What was already known
The Hilbert-space Johnson–Lindenstrauss lemma gives logarithmic dimension at fixed distortion. For 1 < p < 2, earlier finite-set Lp bounds progressed from O_D(n log n) to O_(p,D)(n) coordinates; linear subspace discretization and p = 1 have different limitations (manuscript introduction, pp. 1–2).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Replaces linear dependence on the number of points by subpolynomial dimension for nonlinear finite-set embeddings in every fixed real Lp space with 1 < p < infinity.
Limitations
The explicit Lean scope covers p != 2, fixed D > 1, real spaces and existential nonlinear embeddings. The p = 2 case is the established Hilbert result. No efficient embedding algorithm or endpoint p = 1 claim is made.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note gives the explicit bound on the least target dimension for every fixed p > 1, p != 2 and D > 1, including its subpolynomial asymptotic.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every n-point subset of real Lp for fixed 1 < p < infinity, p != 2 and D > 1 embeds into l_p of dimension at most exp(C(p,D)(log n)^gamma), with gamma as stated.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision