No relativizing reduction from ROM to ROH

A reduction of class relativizing from ROM to ROH would imply a contradiction.

Statement

Migrated verbatim from random-oracle-model § Known Results:

• IP $\ne$ PSPACE relative to a random oracle — For almost all oracles $A$, ${\mathbf{IP}}^A\ne {\mathbf{PSPACE}}^A$ CCG+94. Since Shamir proved $\mathbf{IP}=\mathbf{PSPACE}$ unrelativized, this is among the most compelling counterexamples to the Random Oracle Hypothesis.

Notes

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• This is a counterexample to a HYPOTHESIS ABOUT PROOFS (the Random Oracle Hypothesis), not a barrier between primitives. Q is ‘contradiction’ but the thing contradicted is a meta-conjecture, so the hyperedge’s hypothesis is again a proof-technique-shaped object with no page.
• ‘this is among the most compelling counterexamples’ — evaluative editorializing of the kind CLAUDE.md’s anti-patterns list bans.
• The intro paragraph (line 15) states the same fact a second time on the same page.