Algebraic and complex geometry·OpenAI Math·Result 038
Fujita’s freeness conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a proof of Fujita’s freeness conjecture (algebraic and complex geometry) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More, is on YouTube.
Chapter 33 of 83 in Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · starts at 11:09 · watch from there on YouTube →
What OpenAI claims
Proves Fujita's freeness conjecture at its sharp bound in every dimension: for a smooth projective complex variety X of dimension n and an ample line bundle L, the adjoint KX+mL is globally generated for every integer m ≥ n+1.
Paper
Fujita's freeness conjecture
OpenAI's abstract We prove Fujita's freeness conjecture. If X is a smooth complex projective variety of dimension n and L is an ample line bundle, then KX+mL is globally generated for every integer m ≥ n+1.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Proves Fujita's freeness conjecture at its sharp bound in every dimension: for a smooth projective complex variety X of dimension n and an ample line bundle L, the adjoint KX+mL is globally generated for every integer m ≥ n+1.
- Where is the proof?
- In the paper, Fujita's freeness conjecture (PDF).
- Is there a video?
- Yes, on YouTube (28:48, chapter 33).
Also in
- Chapter 3 of 10 in Nagata's Conjecture, Bloch's Conjecture and 8 More in Algebraic and Complex Geometry · starts at 0:42 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · Compilation · 28:48 · chapter 33 from 11:09 · description, sources and chapters →
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