Episode 0070: One of Them Published the Prompt

Why it matters. A conjecture about which magnetic bottles can exist, posed by Harold Grad in 1967 and sharpened into a falsifiable statement only in 2025, was contradicted twice in two days in September 2026 — and both times with machine assistance. Javier Gomez-Serrano, Lukas Liehr and Mitchell Taylor published a 147-page existence proof on 21 September. Matt Landreman published explicit closed-form solutions the following day, and stated in his acknowledgements that he had found them with GPT-6 Astra Pro. Thirteen days later, a team of three Google DeepMind researchers plus Landreman generalized his result: arXiv 2610.07304 adds a single symmetry-breaking parameter to each of his two families, producing the first explicit analytic 3D MHD equilibria that break stellarator symmetry — the exact benchmark that half of every stellarator equilibrium code has never been tested against, because assuming the symmetry halves the number of independent Fourier coefficients. Section 5 of that paper says the solutions were proposed by Gemini 4 running as a small team of agents in Google Antigravity, and that promising candidates appeared within hours. Both papers are real mathematics and both are modest about what they mean. The difference between them is who can check the work. Landreman released an MIT-licensed repository containing DESC verification scripts, the HDF5 equilibria, SymPy and autodiff notebooks proving all three equilibrium equations, and the original prompt and chat transcripts — eight pages of them, timestamped, readable by anyone. The DeepMind follow-up released no code, no data statement, no funding statement and no acknowledgements, and on its submission date the model that produced it was available only to invited testers through the Fairwind programme. The asymmetry runs opposite to the resources: the single academic on a Department of Energy grant, who also discloses a consultancy for a private stellarator company, published everything. We hold both halves — the methodology is serious and the provenance gap is real — and we turn the same objection on ourselves, because this show does not publish its prompts either.

The paper

• Analytic non-axisymmetric 3D MHD equilibria without stellarator symmetry — Opal Issan, Jonathan Citrin, Matt Landreman, Brendan Tracey. arXiv:2610.07304, submitted 5 October 2026, 11 pages.
• Affiliations: Google DeepMind (London) for Issan, Citrin and Tracey; UC San Diego Mechanical and Aerospace Engineering for Issan; University of Maryland, College Park for Landreman. Three of four authors carry a DeepMind affiliation.
• Jonathan Citrin is the lead author of DeepMind's TORAX tokamak transport simulator.

The precursor and the companion

• Analytic toroidal 3D MHD equilibria and steady Euler flows with invariant surfaces — M. Landreman. arXiv:2609.26742, 22 September 2026 (v2, 28 September). Funded by US Department of Energy contract DE-FG02-93ER54197. Declaration of interests: the author is a consultant for Type One Energy Group.
• Counterexamples to Grad's conjecture — J. Gomez-Serrano, L. Liehr, M. A. Taylor. arXiv:2609.24739, 21 September 2026. 147 pages, 3 figures. Existence proof with infinite rotational transform; no closed form.
• The conjecture actually refuted is Conjecture 2.5 in Cardona, Duignan & Perrella, Archive for Rational Mechanics and Analysis 249(1), 2025 — a modern formalisation of Grad's 1967 statement.

The artifact

• github.com/landreman/analytic_3d_equilibria — MIT. Figure scripts, DESC verification scripts, DESC equilibria in HDF5, SymPy and autodiff notebooks confirming ∇·B = 0, B·∇ψ = 0 and (∇×B)×B = ∇p, a Mathematica notebook, and the original GPT-6 Astra Pro prompt and chat in three PDFs (iota_2/analytic_3D_equilibrium_iota2_prompt.pdf and two more under sheared_iota/).

The tooling, licence by licence

Every licence below was read from the repository, not taken from a badge.

Code	Repository	Licence
TORAX (DeepMind)	google-deepmind/torax	Apache-2.0 for all code, CC BY 4.0 on bundled third-party data. No rider, no field-of-use restriction.
DESC	PlasmaControl/DESC	MIT
SIMSOPT	hiddenSymmetries/simsopt	MIT
STELLOPT	PrincetonUniversity/STELLOPT	MIT
VMEC2000	hiddenSymmetries/VMEC2000	MIT
SPEC	PrincetonUniversity/SPEC	MIT

TORAX is genuinely Apache-2.0 and DeepMind deserves the credit — GitHub's NOASSERTION tag is a classifier failing on a dual-licence file. But TORAX is a tokamak transport simulator; the benchmarks in this paper test VMEC, SPEC and DESC, which are academic MIT codes. The physics tooling layer is an open commons. The intelligence layer that did the novel work is not.

• Google Antigravity — public preview, free for individuals, closed source. Its "Manager surface" is described by Google as "mission control for spawning, orchestrating, and observing multiple agents across multiple workspaces in parallel," which is the mechanical meaning of the paper's "small team of agents." Rate limits refresh every five hours.
• Gemini 4 Argon — announced 30 September 2026 to trusted testers via the Fairwind Program; public rollout reported around 13 October. The paper was submitted 5 October.

The money

From the Fusion Industry Association's The Global Fusion Industry in 2026 report, read from the PDF:

• Total funding to date: $14,242,143,000
• Twelve months to July 2026: $4,476,143,000
• Private: $13,261,437,000 · Public: $980,706,000

Note the scope: that survey counts private fusion companies. It does not count ITER, the national laboratory programmes, or Wendelstein 7-X. "Public co-funding is just under 7% within the private fusion industry" is the accurate claim; "public investment in fusion is 7% of the total" would be false.

Type One Energy: founded 2019, $200,000,000 declared funding, 213 employees, letter of intent with the Tennessee Valley Authority for the Bull Run site, targeting grid power in 2034. Commonwealth Fusion Systems: $3,000,000,000 declared, and its own FIA partner list includes Google DeepMind, Type One Energy, the University of Maryland and UC San Diego, plus power purchase agreements with Google and Eni.

Honest limits, stated on air

These are static ideal-MHD equilibria. They establish that a force balance exists — not that it is stable, not that a plasma in such a configuration would confine heat, not that coils could be built to produce these fields, and nothing at all about power. The sheared family's rotational transform profile is computed numerically, which the authors state plainly. The agents answered the most tractable of the five open questions Landreman listed; items on vacuum and force-free fields and on exact quasisymmetry remain open. "Promising candidates appeared within hours" is self-reported and unauditable. We found zero Hacker News discussion of either paper across four queries; we did not search Reddit and make no claim about the plasma physics community's own channels.

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• Three Companies Control Commoditized Intelligence. Now What? — the tenancy argument
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• d/acc Has a Build Order — what to build first

Pronunciation note

DESC is spoken as "Desk" throughout, which is the community pronunciation. VMEC is spelled out. TORAX, SIMSOPT, STELLOPT and SPEC are spoken as words.