OpenAI · 290-02 · 2026-09-23 · Operator algebras
Bounded recovery for modular spectral averages
preprints/Bounded-recovery-for-modular-spectral-averages-September-23-2026
Family 290. Connes' bicentralizer conjecture and relative bicentralizers.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Connes' bicentralizer conjecture for every type factor with separable predual and every faithful normal state. More generally, for every inclusion of von Neumann algebras with separable preduals admitting a faithful normal conditional expectation, constructs an amenable expected subalgebra with , resolving the relative bicentralizer conjecture.
We prove a bounded spectral recovery theorem for a von Neumann algebra with a faithful normal state whose centralizer consists only of scalars. A positive averaged squared norm for an arbitrary bounded Hilbert-space operator on shrinking modular spectral bands can be recovered on uniformly bounded algebra elements with shrinking spectral support. We apply this theorem to spectral intertwining rigidity and obtain an alternative proof of bicentralizer triviality for type III1 factors with separable predual.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 290: Relative bicentralizers and modular spectral recovery. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. Family 290-02 is a modular-band witness, not a finite decoder and not bulk reconstruction. Oai290-A restates that witness locally and does not verify this preprint. 290-01 is a different paper and is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
BoundedRecovery.lean · BoundedRecovery.lean
Emergence
A modular-band witness is not bulk reconstruction
Family 290 records a bounded spectral recovery theorem for a scalar modular centralizer, and a separate relative-bicentralizer paper. The Lean note names 290-02 only, not 290-01. That witness is not a finite decoder, not a Page curve, and not a bulk--boundary dictionary. Oai290-A restates the bounded-witness statement locally and does not verify the preprint. Oai211-A does not instantiate that modular theorem. The authors are OpenAI. The companion does not verify those proofs. O.1 stays NOT_CLOSED.
EmergenceOai211-A path-sum certificateOai290-A typed recoveryOai265-B memory certificateXIV-J joint map unresolvedXIV-I internal amplitudeEn07-C Hawking comparison