What was already known
With all equations retained, d independent Gaussian measurements identify the vector almost surely. The manuscript quantifies the extra precision-dependent sample cost when only a finite memory state persists between fresh observations.
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
Establishes a precision-driven sample lower bound even though every observation is noiseless.
Limitations
The bound averages success over a uniform spherical signal prior; measurements are fresh independent Gaussian rows, not chosen or revisited by the learner. The constant depends on fixed A.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every fixed A>0 and sufficiently large dimension d, a one-pass learner retaining at most Ad² bits between independent exact Gaussian linear measurements needs at least c_A d log(1/ε) measurements to estimate a uniformly random unit vector to angular error ε≤1/10 with success probability at least 2/3.
- 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