prh-formal-proof-requires-bijective-observations
IN premise — summaries/2026/08/24/huh-2024-prh-s6-counterexamples-and-limitations.md
Created 2026-08-24T17:10:56+00:00
The formal proof of the Platonic Representation Hypothesis in Section 4 holds only when the observation function is a bijective projection of the underlying world Z; lossy or stochastic observations (e.g., an image cannot convey 'I believe in freedom of speech') violate the assumption and break the convergence guarantee.
Summary
The mathematical guarantee that the system converges to the correct underlying structure only works under the ideal condition that observations are perfectly complete and lossless, like a one-to-one snapshot of reality. In practice, any observation that drops information or adds noise — such as an image being unable to capture an abstract belief — invalidates the proof, meaning the convergence promise does not carry over to real-world sensing and perception.