 2023. The method is a bootstrap: rather than summing every contribution, the calculation imposes the properties the answer must have and solves for it. The numbers Anthropic gives: the bootstrap step \"took around $100 of the budget, corresponding to running 96 CPUs for a week,\" inside a total project cost of one to two thousand dollars; the operating instruction was \"Keep working on this until I tell you to stop. Give me updates every 4-6 hours.\" On verification, Dixon validated the result independently and wrote the addendum himself, and the post records that Song He's group at the Chinese Academy of Sciences obtained concurrent results within two weeks using different methods. On what it opens, the post states that \"from the nine-loop amplitude it is relatively easy to go back to the form factor,\" the quantity Dixon's team had been working toward for years. The context in the same fortnight, all from Anthropic's own newsroom: on September 23 the company published a claim that Claude found a novel enzyme system with CRISPR-like repeats, and on September 4 it published a computer-checked proof of Fermat's Last Theorem written by a model, which is the card this one continues. What the post does not contain: a peer-reviewed publication, a named model version beyond Claude, a wall-clock figure for the whole project, or any claim that the technique bears on the real world rather than on a model theory.","corrections":[],"evidence":{"status":"verified","note":null,"sources":[{"role":"primary","label":"Anthropic research: Yes, Claude Can Do Nine Loops, guest post by Matt von Hippel with an addendum by Lance Dixon, Sep 25, 2026","url":"https://www.anthropic.com/research/yes-claude-can-do-nine-loops"},{"role":"corrob","label":"Anthropic newsroom, including the Sep 23 enzyme claim and the Sep 4 Fermat's Last Theorem proof","url":"https://www.anthropic.com/news"},{"role":"corrob","label":"AI Weekly daily listing carrying the nine-loop result on Sep 27, 2026","url":"https://aiweekly.co/ai-news-today"}]},"strength":{"cost":"Low","commitment":"Medium","reversibility":"Hard","persistence":"Years","rationale":"Cost is low and that is the finding rather than a weakness in it: about 100 dollars of compute for the decisive step, one to two thousand for the whole project. On our own method, cheap actions carry less evidential weight, and we are not going to break the rule because the number is startling, so the bar stays where it belongs. Commitment is medium: Anthropic put the claim on its own research site with a named outside physicist as author and the record holder attached as validator, which is a reputation staked, but it is not a peer-reviewed publication and no model version is named. Reversibility is hard, because a verified calculation cannot be withdrawn; if the answer holds, it holds, and Dixon has already checked it. Persistence is years: a loop order that took three years to move once will not be re-argued, and the form factor it opens is a multi-year programme. The overall bar lands moderate, which is the honest place for a cheap action with a durable result."},"shift":{"prior":"Machine-made mathematics meant reproducing results humans had already established, in a form a computer could check.","action":"Friday September 25, 2026. Anthropic published \"Yes, Claude Can Do Nine Loops\" on its research site, a guest post by Matt von Hippel with an addendum by Lance Dixon. The object computed is the six-particle, or hexagon, amplitude in planar N=4 super-Yang-Mills theory at nine loops. The prior record was eight loops, reached by Dixon, a professor at the SLAC National Accelerator Laboratory, with Andy Liu in 2023. The method is a bootstrap: rather than summing every contribution, the calculation imposes the properties the answer must have and solves for it. The numbers Anthropic gives: the bootstrap step \"took around $100 of the budget, corresponding to running 96 CPUs for a week,\" inside a total project cost of one to two thousand dollars; the operating instruction was \"Keep working on this until I tell you to stop. Give me updates every 4-6 hours.\" On verification, Dixon validated the result independently and wrote the addendum himself, and the post records that Song He's group at the Chinese Academy of Sciences obtained concurrent results within two weeks using different methods. On what it opens, the post states that \"from the nine-loop amplitude it is relatively easy to go back to the form factor,\" the quantity Dixon's team had been working toward for years. The context in the same fortnight, all from Anthropic's own newsroom: on September 23 the company published a claim that Claude found a novel enzyme system with CRISPR-like repeats, and on September 4 it published a computer-checked proof of Fermat's Last Theorem written by a model, which is the card this one continues. What the post does not contain: a peer-reviewed publication, a named model version beyond Claude, a wall-clock figure for the whole project, or any claim that the technique bears on the real world rather than on a model theory.","update":"A model has moved a calculational record one order past where three years of human work left it, and the decisive step cost about a hundred dollars."},"inference":{"established":["Anthropic published on September 25, 2026 that a Claude model computed the six-particle amplitude in planar N=4 super-Yang-Mills theory at nine loops.","The prior record was eight loops, set by Lance Dixon and Andy Liu in 2023.","Dixon validated the result independently and contributed an addendum to Anthropic's post.","The bootstrap step used about 100 dollars of compute, described as 96 processors for a week, inside a total project cost of one to two thousand dollars.","A group led by Song He at the Chinese Academy of Sciences obtained concurrent results within two weeks by different methods."],"unknown":["That this bears on the physical world. Planar N=4 super-Yang-Mills is a model theory chosen for tractability, and the post makes no claim beyond it.","That a model did the work unaided. The problem, the method and the bootstrap framing came from physicists, and the validation came from the previous record holder.","That the result is peer reviewed. It is a post on the company's own site with a paper attached, not a journal publication.","That the hundred dollar figure is the cost of the discovery. It is the cost of one step inside a project Anthropic prices at one to two thousand dollars, and it excludes the human time around it."]},"narrative":{"hook":"Anthropic says Claude finished a physics calculation no person has managed, on about 100 dollars of computing.","plain":"On September 25 Anthropic published a guest post by the physicist Matt von Hippel describing how a Claude model, left running with instructions to report every four to six hours, computed a nine-loop scattering amplitude in a simplified theory of particle physics, one order past the eight-loop record that Lance Dixon and Andy Liu reached in 2023. The decisive step used about 100 dollars of compute, roughly 96 processors for a week, inside a total project budget of one to two thousand dollars, and Dixon checked the result himself and wrote an addendum to the post. The caveat that matters is that this theory is a physicist's laboratory rather than the real world, the post is Anthropic's own and carries no peer review, and a group at the Chinese Academy of Sciences reached matching results within two weeks by different methods, which is good evidence the answer is right and also evidence the problem was ripe.","story":["Three weeks ago the claim was that a model had written a machine-checkable proof of Fermat's Last Theorem, a theorem proved by a person in 1994. That is a real thing to do and it proves a capability, but it proves it against a known answer. This is different in one specific way: nobody had the answer. Eight loops was the edge, it had been the edge since 2023, and the man who put it there checked the ninth himself and then wrote the postscript. The instruction Anthropic quotes is the detail to hold onto, because it is not a prompt so much as an employment arrangement: keep working until I tell you to stop, update me every four to six hours.","Read the price before reading the result. About 100 dollars of compute for the decisive step, one to two thousand for the project. Graduate students are not cheaper than that, and they do not run for a week without sleeping. Two things pull the other way and both belong on the card. The theory is a physicist's laboratory, chosen precisely because it is tractable, so this is not a statement about predicting anything measurable. And a Chinese group got matching results within two weeks by other methods, which means the problem was ready to fall and the machine got there first rather than alone. Hold both and the finding is narrower and more useful than the headline: on problems that are ripe, the binding constraint has stopped being human time. A model has moved a calculational record one order past where three years of human work left it, and the decisive step cost about a hundred dollars."],"trail":[{"d":"2023","t":"Lance Dixon and Andy Liu compute the hexagon amplitude in planar N=4 super-Yang-Mills at eight loops. The record stands for three years."},{"d":"SEP 4","t":"Anthropic publishes a computer-checked proof of Fermat's Last Theorem written by a model, the parent of this card."},{"d":"SEP 23","t":"Anthropic publishes a claim that Claude found a novel enzyme system with CRISPR-like repeats."},{"d":"SEP 25","t":"Anthropic publishes the nine-loop result, with Dixon's independent validation and his addendum, and the 100 dollar compute figure."},{"d":"Reacts","r":true,"t":"Lance Dixon's own field, where the form factor his group has chased for years is now described as relatively easy from here; Song He's group at the Chinese Academy of Sciences, who arrived at the same place by another road; every funding body that allocates postdoctoral years to calculations of this shape; journal editors and referees, who have no procedure for a result whose author ran unattended for a week; the twenty-five Fields Medallists who signed a page in September about the labs racing to solve mathematics; OpenAI, which published a Navier-Stokes proof three weeks ago and is competing on exactly this ground; Anthropic's own enterprise buyers, for whom a hundred dollar figure is a sales argument; and any physicist deciding this month what to spend the next three years on."}],"glossary":[{"term":"Scattering amplitude","def":"The quantity a physicist computes to predict how likely particles are to bounce off one another in a particular way. Harder versions are built out of loops."},{"term":"Loop order","def":"How many closed loops the calculation accounts for. Each extra loop is enormously more work than the last, which is why records move one loop at a time and stand for years."},{"term":"Planar N=4 super-Yang-Mills","def":"A highly symmetric theory that is not the physical world. Physicists work in it because hard calculations are possible there and the techniques carry over."},{"term":"Bootstrap","def":"Solving for an answer by imposing the properties it has to satisfy instead of summing every contribution. It is what makes nine loops feasible at all."}]},"judgment":{"prompt":"Which explanation do you believe?","interpretations":[{"id":"a","label":"The limiting resource in parts of theoretical science has stopped being human time.","text":"A record that stood three years moved while a model worked through the night for a hundred dollars, and the person who held the record checked it. Where a problem is ripe and the method is known, the work is now bounded by compute and by who thinks to point it at the problem.","abstain":false},{"id":"b","label":"One ripe problem in one tractable theory fell to brute patience.","text":"A Chinese group reached the same place within two weeks by other methods, which is the tell: this was next. The theory was chosen because it is solvable, the method was handed over by physicists, and what the model supplied was stamina.","abstain":false},{"id":"c","label":"A capability claim published to win an argument.","text":"This lands three weeks after a rival's proof of a famous open problem, in a month when twenty-five Fields Medallists signed a warning about the labs racing at mathematics and the company is arguing publicly about who may inspect it. A cheap, checkable, prestigious result with a famous validator attached is exactly the artifact that argument needs.","abstain":false},{"id":"d","label":"The normal cycle of a maturing tool.","text":"Computers have been extending calculations in this field for decades, from symbolic algebra onward. This is one more increment on that curve, arriving on schedule as the tools get better, and it will be unremarkable within two years.","abstain":false},{"id":"e","label":"Too early to call.","text":"The evidence cannot yet separate these.","abstain":true}],"distribution":{"status":"held back until you have made your call","calls":null}},"story_thread":"anthropic-flt-lean-e013","what_to_watch":[{"linked_interpretation":"a","direction":"strengthens","observable_event":"A model-produced result beyond the standing human record is published in a peer-reviewed journal or accepted by a recognised problem registry in any field of mathematics or theoretical physics, by March 31, 2027.","window_end":"2027-03-31","state":"unresolved"},{"linked_interpretation":"a","direction":"weakens","observable_event":"The nine-loop result is withdrawn or materially corrected, or the form factor described as relatively easy from here is not published by anyone, by March 31, 2027.","window_end":"2027-03-31","state":"unresolved"}]}