What was already known
Primariness of L1(Lp) was known, and prior factorization work on Lp(L1) was only a first step; the full 1<p<∞ case remained open.
AI involvement
The model supplied the central architecture and much technical content for Antonio Acuaviva’s chosen problem. Antonio and Pablo Acuaviva completed and verified the proof.
The model originated the retained central architecture, but substantial human mathematical completion was needed before a full proof existed.
Importance
Settles the remaining mixed-norm primariness case across the full stated range of p.
Limitations
The model draft was incomplete; Antonio and Pablo Acuaviva reorganized and completed essential arguments before checking the final proof.
Technical verification
The authors report human verification of the completed final proof, including the portions they had to make precise; no machine formalization is claimed.
Formal checking
Completed and checked the model's indicated arguments by mathematical reading
- Checker
- Antonio and Pablo Acuaviva
- Scope
- Uniform primary factorization and primariness of Lp(L1) for 1<p<∞
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the Haar scalar-compression route and why the model's draft required reorganization and completion.
Correction and publication history
Settles the remaining mixed-norm primariness case across the full stated range of p.
Read this published revision