The Linear Communication Bottleneck Conjecture
Withdrawn Spectral Route; Two Surviving Haar-Symmetry Lemmas
The trichotomy is withdrawn. Exact Haar marginals and adjacent-edge pairwise independence remain.
Historical decision · 2026-07-14
Status decision
- Why it was pursued
- The paper tested whether a spectral trichotomy yields a communication lower bound for random encoders.
- Evidence change
- The spectral-gap route did not survive audit.
- No longer claimed
- Spectral-gap trichotomy
- Linear communication bottleneck
- Retained results
- Exact Haar marginals
- Adjacent-edge pairwise independence
SuccessorsSHEAF
Abstract
Withdrawn historical artifact. The spectral-gap trichotomy is withdrawn; only the Haar marginal and adjacent-edge pairwise-independence lemmas survive. See the correction register for the surviving scope.
Evidence and record
Research question
Does the spectral-gap trichotomy imply a linear communication bottleneck?
Status
withdrawnFalsifiedhistorical · v1 · as of 2026-07-22
Corrections
The spectral-gap trichotomy is withdrawn; only the Haar marginal and adjacent-edge pairwise-independence lemmas survive.
Falsification
A counterexample to conditional Haar-ness or adjacent-edge independence falsifies the surviving lemmas; no spectral claim survives.
External review
not requested
Program relations
- survives-in SHEAF