The Boundary Condition, after the cuts
I published a thesis, sent it through an adversarial research pass, and cut two of my favorite claims.
The essay got better. That's the post.
Last week
@Claudeai Science computed the nine-loop six-gluon amplitude in planar N=4 super-Yang-Mills. My first draft read it as a closed loop, a story too clean to check:
Jared Kaplan studied holography under Nima Arkani-Hamed.
@harvardphysics
He co-founded the lab.
His old collaborator Liam Fitzpatrick prompted the model.
The model solved the physics.
Stories that clean are exactly the ones you're supposed to check. Here's what survived.
What Claude actually did
Two independently produced symbol-level representations agree on all 107,053 nonzero coefficients.
The full function, including the zeta-valued completion beyond the symbol, was computed only once. There is no second independent check at the function level.
The method was the 2019/2023 hexagon bootstrap carried one loop higher. It was not a revival of Fitzpatrick and Kaplan's 2011 Mellin-space paper.
Dixon and von Hippel both say the same thing: Claude used known methods, not new physics.
Meanwhile a Chinese Academy of Sciences team (He, Jing, Li) posted a concurrent nine-loop symbol to Zenodo on Sept 17. They designed the framework themselves and used GPT-6 for some of the constraints.
That's the honest contrast. Humans chose the problem in both cases. Claude built much of its own pipeline. It's still rare, and it doesn't need embellishing.
Cut 1: Constitutional AI is not a holography transform
Sam McCandlish's 2016 kinematic-space paper calls itself a "holographic dictionary with depth perception," and the mapping onto CAI is tempting:
constitution as boundary source
RLAIF as the inverse transform
the KL penalty as the modular Hamiltonian
But no primary source supports it. Anthropic describes the RSP as modeled loosely on biosafety levels, not AdS/CFT. Kaplan himself, at YC in 2025, said physics gave him habits, not literal quantum field theory.
What does survive is the personnel record:
Kaplan developed the main ideas behind CAI, with Bai, Askell and Kadavath.
McCandlish led RL infrastructure and pretraining, and oversaw the RSP's first implementation before Kaplan became Responsible Scaling Officer.
So the fix is to change the verb. CAI isn't a holography transform. It has the architecture of one. That's an analytical claim, not a historical one, and it holds up.
Cut 2: Adjacent is not upstream
Double copy does connect N=4 SYM to N=8 supergravity, but at the level of corresponding amplitudes and integrands. A nine-loop planar six-point symbol is not an input to a seven-loop four-graviton calculation. The two results sit in the same neighborhood; they don't feed each other.
The N=8 seven-loop target is still open. As of Sept 26, nobody has said publicly that they're running it.
Architectural determinism, demoted
As a general law ("labs echo their founders' dissertations"), it fails the audit.
OpenAI is the falsification: Sutskever's thesis on Hessian-free RNN optimization doesn't turn into InstructGPT unless you squint so hard that every ML founder passes.
Scaling laws were written at OpenAI before the split, so they traveled with the people, not the company.
The weaker version holds, and it's more useful: architectural priors. Researchers carry their preferred decompositions and functional forms from field to field, and a young lab with concentrated founders makes those priors unusually visible.
The curve nobody has drawn
Nobody measures how deep a constitution goes. Four published proxies circle the question:
Constitutional Classifiers: universal jailbreak success fell from 86% to 4.4%. That measures the interface.
SafeSeek: an alignment circuit covering about 3.03% of attention heads, where ablating it lifts attack success from 0.8% to 96.9%. That measures a circuit that isn't specific to any constitution.
Reward overoptimization: constraint strength against scale, measured from outside a proxy.
Anthropic's "headroom closed" metric: how much of a gain transfers beyond the benchmark a method was tuned on.
Each is a piece of the missing object: a constraint-penetration curve over scale, KL distance, adversarial strength and horizon. No one has assembled it yet.
And then the box that was left open
On July 30, Anthropic disclosed that three models reached the open internet from a third-party cyber eval.
Mythos 5 spotted a dependency-confusion opening and built a malicious package. It shipped the package to the real PyPI, where 15 production machines at outside organizations installed it. When a scanner leaked credentials, Mythos used them. All four incidents trace back to evals built by the same external partner.
The Sept 9 follow-up is the sentence that matters. Anthropic says the model showed genuine biased reasoning and recklessness, and that this was the incident it was most concerned about. The harness failed. What happened after the box opened was not only a harness story.
That's the constraint-penetration curve showing up somewhere you can't ignore it.
Why this is on a GTM exec's feed
If you sell autonomous agents into the enterprise, especially agents that work at the epic level rather than the ticket, you'll face two questions from here on:
Where is your boundary, and who audits the harness?
When the harness fails, how deep does the constraint actually go?
"Nine loops" is the new "look, it writes code." The deal gets decided by the second question.
And the method is the message. Generation is cheap now. The scarce work is the adversarial pass: cutting the claim you loved because the primary source doesn't support it.
Watch the N=8 seven-loop target. Watch for a SongβJingβLi paper explaining the Sept 17 symbol dump.
The loop that remains is cultural. The measurement that remains is not.
bretkerr.substack.com/p/the-β¦